String Gas Cosmology and Structure Formation

TL;DR

String Gas Cosmology offers a non-inflationary route to generating cosmological perturbations through thermodynamics in the Hagedorn phase. The paper develops the background evolution, derives how scalar and tensor metric fluctuations arise from fluctuations of the string gas energy-momentum tensor, and computes the resulting power spectra. It finds an almost scale-invariant scalar spectrum with a slight red tilt and a tensor spectrum that is nearly scale-invariant with a distinctive blue tilt, together with a possibly sizable tensor-to-scalar ratio. The work highlights observational signatures that could distinguish SGC from inflation and discusses current limitations, such as the role of the evolving dilaton and unresolved entropy/flatness issues, pointing to future refinements including dilaton dynamics.

Abstract

It has recently been shown that a Hagedorn phase of string gas cosmology may provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion. A distinctive signature of this structure formation scenario would be a slight blue tilt of the spectrum of gravitational waves. In this paper we give more details of the computations leading to these results.

Figures (3)

• Figure 1: Space-time diagram (sketch) showing the evolution of fixed comoving scales in string gas cosmology. 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 solid 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 (the dotted lines 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 Hubble 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 $t_f(k)$.
• Figure 2: Corresponding space-time diagram (sketch) for inflationary cosmology. The period of exponential expansion is for $t < t_R$. At the time of reheating $t = t_R$ the universe makes a transition to a radiation-dominated phase. As in Figure 1, the vertical axis is time and the horizontal axis is physical distance. The solid curve represents the Hubble radius. Fixed comoving scales (the dotted lines labeled by $k_1$ and $k_2$) which are currently probed in cosmological observations have wavelengths which start out smaller than the Hubble radius at the beginning of the inflationary phase. They exit the Hubble radius at times $t_i(k)$ and propagate with a wavelength larger than the Hubble radius until they reenter the Hubble radius at times $t_f(k)$.
• Figure 3: Power spectrum of gravitational waves in string gas cosmology in the case of an instantaneous transition between the Hagedorn phase and the radiation-dominated period. In this approximation, increasing the factor $1 - T/T_H$ is equivalent to creasing $R$. The range of values of $R$ where our analysis applies to the left of the zero of the curve at the value $(l_s/R)^2$. The increase of the power spectrum (the vertical axis) going towards the left shows that the spectrum has a blue tilt.