MODERN COSMOLOGY

Dark energy,CDM and xCDM or QCDM 205

where
 0 ≡

∑

iρi/ρcr,
i is the fraction of critical density due to the

componenti,pi=wiρiis the pressure of the componenti,ρcr=

3 H 02

8 πG =

1. 88 h^2 × 10 −^29 gcm−^3.

Measurements ofq 0 from high-ZType Ia SuperNovae (SNeIa) [44, 45]
give strong indications in favour of an accelerating universe. CMB data [46]
and cluster mass distribution [47] seem to favour models in which the energy
density contributed by the negative pressure component should be roughly twice
as much as the energy of the matter, thus leading to a flat universe (
tot=1)
with
M ∼ 0 .4and
 ∼ 0 .6. Therefore the universe should be presently
dominated by a smooth component with effective negative pressure; this is, in
fact, the most general requirement in order to explain the observed accelerated
expansion. The most straightforward candidate for that is, of course, a ‘true’
cosmological constant [48]. A plausible alternative that has recently received
much attention is a dynamical vacuum energy given by a scalar field rolling down
its potential: a cosmological scalar field, depending on its dynamics, can easily
fulfil the condition of an equation of statewQ = pQ/ρQbetween−1(which
corresponds to the cosmological constant case) and 0 (that is the equation of state
of matter). Since it is useful to have a short name for the rather long definition
of this dynamical vacuum energy, we follow the literature in calling it briefly
‘quintessence’ [49].

5.7.1 CDM models

At the moment models with
∼ 0 .6 seem to be favoured (see for example [28]).

is given by

≡

8 πG

3 H 02

(5.47)

whereis the cosmological constant, which appears in the most general form of
the Einstein equation. The equation of state forisp=−ρor, equivalently,
w=−1. In order to have
∼O( 1 ),has to be:

∼( 2 × 10 −^3 eV)^4. (5.48)

Being a constant there is no reason in particle physics why this constant
should be so small and not receive corrections at the highest mass scale present in
the theory. This constitutes the most severe hierarchy problem in particle physics
and there are no hints as to how to solve it.
If=0, in the early universe the density of energy and matter is dominant
over the vacuum energy contribution, while the universe expands the average
matter density decreases and at low redshifts theterm becomes important. At
the end the universe starts inflating under the influence of theterm.
At present there are models based on the presence ofcalledCDM
models orCHDM if we allow the presence of a small amount of HDM. Such