Nearby Supernova Factory: Étalonnage des données de SNIFS et ...

tel-00372504, version 1 - 1 Apr 2009
CHAPTER 1. BIG BANG COSMOLOGY
From (1.8) and for a wi constant, we can write the time evolution of the energy density
˙ρi
= −3
ρi
˙a
a (1 + wi) (1.17)
−3(1+wi) a
ρi = ρi0
(1.18)
a0
ρi ∝ a −3(1+wi)
(1.19)
∝ (1 + z) 3(1+wi) , (1.20)
and using (1.5), (1.19) and the fact that, since at early times a is small and the curvature term
can be neglected, we write the time evolution of the scale factor for a single component universe
as
2
3(1+w a(t) ∝ t i ) . (1.21)
So, for the three most common barotropic (with pressure linearly proportional to density)
fluids present in the universe, we can divide the history of the universe (Fig. 1.2) into three
epochs:
Log [energy density (GeV 4 )]
-36
-40
-44
-48
4
radiation matter
dark energy
3
2
1
Log [1+z]
Figure 1.2: Evolution of radiation, matter, and dark energy densities with redshift. From Frieman et al.
(2008a).
Radiation-dominated In the early hot and dense universe, it is appropriate to assume an
equation of state corresponding to a gas of radiation (or relativistic particles) for which
wr = 1
3 , leading to
ρr ∝ a −4 ; a(t) ∝ t 1
2 . (1.22)
We can see that the radiation density decreases with the forth power of the scale factor.
Three of these powers are accounted for by the volume increase during the expansion,
while the forth one comes from the cosmological redshift.
Matter-dominated At relatively late times, non-relativistic matter eventually dominates the
energy density over radiation. It’s a pressureless gas of particles with temperatures much
smaller than their mass for which wm = 0, and
0
ρm ∝ a −3 ; a(t) ∝ t 2
3 . (1.23)
12
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