Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 21
(see equation 32) and a spectrum which is precisely scale invariant (e.g. Liddle
& Lyth, 1993).
As implied by its name, the CDM is assumed to be cold, which, for most
purposes, means non–relativistic. By definition, dark matter does not interact
significantly with more conventional forms of matter by any means other than
gravity, and, in particular, is beneficial for structure formation in that it is not
subject to pressure forces from interaction with radiation which prevent baryonic
density inhomogeneities on scales smaller than superclusters from collapsing
before radiation decouples from matter. Structure can, thus, start to form earlier
within dark matter, providing initial gravitational wells to kick–start structure
formation within baryonic matter after decoupling (e.g. Liddle & Lyth, 1993).
The current best candidate for CDM are the so–called weakly interacting
massive particles (WIMPs) that might have been produced in the very early
Universe (e.g. Bertone et al., 2005).
Dark energy
Independent measurements of Type Ia supernovae have revealed that the expansion
of the Universe is undergoing a non–linear acceleration rather than
following strictly Hubble’s law. To explain this acceleration, general relativity
requires that much of the Universe consist of an energy component with large
negative pressure. Its true nature remains unknown, although the present observations
indicate that this dark energy can be described by a cosmological
constant Λ (e.g. Boyanovsky et al., 2006).
The model assumes a nearly scale–invariant spectrum of primordial perturbations
and a Universe without spatial curvature (k =0⇒ Ωκ = 0). It also
assumes that it has no observable topology, so that the Universe is much larger
than the observable particle horizon. Those are predictions of cosmic inflation
(Section 1.3).
The ΛCDM model has six parameters: the Hubble constant H0, the baryon
density Ωb, the total matter density Ωm (which includes baryons plus dark
matter), the optical depth to reionization τ (which determines the redshift of
reionization), the amplitude of the primordial fluctuations As and the slope for
the scalar perturbation spectrum ns (which measures how fluctuations change
with scale; ns = 1 corresponds to a scale–invariant spectrum). The values of
these six free parameters as obtained from the WMAP data (Spergel et al.,
2007) are presented in Table 2. The Hubble constant h is given in normalized
units of 100 kms −1 Mpc −1 and the densities Ωm and Ωb are given as functions
of h. Thus, the present value of the Hubble parameter H0 is, according to the
most recent WMAP observations
and
H0 = 73.4 kms −1 Mpc −1 ≈ 2.38 × 10 −18 s −1
(51)
Ωm ≈ 0.24 (52)