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 14 Table 1: The Universe timeline according to the inflationary Big Bang model (data was taken mainly from Unsöld & Bascheck (2002) and Jones & Lambourne (2004). Era t(s) T (K) T (GeV) Comments Planck – – – Quantum Gravity GUT 10 −43 10 32 10 19 Gravity separates Quark 10 −35 10 27 10 14 Strong–electroweak phase transition Inflation begins ∼ 10 −33 10 27 10 14 Inflation ends 3 × 10 −11 172.5 t quark threshold 2.3 − 3.2 × 10 −10 10 15 100 EW phase transition 10 −8 4.2 b quark threshold 10 −7 1.78 Lepton τ threshold 1.25 c quark threshold 1.6 − 1.2 Hyperons threshold 1.2 × 10 −5 0.50 Kaons threshold Hadron 0.63 − 1.1 × 10 −4 10 13 0.17 Formation of neutrons and protons 1.6 × 10 −4 0.14 Pions threshold 2.8 × 10 −4 0.106 Muons threshold Lepton 3.5 × 10 −4 10 12 s quark threshold and last pions decay 1 10 10 Decoupling of νe 2 Neutron production stops Photon 3 7.3 × 10 9 5 × 10 −4 Electron threshold 200 10 9 Nucleosynthesis of 2 H stable 10 3 Nucleosynthesis stops Matter 2.5 × 10 12 Radiation–Matter equality 9.0 × 10 12 4000 Recombination 1.2 × 10 13 3000 Photon decoupling 1.1 × 10 16 30 Reionization Λ 2.8 × 10 17 ≈ 4 Matter–Dark energy equality 4.3 × 10 17 2.725 Present
PBHs and Cosmological Phase Transitions 15 Inflation is, perhaps, the simplest known mechanism to eliminate monopoles from the visible Universe, even though they are still in the spectrum of possible particles. The monopoles are eliminated simply by arranging the parameters so that inflation takes place after (or during) monopole production, so the monopole density is diluted to a completely negligible level (e.g. Guth, 2000). The inflationary era is followed by the radiation–dominated and matter– dominated stages where the acceleration of the scale factor becomes negative. With a negative acceleration of the scale factor, the Hubble radius grows faster than the scale factor, and wavelengths that were outside, can now re–enter the Hubble radius. This is the main concept behind the inflationary paradigm for the generation of temperature fluctuations as well as for providing the seeds for Large Scale Structure (LSS) formation (e.g. Boyanovsky et al., 2006). The basic ingredient for structure formation is the presence of initial density fluctuations, that can, in a later time, act as seeds for the gravitational collapse. Once a small overdensity appears, gravity causes it to grow and finally collapse into a bounded system. As a result we have an inhomogeneous Universe on small scales (e.g. Covi, 2003). The density fluctuations cannot grow while the pressure of the plasma counteracts the gravitational force and, therefore, during the radiation era the system is still in the linear regime and only oscillations in the plasma (the so called acoustic peaks) take place. Later, when matter dominates, the pressure drops to zero and the fluctuations can grow: structures start to form and, consequently, the complicated non–linear regime begins (e.g. Covi, 2003). Inflation gives a possible solution to the crucial problem of where the primordial fluctuations leading to the observed LSS come from. In fact, they have their origin in the ubiquitous vacuum fluctuations. The seed of the LSS has been observed in the form of tiny fluctuations imprinted on the CMB at the time of decoupling (e.g. Bringmann et al., 2002). There are various inflationary scenarios (e.g. slow roll inflation, old inflation, new inflation, chaotic inflation, hybrid inflation, viscous inflation, tepid inflation, natural inflation, supernatural inflation, extranatural inflation, eternal inflation, extended inflation) differing essentially only in the choice of the potential V (φ) where φ represents the inflaton, i.e., the scalar field responsible for inflation (e.g. Boyanovsky et al., 2006). Each inflationary model makes precise predictions about the spectrum of its primordial fluctuations and this is how these models can be constrained by observations (e.g. Bringmann et al., 2002). These different kinds of models can be roughly divided into three types (e.g. Tsujikawa, 2003): Type I: large field model, in which the initial value of the inflaton is large and rolls down to the potential minimum at smaller φ. Chaotic inflation is one of the representative models of this class (see Figure 3); Type II: small field model, in which the inflaton field is small initially and slowly evolves toward the potential minimum at larger φ. New inflation and natural inflation are the examples of this type (see Figure 4); Type III: hybrid (double) inflation model, in which inflation typically ends by the phase transition triggered by the presence of a second scalar field or by the second phase of inflation after the phase transition (see Figure 5).
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Table 49 (continued). PBHs and Cosm
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Table 49 (continued). Radiation EW
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