Pre-Big-Bang Requires the Universe to be Exponentially Large From the Very Beginning

TL;DR

The paper critically examines the initial-condition requirements of the pre-big-bang inflation scenario within string theory. It shows that to solve the horizon and flatness problems, the PBB phase must commence from an exceedingly large and highly homogeneous domain, quantified by stringent bounds on the initial size, mass, entropy, and two ultra-large dimensionless parameters. The analysis differentiates closed and open geometries, demonstrating that both face severe fine-tuning, and it argues that PBB cannot self-reproduce to generate the observed universe. Consequently, the authors conclude that the current PBB framework cannot replace standard inflation, even if a graceful exit mechanism is found, due to its restrictive starting conditions and lack of eternal inflation.

Abstract

We show that in a generic case of the pre-big-bang scenario, inflation will solve cosmological problems only if the universe at the onset of inflation is extremely large and homogeneous from the very beginning. The size of a homogeneous part of the universe at the beginning of the stage of pre-big-bang (PBB) inflation must be greater than $10^{19}$ $l_s$, where $l_s$ is the stringy length. The total mass of an inflationary domain must be greater than $10^{72} M_{s}$, where $M_{s} \sim l_s^{-1}$. If the universe is initially radiation dominated, then its total entropy at that time must be greater than $10^{68}$. If the universe is closed, then at the moment of its formation it must be uniform over $10^{24}$ causally disconnected domains. The natural duration of the PBB stage in this scenario is $M_p^{-1}$. We argue that the initial state of the open PBB universe could not be homogeneous because of quantum fluctuations. Independently of the issue of homogeneity, one must introduce two large dimensionless parameters, $g_0^{-2} > 10^{53}$, and $B > 10^{91}$, in order to solve the flatness problem in the PBB cosmology. A regime of eternal inflation does not occur in the PBB scenario. This should be compared with the simplest versions of the chaotic inflation scenario, where the regime of eternal inflation may begin in a universe of size $O(M_{p}^{-1})$ with vanishing initial radiation entropy, mass $O(M_p)$, and geometric entropy O(1). We conclude that the current version of the PBB scenario cannot replace usual inflation even if one solves the graceful exit problem in this scenario.