Producing a Scale-Invariant Spectrum of Perturbations in a Hagedorn Phase of String Cosmology

Abstract

We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.

String Gas Cosmology and Structure Formation

“…In this paper, we review the analyses of our previous results [14,15,16] and present more details. The outline of this paper is as follows.…”

“…Recently [14,15] it was discovered that, under certain assumptions which will be detailed below, string thermodynamic fluctuations during the Hagedorn phase lead to scalar metric fluctuations which are adiabatic and nearly scale-invariant at late times, thus providing a simple alternative to slow-roll inflation for establishing such perturbations. It is to be emphasized that this mechanism for the generation of the primordial perturbations is intrinsically stringy -particle thermodynamic fluctuations would lead to a spectrum with a large and phenomenologically unacceptable blue tilt [15].…”

S-duality in string gas cosmology

“…As a result, we see that it is possible to obtain a cosmological phase with decreasing Hubble radius which can be matched to the static strongly coupled Hagedorn phase, provided that the flat space is replaced by a sphere, the tachyon field dominates the cosmic evolution and the initial tachyon potential energy is fine tuned with the curvature of the three sphere. Of course, it should be checked that these assumptions do not invalidate the results of [26][27][28][29]. Especially, since the curvature of the sphere in-troduces a new length scale, it may alter the scale independence of the perturbation spectrum.…”

“…Another motivation to consider S-duality in SGC comes from the recently proposed stringy mechanism to generate scale free cosmological perturbations seeded by thermal fluctuations in a strongly coupled Hagedorn phase [26][27][28][29]. According to [26][27][28][29], spacetime should be static in this meta-stable phase with infinite Hubble radius and it should be followed by the so called Hagedorn phase which has decreasing Hubble radius.…”

“…According to [26][27][28][29], spacetime should be static in this meta-stable phase with infinite Hubble radius and it should be followed by the so called Hagedorn phase which has decreasing Hubble radius. During the Hagedorn phase cosmological perturbations exit the Hubble radius and freeze out.…”