**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
(*n*_{} / *n*_{p}
10^{9}). Therefore
the primordial fluid can be treated as radiation-dominated with
*p* = 1 / 3
*c*^{2} = 1 /
3 *T*^{4}
and from (10), we obtain:

(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 *z*_{eq}, we had
_{m}
= _{rad}.
It is easy to show that
_{r} =
_{m}
*R*_{0} / *R*_{eq} = (1 +
*z*_{eq})
_{m}
(the subscript 0 denotes
the present epoch) and using the measured values of
_{i} we
have that:

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

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

(12) |

Using _{} =
^{2}
*k*_{b} *t*^{4} / 15*h*^{3}
*c*^{5} we finally obtain the important relation
between cosmic time and the temperature of the Universe in the
radiation dominated era:

(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 ~ 10^{9}
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,
*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*
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 *T*_{0} = 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:

with *T* 3000 K
and *T*_{0}
2.73 we get that

From (7) and (10) we have that in the matter dominated era
*R*(*t*)
*t*^{2/3}
and thus *z*_{rec} corresponds to a time:

where *t*_{0} 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 *t*_{rec}.

**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:

- a Doppler effect that increases the frequency of photons, and
thus the observed energy, seen in the direction of motion by a
Doppler factor
*D*1 + (*u/c*) cos - the interval of frequencies increases by the same factor in the
direction of motion, and therefore since
*T**E*/ , the above two effects cancel out. - the moving observer selects in the direction of motion relatively
more photons by a factor
*D* - the solid angle in the direction of motion is smaller by a factor
*D*^{-2}due to abberation.

The net effect is that the moving observer sees an intensity of CMB
radiation *I*_{mov} = (1 + *u/c*
cos )^{3}
*I*_{rest}. Due to the adiabatic expansion of
the Universe, (*t*
*R*^{-1}), the shape of the Planck spectrum:

should be preserved, which then necessarily implies that
*T* () = (1 +
*u/c* cos )
*T*_{0} and thus:

(14) |

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

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:

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

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 ×
10^{16}
*M*_{}
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]).