Assisted Contraction

TL;DR

The paper investigates scale-invariant perturbations in string-inspired contracting cosmologies by analyzing a two-field model with exponential potentials. It derives exact power-law background solutions and, via a field-space rotation to adiabatic and isocurvature directions, obtains analytic perturbation equations for ζ and δs. Curvature perturbations are scale-invariant only for dust-like contraction (p=2/3), while isocurvature perturbations can acquire a scale-invariant spectrum for certain parameter regimes (notably small p) due to a tachyonic effective mass, with detailed cases A–C explored. The results support a viable isocurvature route to scale invariance in contracting universes and suggest possible transfer to adiabatic modes during a bounce or stabilization, linking to assisted-inflation ideas in a new context.

Abstract

We consider the dynamics of a contracting universe ruled by two minimally coupled scalar fields with general exponential potentials. This model describes string-inspired scenarios in the Einstein frame. Both background and perturbations can be solved analytically in this model. Curvature perturbations are generated with a scale invariant spectrum only for a dust-like collapse, as happens for a single field model with an exponential potential. We find the conditions for which a scale invariant spectrum for isocurvature perturbation is generated.

Figures (3)

• Figure 1: The potential $\bar{V} (s)$ (in units of $M_{\rm pl}^4$) as a function of $s/M_{\rm pl}$ for $p=0.2$, $d=4$ (solid line) and $d=5$ (dotted line), and for $p=0.1$, $d=4$ (dashed line). For all the curves $x=0.1$.
• Figure 2: The potential $\bar{V} (s)$ (in units of $M_{\rm pl}^4$) as a function of $s/M_{\rm pl}$ for $p=1/2$ case, with $d=1$ (solid line) and $d=2$ (dotted line). For both curves $x=2$.
• Figure 3: The spectral index for isocurvature perturbations in the case $p=1/2$ as a function of $d$ and $x$.