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Bouncing Cosmologies

M. Novello, S. E. Perez Bergliaffa

TL;DR

The paper surveys a broad landscape of nonsingular cosmologies, focusing on bouncing and cyclic models across GR and modified gravity, to address the initial singularity problem. It catalogs mechanisms that produce a cosmological bounce—from SEC violation, higher-curvature corrections ($f(R)$, LCH, saturation), scalar and vector field couplings (including WIST and nonminimal EM), to quantum gravity approaches (BdB, LQC) and braneworld effects—and highlights representative exact or semi-analytic solutions. It discusses observational consequences, especially in the behavior of perturbations during nonsingular phases, and frames how these models could imprint detectable signatures or alleviate standard cosmological problems (horizon, flatness, entropy). Overall, the work provides a structured map of classical, semiclassical, and quantum pathways to nonsingular, potentially cyclic universes with emphasis on their theoretical viability and phenomenology. The significance lies in offering a comprehensive guide to identify, compare, and test bouncing scenarios as viable alternatives or complements to inflation-driven explanations of the early universe.

Abstract

We review the general features of nonsingular universes ({\em i.e.} those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of the perturbations.

Bouncing Cosmologies

TL;DR

The paper surveys a broad landscape of nonsingular cosmologies, focusing on bouncing and cyclic models across GR and modified gravity, to address the initial singularity problem. It catalogs mechanisms that produce a cosmological bounce—from SEC violation, higher-curvature corrections (, LCH, saturation), scalar and vector field couplings (including WIST and nonminimal EM), to quantum gravity approaches (BdB, LQC) and braneworld effects—and highlights representative exact or semi-analytic solutions. It discusses observational consequences, especially in the behavior of perturbations during nonsingular phases, and frames how these models could imprint detectable signatures or alleviate standard cosmological problems (horizon, flatness, entropy). Overall, the work provides a structured map of classical, semiclassical, and quantum pathways to nonsingular, potentially cyclic universes with emphasis on their theoretical viability and phenomenology. The significance lies in offering a comprehensive guide to identify, compare, and test bouncing scenarios as viable alternatives or complements to inflation-driven explanations of the early universe.

Abstract

We review the general features of nonsingular universes ({\em i.e.} those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of the perturbations.

Paper Structure

This paper contains 75 sections, 595 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Notation, conventions, etc
  3. Singularities, bounces, and energy conditions
  4. Extrema of $a(t)$ and $\rho(t)$
  5. Appendix: Energy conditions
  6. Higher-order gravitational theories
  7. Quantized matter on a fixed background
  8. Lagrangians depending on the Ricci scalar
  9. Saturation
  10. The limiting curvature hypothesis (LCH)
  11. Appendix: $f(R)$ and scalar-tensor theories
  12. Theories with a scalar field
  13. Scalar field in the presence of a potential
  14. Dynamical origin of the geometry
  15. WIST (Weyl Integrable Space Time)
  16. ...and 60 more sections

Figures (17)

  • Figure 1: The qualitative plot shows (in conformal time) the scale factor for the bouncing model given by Eqn(\ref{['wistb']}, and the scale factor for radiation in the SCM, $a\propto \eta$.
  • Figure 2: Plot of the Hubble parameter in conformal time for $a_0=1$.
  • Figure 3: Plot of $\varphi$ (full line) and $\dot\varphi$ (dotted line) in conformal time for $a_0=1$.
  • Figure 4: Qualitative plot of $V(s)$.
  • Figure 5: Plot of $a$ and $\varphi$ for $k_0 = 1/7$ and $a_0 = 0.93$, values chosen by imposing that the solution in Eqn.(\ref{['sol']}) enters the radiation era for $t \approx 10^{-8}$ seg.
  • ...and 12 more figures