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1.2. Thermal Beginning of the Universe

The early universe, where very high densities and temperatures dominate, can be treated by using fluid thermodynamics. At very high temperatures, radiation and matter are in thermal equilibrium, coupled via Thomson scattering with the photons dominating over the nucleons (ngamma / np appeq 109). Therefore the primordial fluid can be treated as radiation-dominated with p = 1 / 3 rho c2 = 1 / 3sigma T4 and from (10), we obtain:

Equation 11 (11)

Therefore the temperature of the Universe drops linearly with the expansion scale factor. Furthermore, it is evident from (10), that the radiation density drops faster than the mass density and since we know from measurements that the universe is matter dominated today, then at some epoch in the past, say at a redshift zeq, we had rhom = rhorad. It is easy to show that rhor = rhom R0 / Req = (1 + zeq) rhom (the subscript 0 denotes the present epoch) and using the measured values of rhoi we have that:

Equation

Therefore the thermal history of the Universe can be divided in two main eras: a radiation dominated era (z >> zeq) and a matter dominated era (z << zeq). In the radiation dominated era, in which we can neglect the curvature and Lambda terms in Friedmann's equation (see next section), we have:

Equation

By differentiating this relation with respect to time and using (7) we have:

Equation 12 (12)

Using rhogamma = pi2 kb t4 / 15h3 c5 we finally obtain the important relation between cosmic time and the temperature of the Universe in the radiation dominated era:

Equation 13 (13)

from which it is evident that the Universe at early times was hot enough for nucleosynthesis to occur, as it had been supposed originally by Gamow. The era of nucleosynthesis takes place around ~ 109 K.

The Cosmic Microwave Background: Although the dynamics during the radiation dominated era are unaffected by ordinary matter, the electrons act as a scattering medium of the radiation and thus the Universe at this epoch is opaque. As the Universe cools, propto R-1, electrons bind electrostatically with protons to form Neutral Hydrogen. Using Saha's ionization equation one finds that the temperature at which the number of free electrons drops significantly is t appeq 3000 K.

Therefore when the universe cools at this temperature, the scattering medium disappears and the radiation freely escapes without being absorbed or scattered which means that the Universe becomes transparent. This epoch is called the recombination epoch.

The existence of the relics of this radiation was predicted by Gamow and his collaborators in the 1940s. It was subsequently discovered by Penzias & Wilson in 1965, while the whole spectrum of this radiation was traced to unprecedented accuracy by the COBE satellite observations. The CMB possesses a perfect black-body spectrum with a mean temperature of T0 = 2.728 ± 0.004 K and it is extremely isotropic except for a dipole, which is however a local kinematical effect (due to our motion with respect to the cosmic rest frame defined by the CMB). From what redshift does the CMB radiation originate? From (11) we have that:

Equation

with T appeq 3000 K and T0 appeq 2.73 we get that

Equation

From (7) and (10) we have that in the matter dominated era R(t) propto t2/3 and thus zrec corresponds to a time:

Equation

where t0 is the present age of the Universe. Therefore by studying the microwave background sky we have direct information from the Universe when it was as young as trec.

The CMB dipole anisotropy: Due to our motion with respect to the isotropic CMB radiation we observe a dipole in the distribution of the radiation temperature. Although this has the appearance of a Doppler effect, in reality four different effects add up to produce this dipole seen by an observer moving with a velocity u. These four effects are:

The net effect is that the moving observer sees an intensity of CMB radiation Imov = (1 + u/c cos theta)3 Irest. Due to the adiabatic expansion of the Universe, (t propto R-1), the shape of the Planck spectrum:

Equation

should be preserved, which then necessarily implies that T (theta) = (1 + u/c cos theta) T0 and thus:

Equation 14 (14)

COBE observed a CMB dipole amplitude of deltaT ~ 3.3(±0.2) mK (which corresponds to a fluctuation deltaT / T = 1.2(±0.03) × 10-3). The corresponding velocity of Earth is:

Equation

towards the galactic coordinates (l, b) = (265°, 48°) (see [159]). This motion is due to the vectorial sum of the motion of the Earth around the Sun, of the Sun within the Galaxy, of the Galaxy within the Local Group and of the peculiar motion of the Local Group, due to the gravitational effects of large-scale density fluctuations. The motion of the Earth with respect to the LG centroid is:

Equation

towards (l, b) = (107°, -7°) and thus we find the velocity of the LG centroid with respect to the CMB:

Equation

towards (l, b) = (277°, 30°) .

The Local Group velocity was originally thought as the result of the attraction of the Local Supercluster (Virgo). However, there is a residual velocity of ~ 400 km/sec that must be due to gravitational forces acting on the LG from distances greater than the Local Supercluster's centre-of-mass (cz ~ 1100 km/sec). Many earlier studies pointed towards the ‘Great Attractor', a mass concentration of ~ 5 × 1016 Modot located at a distance of 42 h-1 Mpc and at low Galactic latitudes, as being the sole cause of a relatively local coherent motion, in which the Local Group partakes (cf. [94], [93]). Later studies, indicated that another very massive and more distant (~ 140 h-1 Mpc) attractor could play a significant role in shaping the local dynamics ([151], [152], [122]). It seems that the coherence scale of the velocity field could extend to even larger distances than what originally thought (cf. [11], however for a different view see [40]).

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