Evolution of cosmological perturbations in non-singular string cosmologies

TL;DR

This work develops a comprehensive framework for cosmological perturbations in non-singular string cosmologies engineered by higher-order curvature corrections to the low-energy string action. By formulating a general action with curvature corrections and deriving the background and gauge-ready perturbation equations for scalars, vectors, and tensors, it reveals conserved quantities on large scales and the quantum generation of fluctuations via a unified wave equation with pump-field dynamics. The authors apply the formalism to the pre-Big Bang scenario, showing that $\alpha'$-corrections can flatten the high-frequency spectra while low-frequency modes remain largely unaffected, though fully matching observations may require further corrections or alternate exit mechanisms. Overall, the paper provides a versatile perturbation toolkit applicable beyond standard GR, informing how string-theoretic corrections influence primordial spectra and the evolution of early-universe inhomogeneities.

Abstract

In a class of non-singular cosmologies derived from higher-order corrections to the low-energy bosonic string action, we derive evolution equations for the most general cosmological scalar, vector and tensor perturbations. In the large scale limit, the evolutions of both scalar and tensor perturbations are characterised by conserved quantities, the usual curvature perturbation in the uniform-field gauge and the tensor-type perturbed metric. The vector perturbation is not affected, being described by the conservation of the angular momentum of the fluid component in the absence of any additional dissipative process. For the scalar- and tensor-type perturbations, we show how, given a background evolution during kinetic driven inflation of the dilaton field, we can obtain the final power spectra generated from the vacuum quantum fluctuations of the metric and the dilaton field during the inflation.

Figures (2)

• Figure 1: Here we reproduce (from Cartier:2001gc) a non-singular evolution for the Hubble parameter $H=\dot{a}/a$ and for $\dot{\phi}/3$, as a function of the number of e-folds, $N=\ln a$. The low-energy, dilaton-driven phase takes place approximately for $-\infty < N \leq -3$. After a short transition, this initial period is followed by a string phase with nearly constant Hubble parameter and linearly growing dilaton, for $2 \leq N \leq 55$. After a successful exit triggered by loop corrections, the background evolution enters the FLRW radiation-dominated phase at $N \simeq 68$.
• Figure 2: Here we compare the frequency shifts for scalar and tensor-type perturbations, $s^{(s)}$ and $s^{(t)}$ respectively, in the regular background of Fig. \ref{['f:non-sing']}. The frequency shift for tensor-type perturbations is found to be always positive, whereas $\alpha'$ corrections are responsible for the sign change of the frequency shift of scalar-type perturbations. The latter may imply an exponential instability for the perturbation amplitude of the comoving mode whose physical wavelength is smaller than the size of the Hubble radius during the stringy high-curvature regime.