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

TL;DR

In this 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 ofcosmological inflation.

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.

Figures (1)

• Figure 1: Space-time diagram (sketch) showing the evolution of fixed comoving scales. The vertical axis is time, the horizontal axis is physical distance. The Hagedorn phase ends at the time $t_R$ and is followed by the radiation-dominated phase of standard cosmology. The blue curve represents the Hubble radius $H^{-1}$ which is cosmological during the quasi-static Hagedorn phase, shrinks abruptly to a microphysical scale at $t_R$ and then increases linearly in time for $t > t_R$. Fixed comoving scales (labeled by $k_1$ and $k_2$) which are currently probed in cosmological observations have wavelengths which are smaller than the Hubble radius during the Hagedorn phase. They exit the radius at times $t_i(k)$ just prior to $t_R$, and propagate with a wavelength larger than the Hubble radius until they reenter the Hubble radius at times $t_f(k)$.