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Thermal History of the Universe


									11. Thermal History of the Universe
Radiation dominated approximation:  c2  S 4  S 3 S 1

no. particles  energy/particle
k BT  S 1  t 1/ 2

where the connection to time t comes from the Freedman solution S  t1/ 2 . The above applies with any ‘hot’ matter, defined by k BT  mc 2 such that it is easy to excite PP pairs and that particle energies are typically relativistic. For any given species, once k BT falls below mc 2 the equilibrium concentration rapidly becomes small,  e
 mc 2 k BT


Energy reference :

Proton: mpc2  1 GeV  109 1.6 1019 J Electron: me c 2  0.5 MeV Also quote temperatures in terms of the corresponding thermal energy k BT . (Figure)

Key annihilation energies

100 GeV  mc 2 for W  , Z bosons. Above this energy (and corresponding temperature), weak and electromagnetic interactions are largely equivalent.

1 GeV  mc 2 for n, n , p, p Above this nn , pp pairs readily excited. Below 1 GeV we have only the residual net imbalance of bayons n  p , negligible antibaryons.

The remaining imbalance was relatively tiny, is not understood, and survives as the baryon abundance today. Baryon number n  p is conserved [except perhaps in Black Holes, and GUT suggests proton might decay in 1035 years].
0.5 MeV  mc 2 for e  Above this, plentiful electron-positron pair excitation. Below 0.5 MeV only the residual e  balancing charge of residual protons. Preserved by charge conservation. 13.6 eV H   e   H deionisation (‘recombination’) of Hydrogen eliminates the last free charges.

12. Fate of Residual Baryons: Nucleosynthesis Background  Baryonic matter today is roughly 22-24% and almost all the remainder is 1H . Corresponding neutron ratio is
n  1/ 7 p

He by mass,

  

Stars have not had long enough to produce much of this Helium Most is explained by Big Bang origins.

Key Steps  
k BT  1 GeV residual net baryon number n  p not explained Equilibrium reactions 0.8 MeV  p  e   n   e
1.8 MeV  p   e  n  e 

where  e ,( e )  electron (anti) neutrino. Provided e  , e  , e , e all in equilibrium, these
   n p 13.6 eV n k BT k BT e e p k BT  2.3MeV weak interactions too slow to keep  e , e in equilibrium. Beyond this point the neutrinos are decoupled, concentration diluting as c  S 3 , begging to be observed. Electrons stay in equilibrium due to faster e/m reaction e   e   2
E E

imply 


Due to higher cross-sections, baryon-neutrino reactions do not shut off until about 0.8MeV , leaving n 13.6 eV 0.8 MeV e  1/ 5 ,  p  lepton when the Universe is about 20s old. Neutrons can also decay spontaneously n  p  e   e with a lifetime   15 minutes , so cosmology has just that long to save its neutrons! Key neutron preservation step is formation of deuterons d  2 H  by n  p  d    2 MeV which is highly exothermic but still impeded by the back reaction due to low baryon and high photon concentrations. This only runs net forwards around k BT  0.1MeV , fortunately only t  2.5 minutes on the cosmic clock, leaving us n n  et /    1/ 7 p  p lepton where these remaining neutrons are safely locked up in stable deuterons.



I have desperately simplified a complicated story above, but the bottom line is excellent agreement between Big Bang nucleosynthesis and the observed abundance of Helium in the universe.


From Deuterium to Helium can take its time, first reaching the two nuclei of mass 3 by every conceivable route: d  p  3 He2  

d  n  t ,

t  3H 

d  d  3 He 2  n d d t p Regular mass 4 Helium then follows by 3 He2  n  4 He2
  

t  p  4 He2 There are no nuclei of mass 5 which constitutes a major bottleneck. Mass 6 offers only 6 Li which is still unstable but can live long enough that there is some yield of 6 Li  n  7 Li Mass 8 being another bottleneck, production of heavier nuclei is negligible.

Below k BT  0.1MeV little changes for a long time, with
p, 4 He, 3 He, e interacting via photons, which are heavily scattered. We could only ‘see’ events or structures from this era by their perturbation to the neutrino background, or perhaps gravitational waves.

13. Deionisation of Hydrogen and the CMBR
p  e  H  2 with 13.6 eV available to the photons, but the low concentration of p  e holds up the forward reaction until k BT  0.3eV or T  4000K . This is of the same order as the visible surface of the sun, for related reasons.

Key idea: Last Scattering Surface where photons had last interaction with matter. This is what we ‘see’ when we image the microwave background. It is equivalent to imaging the surface of the sun, but redshifted by z  1100 to T  2.728K (Cobe, 19__) (most accurate Black Body spectrum ever observed in any branch of science). The equivalent neutrino background did not benefit from the deionisation energy of H, so T  1.949 K remains predicted awaiting observation. Structure in CMBR Cobe saw a dipolar perturbation  T T  103 , interpreted as our peculiar motion v  365 km / s relative to the global Hubble flow (and CMBR). When this is subtracted, the remaining intrinsic structure has  T T  105 which it is an even more recent triumph to have mapped out in detail.

Angular Correlation Function  T    T     C ( )  T T


1  (  1) C P (cos ) 4  2   angular wavevector ; angular lengthscale  60  . 
Peak at   200    0.3 : Sakharov oscillations, acoustic standing waves inside LSS: higher peaks predicted and now observed. Particle Horizon of LSS The particle horizon is how far away a past event could have occurred and still have influence on the event of interest. Looking back from the LSS along a light ray c 2 dt 2  S (t ) 2 d 2  0 (and ignoring curvature) gives this distance in terms of t1 ct cdt 1   2 1 S (t ) S1 0 where the estimate of the integral assumes radiation dominance up to the LSS, S (t )  t1/ 2 . Points on the LSS further apart than 2 1S1 can have no past event in common back to the beginning of time, setting a severe limit on the range of intrinsic correlations in the CMBR. We can relate distances in the LSS (e.g.  1S1 ) to small angles in the observed microwave sky by  1S1   0 S11 where  0 is the comoving distance between us and the LSS. Using a light ray from the LSS to us, we obtain


0  


ct cdt 3 0 S (t ) S0

using cold matter dominance, S (t )  t 2 / 3 , and noting that the contribution form the lower limit is comparatively negligible. Combining these results gives us

 2t / S 2 S  1  1  1 1   1   0.02 radians  0 3t0 / S0 3  S0  where we have used S (t )  t 2 / 3 and the observed redshift of the CMBR.
Converted to degrees, this gives the maximum range of common influence about 21  3 , and such an angular scale can indeed be seen in the CMBR correlations. Reheat The WMAP satellite data make quite clear the existence of a weaker feature in the CMBR angular correlation, extending to of order 90 . This is confidently attributed to scattering of CMBR by subsequent hydrogen clouds reheating as density fluctuations grow, leading of course to star and galaxy formation. These are much more recent events, so at much smaller  0 and are seen to influence larger angles in the sky.

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14. Summary of Big Bang Relics
Here are the key relics of the Big Bang. Residual net baryons p  n since k BT  1GeV -observed but not understood Neutrino background -predicted decoupled since k BT  2.3MeV

Neutrons stabilised since k BT  0.1MeV (2minutes) as d  He - observed CMBR photons from k BT  0.3eV - observed including angular structure Reheat from primordial H cloud collapse - observed

In a loose sense you can think of them as signatures of the strong, weak, electromagnetic and gravitational interactions each dominating events in turn. Remaining Puzzles However convincing the agreement of cosmological observations might be, it remains a concern that the Universe today appears quite recently to have turned from deceleration under the influence of matter to acceleration under the influence of the cosmological constant.

Most people can accept the Universe being predominantly propulated by dark matter, which we may not be able to see but which we can certainly see the gravitational influence of in the likes of galaxy rotation curves. Predominant dark energy is for some a step too far. Many things are beyond the scope of this course, including the arguments about structure in the distribution of galaxies. At every turn in the story there has been too much. Recently there has been some matching up of the galaxy distribution with the underlying structure in the CMBR, but in the last two months it has been asserted that the observed galaxy clustering requires m  1 to be able to develop. If that claim holds up, this is the most serious challenge to the new ‘standard cosmology’.

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