Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 9
space is expanding according to the Friedmann–Lemaître model of General Relativity
(Slipher, 1917; Hubble, 1929). Extrapolated into the past, these observations
show that the Universe has expanded from a state in which all its matter
and energy had immense temperatures and densities.
In fact, in the very early Universe the temperatures and densities were so high
that the photons and the great variety of relativistic particles were in thermodynamic
equilibrium. When the mean thermal energy kT ≫ mc 2 , conservation of
energy implies that every elementary particle of rest mass m can be converted
into every other particle. Creation and annihilation of particle–antiparticle pairs
and the interactions with other particles thus keep any particular type of particle
of mass m in equilibrium (and in large numbers) above the energy mc 2 . As
the average energy in the Universe decreased due to its expansion to a value less
than the equivalent mass mc 2 , particles of mass m which had decayed or been
annihilated could no longer be replaced. This point is known as the threshold for
that particular particle. Cosmic evolution is thus characterized by a sequencial
‘dying off’ of the various types of particles, beginning with the most massive.
The temperature T or the average thermal energy kT in the radiation cosmos,
can be written as a function of time as (e.g. Unsöld & Bascheck, 2002)
1.5
t[s]
(T [1010 K])
2
1
2 , (37)
(kT[MeV ])
as long as t ≤ 2 × 10 6 years and leaving out of consideration the details of each
types of relativistic particle.
Before one Planck time (tP ∼ 10 −43 s) all the four fundamental forces were
unified into a single force. This phase of the Universe is called the Planck Era.
During this era the theory of General Relativity, which treats space–time as
a continuum, would have to be replaced by a still lacking Quantum Theory of
Gravity. Only at the end of this era, i.e., when the Universe was ∼ 10 −43 s old,
gravity separated from the other three forces (e.g. Unsöld & Bascheck, 2002).
The period 10 −43 s < t < 10 −35 s is is called the Grand Unification Era.
During this era the electromagnetic, strong and weak interactions are unified
in a single force mediated by an hypothetical boson X, with mass (energy) of
order 10 14 GeV, which converts leptons into quarks and vice versa. At this stage
the Universe consists of a plasma composed of quarks, gluons, leptons, photons,
bosons X as well as their respective antiparticles. They are all present in equal
abundances and are continuoslly being interconverted due to mutual collisions
(e.g. Unsöld & Bascheck, 2002).
When the temperature of the Universe goes below 10 14 GeV it turns out
that the decaying X bosons are no longer replaced by new X bosons. As a
result, we have the strong–electroweak phase transition, i.e., the separation of
the strong and EW interactions (e.g. Unsöld & Bascheck, 2002).
In order to explain problems such as ‘flatness’, ‘horizon’ and ‘monopole’, the
present paradigm makes use of an inflationary stage of expansion in the very
early Universe (Section 1.3). During inflation the scale factor R(t) growns exponentially
from an initial value Ri, corresponding to the instant ti ∼ 10 −35 s