Non-perturbative Gravity, Hagedorn Bounce & CMB

TL;DR

This work addresses the big-bang singularity by embedding a ghost-free, non-perturbative gravity action with infinite-derivative corrections into a cosmological bounce, explicitly realized by $a(t)=\cosh\left(\frac{\lambda t}{\sqrt{2}}\right)$. It then couples this background to a string-theoretic Hagedorn phase, showing that a gas of strings near the onset of the phase yields thermodynamic fluctuations with $C_V\propto r^2$ that seed a scale-invariant curvature spectrum via the relativistic Poisson equation, up to a small red tilt if the transition is not instantaneous. The authors derive a general expression for the spectral tilt $\eta_s-1$ and compute its magnitude in the bouncing-Hagedorn scenario, finding a very small tilt for typical parameters but the possibility of observable tilt if the string scale is low (e.g., TeV). Overall, the paper provides an explicit background realization of the NBV mechanism, linking non-perturbative gravity, string thermodynamics, and CMB-like fluctuations in a single coherent framework.

Abstract

In hep-th/0508194 it was shown how non-perturbative corrections to gravity can resolve the big bang singularity, leading to a bouncing universe. Depending on the scale of the non-perturbative corrections, the temperature at the bounce may be close to or higher than the Hagedorn temperature. If matter is made up of strings, then massive string states will be excited near the bounce, and the bounce will occur inside (or at the onset of) the Hagedorn phase for string matter. As we discuss in this paper, in this case cosmological fluctuations can be generated via the string gas mechanism recently proposed in hep-th/0511140. In fact, the model discussed here demonstrates explicitly that it is possible to realize the assumptions made in hep-th/0511140 in the context of a concrete set of dynamical background equations. We also calculate the spectral tilt of thermodynamic stringy fluctuations generated in the Hagedorn regime in this bouncing universe scenario. Generally we find a scale-invariant spectrum with a red tilt which is very small but does not vanish.

Figures (1)

• Figure 1: Space-time diagram (sketch) showing the evolution of a fixed comoving scale in our bouncing cosmology under the assumption that the bounce phase lies entirely within the Hagedorn phase. The vertical axis is time, the horizontal axis is comoving distance. The bounce time is chosen to be $t = 0$. The Hagedorn phase corresponds to the time interval $-t_H < t < t_H$, the bounce phase is the interval $-t_B < t < t_B$. Outside of the bounce phase, the Hubble radius evolves as in a radiation phase of standard cosmology The black solid curve represents the Hubble radius $H^{-1}$. The red vertical line labelled by $k$ depicts a fixed comoving scale. This scale is smaller than the Hubble radius in the central region of the bounce, exits the Hubble radius at the time $t_i(k)$, and re-enters at a late time $t_f(k)$.