Primordial Black Holes and Cosmological Phase Transitions Report ...

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PBHs and Cosmological Phase Transitions xvi Physical Constants and Parameters speed of light in vacuum c 299792458 ms −1 Planck constant h 6.62606896(33) × 10 −34 Js gravitational constant G 6.67428(67) × 10 −11 m 3 kg −1 s −2 Boltzmann constant k 1.3806504(24) × 10 −23 JK −1 Fermi coupling constant GF 1.16637(1) × 10 −5 GeV −2 electron charge e 1.602176487(40) × 10 −19 C astronomical unit AU 149597870660(20) m parsec pc 3.0856775807(4) × 10 16 m ≈ 3.262 ly Planck mass mP 2.17645(16) × 10 −8 kg Planck length lP 1.61624(12) × 10 −35 m Planck time tP 5.39121(40) × 10 −44 s Solar mass M⊙ 1.98844(30) × 10 30 kg

PBHs and Cosmological Phase Transitions xvii Preface Black Holes are objects predicted by the laws of Physics. So far, black holes (or black hole candidates) have been detected only by indirect means. On this PhD thesis we plan to investigate the possibility of direct detection of a black hole. We have started with primordial black holes (i.e., black holes formed in the early universe) because, as far as we know, those are the only ones that could have formed with substellar masses which makes them potential candidates for the nearest detectable black hole. In this report we present the PhD work done during the second year (full time) mainly devoted to the determination of the fraction of the universe going into PBHs (β) during cosmological phase transitions. Sections 1 to 6 are devoted to a literature review although they have also some original work. In Section 1 we review the primordial Universe, in the context of the present work (e.g. number of degrees of freedom, scale factor, particle physics, inflation). Section 2 is dedicated to the QCD phase transition with particular attention to the different models often used to describe it: Bag Model, Lattice Fit and Crossover. In Section 3 we discuss the EW phase transition and in Section 4 the cosmological electron–positron annihilation epoch. In Section 5 we have considered the behaviour of primordial density fluctuations in the context of the mentioned cosmological phase transitions. In Section 6 we study the conditions for PBH formation and how this changes in the presence of a phase transition (δc decreases). In Sections 7 to 11 we present our original results. In Section 7 we determine the variation of δc for the QCD phase transition in the case of a Bag Model, Lattice Fit or Crossover. In Section 8 we do the same for the EW phase transition in the case of a Crossover (SMPP) and in the case of a Bag Model (MSSM) while in Section 9 we do it for the electron–positron annihilation epoch. In Section 10 we discuss the adopted power spectrum for the density fluctuations. In general, the requirement for abundant PBH formation demands fine–tunning. This is achieved, in our case, with two parameters giving the location and the amplitude of the peak on the spectral index. Section 11 is devoted to the calculus of the fraction of the Universe going into PBHs during the considered cosmological phase transitions. We have explored the cases for which one gets the highest values for β (up to ∼ 10 −4 ). In Section 12 we present our future work plan. In the near future we want to determine the PBH distribution function in the universe and consequently determine the mean distance to the nearest one. In the not so near future we want to improve our results addressing other subjects such as the PBH merging and PBH relics. With the Large Hadron Collider (LHC) already in operation (since 10 September 2008), which might produce BHs, our work is very exciting indeed! José Laurindo de Góis Nóbrega Sobrinho Universidade da Madeira October 2008

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