Primordial Black Holes and Cosmological Phase Transitions Report ...

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$Kawasaki dynamic in continuum Math. Encounters XXXV ... - CCM$

PBHs and Cosmological Phase Transitions 20 1.5 The Lambda–Cold Dark Matter Model In the last few years there has been a wealth of observational evidence from CMB, LSS and high redshift supernovae Ia data that leads to the remarkable conclusions that: i) the spatial geometry of the Universe is flat (κ = 0), ii) the Universe is accelerating today, and iii) most of the matter is in the form of dark matter. The current understanding of cosmology is based on the so called Lambda–Cold Dark Matter Model (ΛCDM) in which the total energy density of the Universe has as main ingredients: 5% of baryonic matter, 25% of dark matter and 70% of dark energy (e.g. Boyanovsky et al., 2006). Baryonic matter Ordinary matter is mainly composed of protons and neutrons (which are baryons) and electrons (which are leptons). Since the baryons vastly outweigth the electrons, in the context of Cosmology, ordinary matter is called baryonic matter (e.g. Lyth, 1993). The luminous matter in the Universe accounts for only Ωb ≈ 0.042 (Spergel et al., 2007) which means that there exists a great amount of baryonic dark matter in the Universe. This discrepancy is refered as the missing matter problem (e.g. d’Inverno, 1993). Within a galaxy, baryons are expected to concentrate more in the central luminous part than in the dark halo. The reason is that baryons (electrons included) can emit radiation whereas non–baryonic dark matter interacts too weakly to do so (or it would not be dark). Baryons lose more energy, allowing them to settle more deeply into the galaxy centre. Baryons within galaxies could be in the form of non–emitting gas, failed stars or planets, (∼ 0.01 − 0.1M⊙), and dead stars (old white dwarfs, non–emitting neutron stars and black holes). In the intergalactic space, baryons can only be in the form of non–emitting gas because, as far as we know, bound objects form only within galaxies (e.g. Lyth, 1993) or within galaxy clusters. Non–Baryonic Dark Matter If Ωm ≈ 0.24 as measured by WMAP (Spergel et al., 2007) then, besides baryonic matter (luminous and dark), there might exist a huge amount of non– baryonic dark matter (e.g. Lyth, 1993). We can estimate the total amount of matter in a bound system, such as a galaxy or galaxy cluster, through its gravitational field, which can be deduced from the velocities of its components. One finds that each galaxy is surrounded by a dark halo accounting for most of its mass (e.g. Lyth, 1993). Soon after the need for dark matter came to be widely accepted in the early 1980s, it became clear that the hypothesis fails completely if the dark matter consists of massive neutrinos, because their thermal motion wipes out small scale structure. Given the failure of this Hot Dark Matter (HDM) model, attention turned to the other extreme, of matter which has, by definition, negligible random motion. In its standard form, the Cold Dark Matter (CDM) model assumes that the Universe has a flat spatial geometry, a critical matter density
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)
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Table 49 (continued). PBHs and Cosm
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Table 49 (continued). Radiation EW
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