Decoupling (cosmology)

<h2 id="photon-decoupling">Photon decoupling</h2>
<p class="note">Main article: <a href="/facts/Recombination_(cosmology)/cUGysC0q">Recombination (cosmology)</a></p>
<p>Photon decoupling occurred during the <a href="/facts/Epoch_(cosmology)/wcDpG3CL">epoch</a> known as the recombination. During this time, electrons combined with protons to form <a href="/facts/Hydrogen_atoms/ncVpPbuE">hydrogen atoms</a>, resulting in a sudden drop in free electron density. Decoupling occurred abruptly when the rate of <a href="/facts/Compton_scattering/Q98Ty8rz">Compton scattering</a> of photons 
  
    
      
        Γ
      
    
    {\displaystyle \Gamma }
  
 was approximately equal to the rate of <a href="/facts/Accelerating_universe/F7X1PAMq">expansion of the universe</a> 
  
    
      
        H
      
    
    {\displaystyle H}
  
,  or alternatively when the <a href="/facts/Mean_free_path/6M7eofRq">mean free path</a> of the photons 
  
    
      
        λ
      
    
    {\displaystyle \lambda }
  
 was approximately equal to the <a href="/facts/Particle_horizon/sxfNTy8E">horizon size</a> of the universe 
  
    
      
        
          H
          
            −
            1
          
        
      
    
    {\displaystyle H^{-1}}
  
. After this photons were able to <a href="/facts/Free_streaming/6a3EN5op">stream freely</a>, producing the cosmic microwave background as we know it, and the universe became transparent.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p><p>The interaction rate of the photons is given by
</p>

Γ
        =
        
          
            c
            λ
          
        
        =
        
          n
          
            e
          
        
        
          σ
          
            t
          
        
        c
      
    
    {\displaystyle \Gamma ={\frac {c}{\lambda }}=n_{e}\sigma _{t}c}

<p>where 
  
    
      
        
          n
          
            e
          
        
      
    
    {\displaystyle n_{e}}
  
 is the <a href="/facts/Number_density/qtyDnLhz">number density</a> of free electrons, 
  
    
      
        
          σ
          
            t
          
        
      
    
    {\displaystyle \sigma _{t}}
  
 is the electron <a href="/facts/Thomson_scattering/hUj6gSgB">Thomson scattering</a> area, and 
  
    
      
        c
      
    
    {\displaystyle c}
  
 is the <a href="/facts/Speed_of_light/sKSQwdNx">speed of light</a>.
</p><p>In the <a href="/facts/Matter-dominated_era/hN9JlB3v">matter-dominated era</a> (when recombination takes place),
</p>

H
        ≈
        
          H
          
            0
          
        
        
          a
          
            −
            
              3
              
                /
              
              2
            
          
        
      
    
    {\displaystyle H\approx H_{0}a^{-{3/2}}}

<p>where 
  
    
      
        a
      
    
    {\displaystyle a}
  
 is the <a href="/facts/Scale_factor_(cosmology)/hN9JlB3v">cosmic scale factor</a> and H₀ is the <a href="/facts/Hubble_constant/FJYfELCP">Hubble constant</a>. 
  
    
      
        Γ
      
    
    {\displaystyle \Gamma }
  
 also decreases as a more complicated function of 
  
    
      
        a
      
    
    {\displaystyle a}
  
, at a faster rate than 
  
    
      
        H
      
    
    {\displaystyle H}
  
.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> By working out the precise dependence of 
  
    
      
        H
      
    
    {\displaystyle H}
  
 and 
  
    
      
        Γ
      
    
    {\displaystyle \Gamma }
  
 on the scale factor and equating 
  
    
      
        Γ
        =
        H
      
    
    {\displaystyle \Gamma =H}
  
, it is possible to show that photon decoupling occurred approximately 380,000 years after the <a href="/facts/Big_Bang/I5T1vTnv">Big Bang</a>, at a <a href="/facts/Redshift/Qfl4VjDF">redshift</a> of 
  
    
      
        z
        =
        1100
      
    
    {\displaystyle z=1100}
  
 <a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> when the universe was at a temperature around 3000 K.
</p>
<h2 id="neutrino-decoupling">Neutrino decoupling</h2>
<p class="note">Main article: <a href="/facts/Neutrino_decoupling/VXsoDNdz">Neutrino decoupling</a></p>
<p>Another example is the neutrino decoupling which occurred within one second of the Big Bang.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> Analogous to the decoupling of photons, neutrinos decoupled when the rate of <a href="/facts/Weak_interaction/f6upmKMs">weak interactions</a> between neutrinos and other forms of matter dropped below the rate of expansion of the universe, which produced a cosmic neutrino background of freely streaming neutrinos. An important consequence of neutrino decoupling is that the <a href="/facts/Cosmic_neutrino_background/J9jzIPC0">temperature</a> of this neutrino background is lower than the temperature of the cosmic microwave background, since they were no more heated by the shortly following annihilation of positrons.
</p>
<h2 id="wimps-non-relativistic-decoupling">WIMPs: non-relativistic decoupling</h2>
<p>Decoupling may also have occurred for the <a href="/facts/Dark_matter/y5HgX55N">dark matter</a> candidate, <a href="/facts/Weakly_interacting_massive_particles/EbWC6o3w">WIMPs</a>. These are known as "cold relics", meaning they decoupled after they became <a href="/facts/Relativistic_particle/pbC4pdtD">non-relativistic</a> (by comparison, photons and neutrinos decoupled while still relativistic and are known as "hot relics"). By calculating the hypothetical time and temperature of decoupling for non-relativistic WIMPs of a particular mass, it is possible to find their <a href="/facts/Density/92p6hh9I">density</a>.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> Comparing this to the measured <a href="/facts/Friedmann_equations/B9s5rjB9">density parameter</a> of <a href="/facts/Cold_dark_matter/vL4134Kd">cold dark matter</a> today of 0.222 
  
    
      
        ±
      
    
    {\displaystyle \pm }
  
 0.0026 <a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> it is possible to rule out WIMPs of certain masses as reasonable dark matter candidates.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a>
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Recombination_(cosmology)/cUGysC0q">Recombination</a></li>
<li><a href="/facts/Chronology_of_the_universe/ezBKAdjy">Chronology of the universe</a></li>
<li><a href="/facts/Wouthuysen%25E2%2580%2593Field_coupling/FfQwVlLF">Wouthuysen–Field coupling</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Ryden, Barbara Sue (2003). Introduction to cosmology. San Francisco: Addison-Wesley. <a href="/wiki/Addison-Wesley" target="_blank">/wiki/Addison-Wesley</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Kolb, Edward; Turner, Michael (1994). The Early Universe. New York: Westview Press. <a href="/wiki/Westview_Press" target="_blank">/wiki/Westview_Press</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Hinshaw, G.; Weiland, J. L.; Hill, R. S.; Odegard, N.; Larson, D.; Bennett, C. L.; Dunkley, J.; Gold, B.; Greason, M. R.; Jarosik, N. (1 February 2009). "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results". The Astrophysical Journal Supplement Series. 180 (2): 225–245. arXiv:0803.0732. Bibcode:2009ApJS..180..225H. doi:10.1088/0067-0049/180/2/225. S2CID 3629998. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Longair, M.S. (2008). Galaxy formation (2nd ed.). Berlin: Springer. ISBN 9783540734772. <a href="9783540734772" target="_blank">9783540734772</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Bringmann, Torsten; Hofmann, Stefan (23 April 2007). "Thermal decoupling of WIMPs from first principles". Journal of Cosmology and Astroparticle Physics. 2007 (4): 016. arXiv:hep-ph/0612238. Bibcode:2007JCAP...04..016B. doi:10.1088/1475-7516/2007/04/016. S2CID 18178435. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Jarosik, N. (4 December 2010). "Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results. Table 8". Astrophysical Journal Supplement Series. 192 (2): 14. arXiv:1001.4744. Bibcode:2011ApJS..192...14J. doi:10.1088/0067-0049/192/2/14. S2CID 46171526. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Weinheimer, C. (2011). "Dark Matter Results from 100 Live Days of XENON100 Data". Physical Review Letters. 107 (13): 131302. arXiv:1104.2549. Bibcode:2011PhRvL.107m1302A. doi:10.1103/physrevlett.107.131302. PMID 22026838. S2CID 9685630. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
</ol>

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Decoupling (cosmology)