Environmental Engineering Reference
In-Depth Information
1 Introduction
Currently, the most accepted picture for the study of our Universe as a whole is
given by the so called
CDM) model of Cosmology. The
first pillar of this model is Einstein's theory of General Relativity (GR) (Einstein
1916 ), in which the spacetime itself and the matter-energy fields that live in there
are related by second order partial differential equations, thus any distribution of
matter will effectively curve the arena where these matter fields evolve. Despite this
fact, many features of the evolution of the Universe can be well understood in the
context of Newtonian gravity; qualitatively, consider the spacetime as a curved four
dimensional manifold with some characteristic curvature scale l H , well below this
scale the effects of curvature could be neglected and the Newtonian limit of GR
becomes a good approximation to the whole, complete description. In the cosmic
epochs that are relevant in this short review the characteristic scale is given by the
inverse of the rate of expansion of the Universe, that is, the inverse of the Hubble
factor H , thus we expect the Newtonian results to be valid up to the length scale
cH 1 , where c is the speed of light. In this work we derive the relevant equations
that govern the cosmic fluids evolution in Newtonian gravity and once we have done
this we will add relativistic corrections in order to reach the complete set of equations.
A second pillar of the
ʛ
-Cold Dark Matter (
ʛ
CDM model is the Standard Model of Particles. The
known matter fields of the Universe are essentially baryons, 1 neutrinos and pho-
tons. These components can be approximated as fluids as long as the mean free
path of their microscopic entities are much smaller than the typical smallest macro-
scopic scale of the structure of interest. In this review we will follow this approach
by considering the matter fields as fluids that evolve according to hydrodynamical
equations. This approximation is also valid for incoherent electromagnetic radiation,
while coherency requires a detailed analysis of their distribution functions through
the coupled Boltzmann and Einstein equations; for such a treatment see for example
Ma and Bertschinger ( 1994 ).
It turns out that to describe the Universe we observe it does not suffice with the
ingredients mentioned in the two previous paragraphs. Several independent cosmo-
logical probes show that nowadays the nature of about 96% of the energy content of
the Universe is unknown to us (Cervantes-Cota and Smoot 2011 ). As far as today all
our knowledge of these components comes from their gravitational interaction with
the standard matter fields, in this sense we refer to them as dark. This dark sector is
usually decomposed into dark matter and dark energy, fromwhich the
ʛ
CDMmodel
inherits its name. The darkmatter component has the property that clumps at all scales
and it is responsible for the formation of the cosmic structures we observe, while
dark energy fills the space homogeneously and provides a negative pressure which
counteracts gravitational attraction and ultimately accelerates the Universe. Never-
theless, we will show—as it is done in Ref. Aviles and Cervantes-Cota ( 2011 )—that
ʛ
1 In the jargon of Cosmology we refer to any particle of the standard model that is not relativistic
as a baryon, referring mainly to protons and neutrons. In contrast, in particle physics a baryon is a
composite subatomic particle made up of three quarks.
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