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Cosmic Initial Conditions for a Habitable Universe

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Cosmic Initial Conditions for a Habitable Universe MNRAS 470, 3095–3102 (2017) doi:10.1093/mnras/stx1448 Cosmic initial conditions for a habitable universe Sohrab Rahvar‹ Physics Department, Sharif University, PO Box 11365-9161, Azadi Avenue, Tehran, Iran Accepted 2017 June 8. Received 2017 May 31; in original form 2016 August 5 ABSTRACT Downloaded from https://academic.oup.com/mnras/article/470/3/3095/3956582 by guest on 23 September 2021 Within the framework of an eternal inflationary scenario, a natural question regarding the production of eternal bubbles is the essential conditions required to have a universe capable of generating life. In either an open or a closed universe, we find an anthropic lower bound on the amount of e-folding in the order of 60 for the inflationary epoch, which results in the formation of large-scale structures in both linear and non-linear regimes. We extend the question of the initial condition of the universe to the sufficient condition in which we have enough initial dark matter and baryonic matter asymmetry in the early universe for the formation of galactic halos, stars, planets and consequently life. We show that the probability of a habitable universe is proportional to the asymmetry of dark and baryonic matter, while the cosmic budget of baryonic matter is limited by astrophysical constraints. Key words: inflation – large-scale structure of Universe. tion of large-scale structures. These small density fluctuations in 1 INTRODUCTION the dark matter fluid, of order ∼10−5, eventually grow and pro- The habitability of the Universe is one of the fundamental issues duce potential wells and, through gravitational condensation and of cosmology. In other words, what are the specifications required cooling, the baryonic matter of cosmic fluid forms galaxies, stars for a universe to be habitable? In terms of fundamental physics, we and planets. Recent observations of the CMB by the Wilkinson can think about possible different physical parameters for which Microwave Anisotropy Probe (WMAP)andPlanck satellites show our Universe is adapted. This possibility might be realized in mul- the compatibility of the observational data with the predictions tiverse models, where the physical parameters vary in an ensemble of inflationary models (Planck Collaboration et al. 2016;Peiris of parallel universes (Carr 2007). Here in this work, we adapt the et al. 2003). ‘weak anthropic’ principle, by means of which physical constants While inflationary cosmology is successful in its explanation of are given and we investigate the initial conditions of different uni- the flatness, homogeneity and power spectrum of large-scale struc- verses. We study the formation of a habitable universe based on tures, there are challenging questions for this theory, such as the the initial conditions in the early epoch of the universe, during the entropy problem. Since the entropy of all systems as well as the inflationary period. universe increases with time, the early universe must start with very In the standard inflationary model for an early universe, a scalar low entropy (Penrose 1989), which means that fine tuning for the field, the so-called inflaton field, drives a rapid phase of expan- initial conditions of the universe might be needed. A possible so- sion of the universe. This inflationary phase stretches any local lution to this problem is the chaotic inflationary model introduced features in the curvature of the early universe into spatially flat by Linde (1983). In this model, the initial condition of the universe space (Starobinsky 1980;Guth1981). Also during this inflationary from a large pre-inflationary domain has arbitrary uncorrelated val- phase, all primordial defects from the phase transition manifesting ues within Planck-size patches and a successful universe with low as topological defects are diluted (Liddle & Lyth 2000). The other entropy at a given patch produces a sufficiently large domain. The consequence of inflation is that all parts of the universe that were parameter associated with this expansion is defined by the e-folding thermalized within the horizon before the beginning of inflation number, which is the logarithm of the ratio of the scale factor at the stretch out and make the universe uniform at super-horizon scales. end to that at the beginning of inflation (i.e. N = ln af/ai). For a This uniformity has been observed at a level of 10−5 on the map large value of e-folding, the spatial part of the curvature turns out to of cosmic microwave background (CMB) radiation (de Bernardis be nearly flat. For each inflationary area, the quantum fluctuation of et al. 2000). the inflaton field can be larger than the classical decline of the field. The other advantage of inflationary cosmology is that quantum The result would be to produce new inflationary areas, or in other fluctuations of the inflaton field result in seeds for the forma- words bubbles, out of a parent domain (Linde 1986). The conse- quence of eternal inflation is the production of infinite inflationary areas, of which some can meet the condition for the formation E-mail: [email protected] of life. C 2017 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society 3096 S. Rahvar For an unsuccessful inflationary phase owing to an insufficient As a brief introduction to inflation dynamics, let us assume a number of e-foldings, the density of the universe after the end of scalar field that drives the dynamics of the early universe. For a μ inflation, depending on the initial conditions, could be either dense scalar field with Lagrangian L = 1/2∂μφ∂ φ − V (φ), we assume or dilute compared with a flat universe. As a result, after inflation the slow-rolling condition, where the kinetic energy is negligible ends, the universe would either collapse in a short cosmological compared with the potential term. Also, we ignore the spatial com- time-scale or expand and dilute, with no chance for the formation ponents of the Lagrangian, as they are diluted by fast expansion of of structures. After the end of inflation, all the energy in the infla- the universe. This condition can also be given by two parameters, = m2 V φ /V φ 2/ ton field turns into matter and radiation during reheating (Bassett, the so-called slow-rolling conditions pl( ( ) ( )) 2 1 Tsujikawa & Wands 2006). For a sufficient asymmetry between η = m2 |V φ /V φ | and pl ( ) ( ) 1, which implies the Friedmann– baryons and anti-baryons, the remaining baryonic matter after an- Robertson–Walker (FRW) equation; the continuity equation sim- nihilation can form baryonic structures within dark haloes. H 2 πV φ / m2 H φ˙ =−V φ plifies to 8 ( ) 3 p and 3 ( ). Here, for sim- In this work, we investigate the inflationary scenario and post- plicity, we take natural units. inflation epoch from the point of view of the anthropic principle. One of the main characteristics of inflationary models is the Downloaded from https://academic.oup.com/mnras/article/470/3/3095/3956582 by guest on 23 September 2021 This kind of investigation was started in the early days of developing number of e-foldings and its dependence on the initial conditions modern cosmology. Dicke (1961) noted that the age of the Universe of the scalar field at the beginning of the inflationary phase of cannot be a random value: biological factors constrain it to be not the universe. Within the framework of chaotic inflation, different too young and not too old. A young universe does not have enough domains of the universe at the Planck time have scalar fields with metals for the formation of life and in an old universe all the stars stochastic distributions and, for a sufficiently large scalar field that would have left the main sequence. The effect of the cosmological satisfies the slow-rolling condition, inflation can start. If we treat constant on the formation of structures within the framework of the φ as the classical scalar field, starting from an arbitrary position in anthropic principle has also been studied by Weinberg (1987). He phase space (i.e. (φ,φ˙ )), the well-known classical attractor tends concluded that having a larger value for the cosmological constant asymptotically the scalar field to hold the slow-rolling condition, prevents the collapse of structures and formation of galaxies and whereas for quadratic and quartic potentials there is a lower bound stars. A general study of the set of physical constants and parameters on the initial value of the scale field to produce successful inflation that support life can be found in Tegmark et al. (2006), as well as (Yi & Vishniac 1993). a detailed discussion of the anthropic principle in Barrow & Tipler Here, the φ˙ term, which is related to the kinetic energy, is also (1986). produced by quantum fluctuations. If quantum fluctuations of infla- In the first part of this work, we study the prior probability of the tons become larger than the potential term, then we can ignore the formation of structures from the initial conditions of the inflationary potential term in the density and pressure of the inflaton field and scenario. We then discuss the selection condition to have enough the equation of state would be p ρ. Then, from the continuity baryonic numbers in the universe for the formation of galaxies, stars, equation, the energy density or the kinetic energy term of the infla- planets and consequently life. In Section 2, we briefly introduce ton field decreases as 1/2φ˙ 2 ∝ 1/a6, much faster than the radiation. inflationary cosmology, with an emphasis on eternal inflation. Here The result is that the slow-rolling condition can hold for a shorter we investigate the initial condition for pre-inflationary patches to time-scale.
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