String Gas Cosmology

TL;DR

String Gas Cosmology proposes a non-singular early-universe scenario in which a gas of strings on a compact space, governed by T-duality and the Hagedorn temperature $T_H$, drives the dynamics and stabilizes moduli through winding and momentum modes. A long Hagedorn phase allows three spatial dimensions to expand via winding mode annihilation, while the resulting string-thermodynamic fluctuations seed nearly scale-invariant scalar perturbations and a tensor spectrum with a characteristic blue tilt, providing an observationally testable alternative to inflation. Realization requires stabilizing the dilaton (e.g., via gaugino condensation or other non-perturbative effects) alongside radion and shape moduli stabilization, yielding a potentially consistent cosmology without initial singularities. The framework makes distinctive predictions, notably a blue-tilted tensor spectrum and testable consistency relations among observable spectra and cosmic-string signatures, though it faces challenges such as Jeans instabilities and the need for a robust non-perturbative background.

Abstract

String gas cosmology is a string theory-based approach to early universe cosmology which is based on making use of robust features of string theory such as the existence of new states and new symmetries. A first goal of string gas cosmology is to understand how string theory can effect the earliest moments of cosmology before the effective field theory approach which underlies standard and inflationary cosmology becomes valid. String gas cosmology may also provide an alternative to the current standard paradigm of cosmology, the inflationary universe scenario. Here, the current status of string gas cosmology is reviewed.

Figures (6)

• Figure 1: Space-time diagram (sketch) of inflationary cosmology. Time increases along the vertical axis. The period of inflation begins at time $t_i$, ends at $t_R$, and is followed by the radiation-dominated phase of standard big bang cosmology. If the expansion of space is exponential, the Hubble radius $H^{-1}$ is constant in physical spatial coordinates (the horizontal axis), whereas it increases linearly in time after $t_R$. The physical length corresponding to a fixed co-moving length scale is labelled by its wave number $k$ and increases exponentially during inflation but increases less fast than the Hubble radius (namely as $t^{1/2}$), after inflation. Hence, the wavelength crosses the Hubble radius twice. It exits the Hubble radius during the inflationary phase at the time $t_i(k)$ and re-enters during the period of standard cosmology at time $t_f(k)$.
• Figure 2: Space-time diagram (sketch) of inflationary cosmology including the two zones of ignorance - sub-Planckian wavelengths and trans-Planckian densities. The symbols have the same meaning as in Figure 1. Note, specifically, that - as long as the period of inflation lasts a couple of e-foldings longer than the minimal value required for inflation to address the problems of standard big bang cosmology - all wavelengths of cosmological interest to us today start out at the beginning of the period of inflation with a wavelength which is in the zone of ignorance.
• Figure 3: The temperature (vertical axis) as a function of radius (horizontal axis) of a gas of closed strings in thermal equilibrium. Note the absence of a temperature singularity. The range of values of $R$ for which the temperature is close to the Hagedorn temperature $T_H$ depends on the total entropy of the universe. The upper of the two curves corresponds to a universe with larger entropy.
• Figure 4: The dynamics of string gas cosmology. The vertical axis represents the scale factor of the universe, the horizontal axis is time. Along the horizontal axis, the approximate equation of state is also indicated. During the Hagedorn phase the pressure is negligible due to the cancellation between the positive pressure of the momentum modes and the negative pressure of the winding modes, after time $t_R$ the equation of state is that of a radiation-dominated universe.
• Figure 5: The process by which string loops are produced via the intersection of winding strings. The top and bottom lines are identified and the space between these lines represents space with one toroidal dimension un-wrapped.