Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 1
1 The Primordial Universe
The modern understanding of the early and present Universe hinges upon two
standard models: the Standard Model of Cosmology and the Standard Model
of Particle Physics (SMPP) (e.g. Boyanovsky et al., 2006). In this chapter we
review a few topics, within the contexts of Cosmology and Particle Physics,
which are important to our subsequent work.
1.1 Relativistic cosmology
According to observation we live in a flat, homogeneous and isotropic (on scales
larger than 100 Mpc) expanding Universe (e.g. Jones & Lambourne, 2004).
Thus, Cosmology, i.e. the study of the dynamical structure of the Universe as
a whole, is based on the (e.g. d’Inverno, 1993)
Cosmological Principle– At each epoch, the Universe presents the same aspect
from every point, except for local irregularities,
which is in essence, a generalization of the Copernican Principle that the Earth
is not at the center of the Solar System. We are assuming that there is a cosmic
time t with the Cosmological Principle valid for each spacelike hypersurface
t = const. The statement that each hypersurface has no privileged points means
that it is homogeneous. The principle also requires that each hypersurface has
no privileged directions about any point, i.e., the spacelike hypersurfaces are
isotropic and necessarily spherically symmetric about each point. The concepts
of homogeneity and isotropy, however, do not apply to the Universe in detail
(e.g. d’Inverno, 1993).
In 1923, H. Weyl addressed the problem of how a theory like General Relativity
can be applied to a unique system like the Universe. He considered the
assumption that there is a privileged class of observers in the Universe, namely,
those associated with the smeared–out motion of the galaxies. We can work
with this smeared–out motion because the relative velocities in each group of
galaxies are, according to observation, small. Weyl introduced a fluid pervading
space, which he called the substractum, in which the galaxies move like particles
in a fluid. These ideas are contained on the (e.g. d’Inverno, 1993)
Weyl’s Postulate – The particles of the substractum lie in space–time on a
congruence of timelike geodesics diverging from a point in the finite or infinite
past.
The postulate requires that the geodesics do not intersect except at a singular
point in the past and possibly at a similar singular point in the future.
There is, therefore, one and only one geodesic passing through each point of
space–time, and consequently the matter at any point possesses a unique velocity.
This means that the substractum may be taken to be a perfect fluid.
Although galaxies do not follow this motion exactly, the deviations appear to