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  <div class="section" id="flrw">
<h1>FLRW<a class="headerlink" href="#flrw" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="astropy.cosmology.core.FLRW">
<em class="property">class </em><tt class="descclassname">astropy.cosmology.core.</tt><tt class="descname">FLRW</tt><big>(</big><em>H0</em>, <em>Om0</em>, <em>Ode0</em>, <em>Tcmb0=2.725</em>, <em>Neff=3.04</em>, <em>name='FLRW'</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L61" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">astropy.cosmology.core.Cosmology</span></tt></p>
<p>A class describing an isotropic and homogeneous
(Friedmann-Lemaitre-Robertson-Walker) cosmology.</p>
<p>This is an abstract base class &#8211; you can&#8217;t instantiate
examples of this class, but must work with one of its
subclasses such as <a class="reference internal" href="astropy.cosmology.core.LambdaCDM.html#astropy.cosmology.core.LambdaCDM" title="astropy.cosmology.core.LambdaCDM"><tt class="xref py py-obj docutils literal"><span class="pre">LambdaCDM</span></tt></a> or <a class="reference internal" href="astropy.cosmology.core.wCDM.html#astropy.cosmology.core.wCDM" title="astropy.cosmology.core.wCDM"><tt class="xref py py-obj docutils literal"><span class="pre">wCDM</span></tt></a>.</p>
<p class="rubric">Notes</p>
<p>Class instances are static &#8211; you can&#8217;t change the values
of the parameters.  That is, all of the attributes above are
read only.</p>
<p>The neutrino treatment assumes all neutrino species are massless.</p>
<p class="rubric">Attributes Summary</p>
<table border="1" class="longtable docutils">
<colgroup>
<col width="10%" />
<col width="90%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.H0" title="astropy.cosmology.core.FLRW.H0"><tt class="xref py py-obj docutils literal"><span class="pre">H0</span></tt></a></td>
<td>Return the Hubble constant in [km/sec/Mpc] at z=0</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Neff" title="astropy.cosmology.core.FLRW.Neff"><tt class="xref py py-obj docutils literal"><span class="pre">Neff</span></tt></a></td>
<td>Number of effective neutrino species</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Ode0" title="astropy.cosmology.core.FLRW.Ode0"><tt class="xref py py-obj docutils literal"><span class="pre">Ode0</span></tt></a></td>
<td>Omega dark energy; dark energy density/critical density at z=0</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Ogamma0" title="astropy.cosmology.core.FLRW.Ogamma0"><tt class="xref py py-obj docutils literal"><span class="pre">Ogamma0</span></tt></a></td>
<td>Omega gamma; the density/critical density of photons at z=0</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Ok0" title="astropy.cosmology.core.FLRW.Ok0"><tt class="xref py py-obj docutils literal"><span class="pre">Ok0</span></tt></a></td>
<td>Omega curvature; the effective curvature density/critical density</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Om0" title="astropy.cosmology.core.FLRW.Om0"><tt class="xref py py-obj docutils literal"><span class="pre">Om0</span></tt></a></td>
<td>Omega matter; matter density/critical density at z=0</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Onu0" title="astropy.cosmology.core.FLRW.Onu0"><tt class="xref py py-obj docutils literal"><span class="pre">Onu0</span></tt></a></td>
<td>Omega nu; the density/critical density of neutrinos at z=0</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Tcmb0" title="astropy.cosmology.core.FLRW.Tcmb0"><tt class="xref py py-obj docutils literal"><span class="pre">Tcmb0</span></tt></a></td>
<td>Temperature of the CMB in Kelvin at z=0</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.critical_density0" title="astropy.cosmology.core.FLRW.critical_density0"><tt class="xref py py-obj docutils literal"><span class="pre">critical_density0</span></tt></a></td>
<td>Critical density in [g cm^-3] at z=0</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.h" title="astropy.cosmology.core.FLRW.h"><tt class="xref py py-obj docutils literal"><span class="pre">h</span></tt></a></td>
<td>Dimensionless Hubble constant: h = H_0 / 100 [km/sec/Mpc]</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.hubble_distance" title="astropy.cosmology.core.FLRW.hubble_distance"><tt class="xref py py-obj docutils literal"><span class="pre">hubble_distance</span></tt></a></td>
<td>Hubble distance in [Mpc]</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.hubble_time" title="astropy.cosmology.core.FLRW.hubble_time"><tt class="xref py py-obj docutils literal"><span class="pre">hubble_time</span></tt></a></td>
<td>Hubble time in [Gyr]</td>
</tr>
</tbody>
</table>
<p class="rubric">Methods Summary</p>
<table border="1" class="longtable docutils">
<colgroup>
<col width="10%" />
<col width="90%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.H" title="astropy.cosmology.core.FLRW.H"><tt class="xref py py-obj docutils literal"><span class="pre">H</span></tt></a>(z)</td>
<td>Hubble parameter (km/s/Mpc) at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Ode" title="astropy.cosmology.core.FLRW.Ode"><tt class="xref py py-obj docutils literal"><span class="pre">Ode</span></tt></a>(z)</td>
<td>Return the density parameter for dark energy at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Ogamma" title="astropy.cosmology.core.FLRW.Ogamma"><tt class="xref py py-obj docutils literal"><span class="pre">Ogamma</span></tt></a>(z)</td>
<td>Return the density parameter for photons at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Ok" title="astropy.cosmology.core.FLRW.Ok"><tt class="xref py py-obj docutils literal"><span class="pre">Ok</span></tt></a>(z)</td>
<td>Return the equivalent density parameter for curvature at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Om" title="astropy.cosmology.core.FLRW.Om"><tt class="xref py py-obj docutils literal"><span class="pre">Om</span></tt></a>(z)</td>
<td>Return the density parameter for non-relativistic matter at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Onu" title="astropy.cosmology.core.FLRW.Onu"><tt class="xref py py-obj docutils literal"><span class="pre">Onu</span></tt></a>(z)</td>
<td>Return the density parameter for massless neutrinos at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.Tcmb" title="astropy.cosmology.core.FLRW.Tcmb"><tt class="xref py py-obj docutils literal"><span class="pre">Tcmb</span></tt></a>(z)</td>
<td>Return the CMB temperature at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.absorption_distance" title="astropy.cosmology.core.FLRW.absorption_distance"><tt class="xref py py-obj docutils literal"><span class="pre">absorption_distance</span></tt></a>(z)</td>
<td>Absorption distance at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.age" title="astropy.cosmology.core.FLRW.age"><tt class="xref py py-obj docutils literal"><span class="pre">age</span></tt></a>(z)</td>
<td>Age of the universe in Gyr at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.angular_diameter_distance" title="astropy.cosmology.core.FLRW.angular_diameter_distance"><tt class="xref py py-obj docutils literal"><span class="pre">angular_diameter_distance</span></tt></a>(z)</td>
<td>Angular diameter distance in Mpc at a given redshift.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.angular_diameter_distance_z1z2" title="astropy.cosmology.core.FLRW.angular_diameter_distance_z1z2"><tt class="xref py py-obj docutils literal"><span class="pre">angular_diameter_distance_z1z2</span></tt></a>(z1,&nbsp;z2)</td>
<td>Angular diameter distance between objects at 2 redshifts.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.arcsec_per_kpc_comoving" title="astropy.cosmology.core.FLRW.arcsec_per_kpc_comoving"><tt class="xref py py-obj docutils literal"><span class="pre">arcsec_per_kpc_comoving</span></tt></a>(z)</td>
<td>Angular separation in arcsec corresponding to a comoving kpc at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.arcsec_per_kpc_proper" title="astropy.cosmology.core.FLRW.arcsec_per_kpc_proper"><tt class="xref py py-obj docutils literal"><span class="pre">arcsec_per_kpc_proper</span></tt></a>(z)</td>
<td>Angular separation in arcsec corresponding to a proper kpc at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.comoving_distance" title="astropy.cosmology.core.FLRW.comoving_distance"><tt class="xref py py-obj docutils literal"><span class="pre">comoving_distance</span></tt></a>(z)</td>
<td>Comoving line-of-sight distance in Mpc at a given redshift.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.comoving_transverse_distance" title="astropy.cosmology.core.FLRW.comoving_transverse_distance"><tt class="xref py py-obj docutils literal"><span class="pre">comoving_transverse_distance</span></tt></a>(z)</td>
<td>Comoving transverse distance in Mpc at a given redshift.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.comoving_volume" title="astropy.cosmology.core.FLRW.comoving_volume"><tt class="xref py py-obj docutils literal"><span class="pre">comoving_volume</span></tt></a>(z)</td>
<td>Comoving volume in cubic Mpc at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.critical_density" title="astropy.cosmology.core.FLRW.critical_density"><tt class="xref py py-obj docutils literal"><span class="pre">critical_density</span></tt></a>(z)</td>
<td>Critical density in grams per cubic cm at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.de_density_scale" title="astropy.cosmology.core.FLRW.de_density_scale"><tt class="xref py py-obj docutils literal"><span class="pre">de_density_scale</span></tt></a>(z)</td>
<td>Evaluates the redshift dependence of the dark energy density.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.distmod" title="astropy.cosmology.core.FLRW.distmod"><tt class="xref py py-obj docutils literal"><span class="pre">distmod</span></tt></a>(z)</td>
<td>Distance modulus at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.efunc" title="astropy.cosmology.core.FLRW.efunc"><tt class="xref py py-obj docutils literal"><span class="pre">efunc</span></tt></a>(z)</td>
<td>Function used to calculate H(z), the Hubble parameter.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.inv_efunc" title="astropy.cosmology.core.FLRW.inv_efunc"><tt class="xref py py-obj docutils literal"><span class="pre">inv_efunc</span></tt></a>(z)</td>
<td>Inverse of efunc.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.kpc_comoving_per_arcmin" title="astropy.cosmology.core.FLRW.kpc_comoving_per_arcmin"><tt class="xref py py-obj docutils literal"><span class="pre">kpc_comoving_per_arcmin</span></tt></a>(z)</td>
<td>Separation in transverse comoving kpc corresponding to an arcminute at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.kpc_proper_per_arcmin" title="astropy.cosmology.core.FLRW.kpc_proper_per_arcmin"><tt class="xref py py-obj docutils literal"><span class="pre">kpc_proper_per_arcmin</span></tt></a>(z)</td>
<td>Separation in transverse proper kpc corresponding to an arcminute at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.lookback_time" title="astropy.cosmology.core.FLRW.lookback_time"><tt class="xref py py-obj docutils literal"><span class="pre">lookback_time</span></tt></a>(z)</td>
<td>Lookback time in Gyr to redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.luminosity_distance" title="astropy.cosmology.core.FLRW.luminosity_distance"><tt class="xref py py-obj docutils literal"><span class="pre">luminosity_distance</span></tt></a>(z)</td>
<td>Luminosity distance in Mpc at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.scale_factor" title="astropy.cosmology.core.FLRW.scale_factor"><tt class="xref py py-obj docutils literal"><span class="pre">scale_factor</span></tt></a>(z)</td>
<td>Scale factor at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.FLRW.w" title="astropy.cosmology.core.FLRW.w"><tt class="xref py py-obj docutils literal"><span class="pre">w</span></tt></a>(z)</td>
<td>The dark energy equation of state.</td>
</tr>
</tbody>
</table>
<p class="rubric">Attributes Documentation</p>
<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.H0">
<tt class="descname">H0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.H0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.H0" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the Hubble constant in [km/sec/Mpc] at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.Neff">
<tt class="descname">Neff</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Neff"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Neff" title="Permalink to this definition">¶</a></dt>
<dd><p>Number of effective neutrino species</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.Ode0">
<tt class="descname">Ode0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Ode0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Ode0" title="Permalink to this definition">¶</a></dt>
<dd><p>Omega dark energy; dark energy density/critical density at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.Ogamma0">
<tt class="descname">Ogamma0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Ogamma0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Ogamma0" title="Permalink to this definition">¶</a></dt>
<dd><p>Omega gamma; the density/critical density of photons at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.Ok0">
<tt class="descname">Ok0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Ok0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Ok0" title="Permalink to this definition">¶</a></dt>
<dd><p>Omega curvature; the effective curvature density/critical density
at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.Om0">
<tt class="descname">Om0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Om0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Om0" title="Permalink to this definition">¶</a></dt>
<dd><p>Omega matter; matter density/critical density at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.Onu0">
<tt class="descname">Onu0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Onu0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Onu0" title="Permalink to this definition">¶</a></dt>
<dd><p>Omega nu; the density/critical density of neutrinos at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.Tcmb0">
<tt class="descname">Tcmb0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Tcmb0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Tcmb0" title="Permalink to this definition">¶</a></dt>
<dd><p>Temperature of the CMB in Kelvin at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.critical_density0">
<tt class="descname">critical_density0</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.critical_density0"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.critical_density0" title="Permalink to this definition">¶</a></dt>
<dd><p>Critical density in [g cm^-3] at z=0</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.h">
<tt class="descname">h</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.h"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.h" title="Permalink to this definition">¶</a></dt>
<dd><p>Dimensionless Hubble constant: h = H_0 / 100 [km/sec/Mpc]</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.hubble_distance">
<tt class="descname">hubble_distance</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.hubble_distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.hubble_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Hubble distance in [Mpc]</p>
</dd></dl>

<dl class="attribute">
<dt id="astropy.cosmology.core.FLRW.hubble_time">
<tt class="descname">hubble_time</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.hubble_time"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.hubble_time" title="Permalink to this definition">¶</a></dt>
<dd><p>Hubble time in [Gyr]</p>
</dd></dl>

<p class="rubric">Methods Documentation</p>
<dl class="method">
<dt id="astropy.cosmology.core.FLRW.H">
<tt class="descname">H</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L532" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.H"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.H" title="Permalink to this definition">¶</a></dt>
<dd><p>Hubble parameter (km/s/Mpc) at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>H</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Hubble parameter in km/s/Mpc at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.Ode">
<tt class="descname">Ode</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L281" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Ode"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Ode" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the density parameter for dark energy at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>Ode</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The density of non-relativistic matter relative to the critical
density at each redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.Ogamma">
<tt class="descname">Ogamma</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L301" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Ogamma"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Ogamma" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the density parameter for photons at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>Ogamma</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The energy density of photons relative to the critical
density at each redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.Ok">
<tt class="descname">Ok</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L258" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Ok"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Ok" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the equivalent density parameter for curvature
at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>Ok</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The equivalent density parameter for curvature at each redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.Om">
<tt class="descname">Om</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L238" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Om"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Om" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the density parameter for non-relativistic matter
at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>Om</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The density of non-relativistic matter relative to the critical
density at each redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.Onu">
<tt class="descname">Onu</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L325" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Onu"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Onu" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the density parameter for massless neutrinos at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>Onu</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The energy density of photons relative to the critical
density at each redshift.  Note that this includes only
their relativistic energy, since they are assumed massless.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.Tcmb">
<tt class="descname">Tcmb</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L350" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.Tcmb"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.Tcmb" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the CMB temperature at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>Tcmb</strong> : ndarray, or float if z is scalar</p>
<blockquote class="last">
<div><p>The temperature of the CMB in K.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.absorption_distance">
<tt class="descname">absorption_distance</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L805" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.absorption_distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.absorption_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Absorption distance at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<p>This is used to calculate the number of objects with some
cross section of absorption and number density intersecting a
sightline per unit redshift path.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Absorption distance (dimensionless) at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">References</p>
<p>Hogg 1999 Section 11. (astro-ph/9905116)
Bahcall, John N. and Peebles, P.J.E. 1969, ApJ, 156L, 7B</p>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.age">
<tt class="descname">age</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L594" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.age"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.age" title="Permalink to this definition">¶</a></dt>
<dd><p>Age of the universe in Gyr at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>t</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The age of the universe in Gyr at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.angular_diameter_distance">
<tt class="descname">angular_diameter_distance</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L692" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.angular_diameter_distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.angular_diameter_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Angular diameter distance in Mpc at a given redshift.</p>
<p>This gives the proper (sometimes called &#8216;physical&#8217;) transverse
distance corresponding to an angle of 1 radian for an object
at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<p>Weinberg, 1972, pp 421-424; Weedman, 1986, pp 65-67; Peebles,
1993, pp 325-327.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Angular diameter distance in Mpc at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.angular_diameter_distance_z1z2">
<tt class="descname">angular_diameter_distance_z1z2</tt><big>(</big><em>z1</em>, <em>z2</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L745" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.angular_diameter_distance_z1z2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.angular_diameter_distance_z1z2" title="Permalink to this definition">¶</a></dt>
<dd><p>Angular diameter distance between objects at 2 redshifts.
Useful for gravitational lensing.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z1, z2</strong> : array_like, shape (N,)</p>
<blockquote>
<div><p>Input redshifts. z2 must be large than z1.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, shape (N,) or float if input scalar</p>
<blockquote>
<div><p>The angular diameter distance between each input redshift
pair.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Raises :</th><td class="field-body"><p class="first"><strong>CosmologyError</strong> :</p>
<blockquote class="last">
<div><p>If omega_k is &lt; 0.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>This method only works for flat or open curvature
(omega_k &gt;= 0).</p>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.arcsec_per_kpc_comoving">
<tt class="descname">arcsec_per_kpc_comoving</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L925" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.arcsec_per_kpc_comoving"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.arcsec_per_kpc_comoving" title="Permalink to this definition">¶</a></dt>
<dd><p>Angular separation in arcsec corresponding to a comoving kpc
at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>theta</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The angular separation in arcsec corresponding to a comoving kpc
at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.arcsec_per_kpc_proper">
<tt class="descname">arcsec_per_kpc_proper</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L944" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.arcsec_per_kpc_proper"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.arcsec_per_kpc_proper" title="Permalink to this definition">¶</a></dt>
<dd><p>Angular separation in arcsec corresponding to a proper kpc at
redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>theta</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The angular separation in arcsec corresponding to a proper kpc
at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.comoving_distance">
<tt class="descname">comoving_distance</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L631" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.comoving_distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.comoving_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Comoving line-of-sight distance in Mpc at a given
redshift.</p>
<p>The comoving distance along the line-of-sight between two
objects remains constant with time for objects in the Hubble
flow.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Comoving distance in Mpc to each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.comoving_transverse_distance">
<tt class="descname">comoving_transverse_distance</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L657" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.comoving_transverse_distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.comoving_transverse_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Comoving transverse distance in Mpc at a given redshift.</p>
<p>This value is the transverse comoving distance at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>
corresponding to an angular separation of 1 radian. This is
the same as the comoving distance if omega_k is zero (as in
the current concordance lambda CDM model).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Comoving transverse distance in Mpc at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>This quantity also called the &#8216;proper motion distance&#8217; in some
texts.</p>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.comoving_volume">
<tt class="descname">comoving_volume</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L855" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.comoving_volume"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.comoving_volume" title="Permalink to this definition">¶</a></dt>
<dd><p>Comoving volume in cubic Mpc at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<p>This is the volume of the universe encompassed by redshifts
less than <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>. For the case of omega_k = 0 it is a sphere of
radius <tt class="xref py py-obj docutils literal"><span class="pre">comoving_distance(z)</span></tt> but it is less intuitive if
omega_k is not 0.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>V</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Comoving volume in Mpc^3 at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.critical_density">
<tt class="descname">critical_density</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L615" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.critical_density"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.critical_density" title="Permalink to this definition">¶</a></dt>
<dd><p>Critical density in grams per cubic cm at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>rho</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Critical density in g/cm^3 at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.de_density_scale">
<tt class="descname">de_density_scale</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L378" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.de_density_scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.de_density_scale" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluates the redshift dependence of the dark energy density.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>I</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The scaling of the energy density of dark energy with redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The scaling factor, I, is defined by <span class="math">\rho(z) = \rho_0 I</span>,
and is given by</p>
<div class="math">
<p><span class="math">I = \exp \left( 3 \int_{a}^1 \frac{ da^{\prime} }{ a^{\prime} }
\left[ 1 + w\left( a^{\prime} \right) \right] \right)</span></p>
</div><p>It will generally helpful for subclasses to overload this method if
the integral can be done analytically for the particular dark
energy equation of state that they implement.</p>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.distmod">
<tt class="descname">distmod</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L835" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.distmod"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.distmod" title="Permalink to this definition">¶</a></dt>
<dd><p>Distance modulus at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<p>The distance modulus is defined as the (apparent magnitude -
absolute magnitude) for an object at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>distmod</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Distance modulus at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.efunc">
<tt class="descname">efunc</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L428" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.efunc"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.efunc" title="Permalink to this definition">¶</a></dt>
<dd><p>Function used to calculate H(z), the Hubble parameter.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>E</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The redshift scaling of the Hubble constant.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The return value, E, is defined such that <span class="math">H(z) = H_0 E</span>.</p>
<p>It is not necessary to override this method, but if de_density_scale
takes a particularly simple form, it may be advantageous to.</p>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.inv_efunc">
<tt class="descname">inv_efunc</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L459" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.inv_efunc"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.inv_efunc" title="Permalink to this definition">¶</a></dt>
<dd><p>Inverse of efunc.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>E</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The redshift scaling of the inverse Hubble constant.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.kpc_comoving_per_arcmin">
<tt class="descname">kpc_comoving_per_arcmin</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L889" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.kpc_comoving_per_arcmin"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.kpc_comoving_per_arcmin" title="Permalink to this definition">¶</a></dt>
<dd><p>Separation in transverse comoving kpc corresponding to an
arcminute at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The distance in comoving kpc corresponding to an arcmin at each
input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.kpc_proper_per_arcmin">
<tt class="descname">kpc_proper_per_arcmin</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L907" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.kpc_proper_per_arcmin"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.kpc_proper_per_arcmin" title="Permalink to this definition">¶</a></dt>
<dd><p>Separation in transverse proper kpc corresponding to an
arcminute at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The distance in proper kpc corresponding to an arcmin at each
input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.lookback_time">
<tt class="descname">lookback_time</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L570" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.lookback_time"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.lookback_time" title="Permalink to this definition">¶</a></dt>
<dd><p>Lookback time in Gyr to redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<p>The lookback time is the difference between the age of the
Universe now and the age at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>t</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Lookback time in Gyr to each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.luminosity_distance">
<tt class="descname">luminosity_distance</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L718" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.luminosity_distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.luminosity_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Luminosity distance in Mpc at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<p>This is the distance to use when converting between the
bolometric flux from an object at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt> and its
bolometric luminosity.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>d</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Luminosity distance in Mpc at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">References</p>
<p>Weinberg, 1972, pp 420-424; Weedman, 1986, pp 60-62.</p>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.scale_factor">
<tt class="descname">scale_factor</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L548" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.scale_factor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.scale_factor" title="Permalink to this definition">¶</a></dt>
<dd><p>Scale factor at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p>
<p>The scale factor is defined as <span class="math">a = 1 / (1 + z)</span>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>a</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>Scale factor at each input redshift.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="astropy.cosmology.core.FLRW.w">
<tt class="descname">w</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L213" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link">&nbsp;[edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#FLRW.w"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.FLRW.w" title="Permalink to this definition">¶</a></dt>
<dd><p>The dark energy equation of state.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p>
<blockquote>
<div><p>Input redshifts.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>w</strong> : ndarray, or float if input scalar</p>
<blockquote class="last">
<div><p>The dark energy equation of state</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The dark energy equation of state is defined as
<span class="math">w(z) = P(z)/\rho(z)</span>, where <span class="math">P(z)</span> is the
pressure at redshift z and <span class="math">\rho(z)</span> is the density
at redshift z, both in units where c=1.</p>
<p>This must be overridden by subclasses.</p>
</dd></dl>

</dd></dl>

</div>


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