The Cyclic Model Simplified

TL;DR

The paper reframes cosmology around the Cyclic Model, proposing a slow contraction phase with equation of state $w>1$ driven by inter-brane dynamics that precedes a brane collision (the bounce) and a new expansion. It demonstrates that $w>1$ contraction suppresses anisotropy, curvature, and inhomogeneities, yielding ultralocal evolution and a nearly scale-invariant spectrum of density perturbations that is dual to the inflationary case via $\epsilon \to 1/\epsilon$; however, tensor perturbations distinguish the models, predicting a blue spectrum in the Cyclic Scenario. The authors argue that brane collisions fix a precise bounce hypersurface, enabling a well-defined transfer of long-wavelength perturbations to the expanding phase, and they discuss non-linear dynamics near the bounce, including possible tiny black holes whose evaporation could generate entropy, baryogenesis, and dark matter. Finally, they outline observational tests—particularly measurements of tensor modes and non-Gaussianity—that could distinguish the Cyclic Model from inflation and open empirical access to pre-bang physics and extra-dimensional dynamics.

Abstract

The Cyclic Model attempts to resolve the homogeneity, isotropy, and flatness problems and generate a nearly scale-invariant spectrum of fluctuations during a period of slow contraction that precedes a bounce to an expanding phase. Here we describe at a conceptual level the recent developments that have greatly simplified our understanding of the contraction phase and the Cyclic Model overall. The answers to many past questions and criticisms are now understood. In particular, we show that the contraction phase has equation of state w>1 and that contraction with w>1 has a surprisingly similar properties to inflation with w < -1/3. At one stroke, this shows how the model is different from inflation and why it may work just as well as inflation in resolving cosmological problems.

Figures (2)

• Figure 1: Scalar potentials suitable for a cyclic universe model. Running forward in cosmic time, Region (a) governs the decay of the vacuum energy, leading to the end of the slow acceleration epoch. Region (b) is the region where scale invariant perturbations are generated. In Region (c), as one approaches the big crunch ($\varphi \rightarrow -\infty$), the kinetic energy dominates.
• Figure 2: The cyclic model has an average positive energy density per cycle, so its conformal diagram is similar to an expanding de Sitter space with constant density. The bounces occur along flat slices (curves) that, in this diagram, pile up near the diagonal and upper boundaries. For true de Sitter space, entropy bounds limit the total entropy in the entire spacetime. For the cyclic model, the bounds only limit the entropy between caustics (the bounces). Particles or light-signals emitted in an earlier cycle (or before cycling commences) are likely to be scattered or annihilated as they travel through many intervening cycles (dashed line) to reach a present-day observer. The observer is effectively insulated from what preceded the cycling phase, and there are no measurements to determine how many cycles have taken place.