Designing Cyclic Universe Models

TL;DR

It is shown that cyclic models require a comparable degree of tuning to that needed for inflationary models, and the constraints are reduced to a set of simple design rules including "fast-roll" parameters analogous to the "slow- roll" parameters in inflation.

Abstract

Recent advances in understanding the propagation of perturbations through the transition from big crunch to big bang (esp. Tolley et al. hep-th/0306109) make it possible for the first time to consider the full set of phenomenological constraints on the scalar field potential in cyclic models of the universe. We show that cyclic models require a comparable degree of tuning to that needed for inflationary models. The constraints are reduced to a set of simple design rules including "fast-roll" parameters analogous to the "slow-roll" parameters in inflation.

Figures (2)

• Figure 1: Examples of cyclic potentials.
• Figure 2: The shaded region shows the range $V_{end}^{1/4}$, the reheat temperature $T_r$, and the relative speed of the colliding branes $v_{coll}$ over which the cyclic model satisfies all known cosmological constraints, with fixed $\epsilon=10^{-2}$ and $L=3 \times 10^4$ (in units where $8\pi G=1$). Note that the reheat temperature is well below the grand unified monopole mass in all cases.