Primordial Black Holes and Cosmological Phase Transitions Report ...

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PBHs and Cosmological Phase Transitions 32 Figure 8: The theoretical CMB anisotropy power spectrum, using a standard ΛCDM model. The horizontal axis is logarithmic. Four regions, each covering roughly a decade in l, are labeled as: the ISW Rise; Sachs–Wolfe Plateau; Acoustic Peaks (numbers indicate the first, the second and, the third acoustic peak); and Damping Tail. Also shown is the shape of the tensor (gravity wave) contribution, with an arbitrary normalization (adapted from Yao et al., 2006). the initial conditions. The combination of gravitational redshift and intrinsic temperature fluctuations leads to δT T 1 δφ 3 c2 (94) where δφ is the perturbation to the gravitational potential. This is usually referred to as the Sachs–Wolfe effect. Assuming, in addition, a nearly scale– invariant spectrum of density perturbations, then l(l + 1)Cl is almost constant at large scales (l
PBHs and Cosmological Phase Transitions 33 in the temperature–polarization angular power spectrum at l ∼ 150 (Spergel et al., 2007). The recombination process is not instantaneous, giving a thickness to the last scattering surface. This leads to a damping of the anisotropies at the highest multipoles (l >1000), corresponding to scales smaller than that subtended by this thickness. This effect leads to a cut off on the anisotropies for l 2000. Also, gravitational lensing, caused by structures at low redshift (z ≪ 1000), would have the effect of partially flatten the peaks, generating a power-law tail. The WMAP data can reach the multipole l 900, up to the third acoustic peak (see Figure 8). In order to extend to higher multipoles (including the Damping Tail region), the WMAP team included in their analysis the data of other two CMB ground–based experiments: the Arcminute Cosmology Bolometer Array Receiver (ACBAR) and the Cosmic Background Imager (CBI) (e.g. Covi, 2003). Information on the density contrast can also be obtained from the distribution of galaxies in our Universe. The main assumption, in this case, is that the visible matter follows the distribution of the invisible Dark Matter. Recent surveys include the 2 degree Field Galaxy Redshift Survey (2dFGRS) which released data on 221 414 galaxies with measured redshift (e.g. Colless et al., 2003; Cole et al., 2005). An even larger survey is the Sloan Digital Sky Survey (SDSS). Its 6 th release of data (Adelman–McCarthy et al., 2008) already contains a total of 790 860 galaxies. From the distribution of the galaxies in the sky one can obtain the two point correlation function and the density contrast power spectrum (e.g. Covi, 2003). Other ways to measure the density contrast rely on using photons of distant objects as a probe of the intervening matter or gas densities. Lyman α forest data measure the absorption lines in the spectra of distant quasars caused by intergalactic hydrogen and estimate the cosmic gas distribution out to large distances (e.g. Covi, 2003). On Figure 9 we show, as an example, the Lyman α forest of quasar RD J030117 + 002025. 1.8 The Standard Model of Particle Physics The combination of the QCD theory and the EW is known as the Standard Model of Particle Physics (SMPP). The SMPP contains a finite number of parameters, which are unrelated, at least within the context of the theory itself. The SMPP is based on only two basic components: the fundamental quantum particles and the concept of interactions between them. A more complete theory of fundamental physics should explain the relationships among these parameters. The ultimate goal would be to determine the values of the parameters from pure mathematics, once the correct theory is discovered (e.g. Scott, 2006). The current SMPP, experimentally tested with remarkable precision, describes the theory of strong, weak and electromagnetic interactions as a gauge theory 11 . The particle content is (see Figure 10): three families of quarks, three 11 In Physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. Many powerful theories in Physics (e.g. EW theory, Electrodynamics, QCD) are described by Lagrangians which are
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