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Cosmic Perturbations Through the Cyclic Ages

Joel K. Erickson, Steven Gratton, Paul J. Steinhardt, Neil Turok

TL;DR

This work shows that in the cyclic universe, ekpyrotic contraction with $w \gg 1$ can render the observable patch homogeneous, isotropic, and flat without any inflationary phase. It demonstrates that galaxies and large-scale structure in a cycle originate from quantum fluctuations in the preceding cycle and that a five-dimensional bounce matching preserves the perturbation spectrum across cycles. The global structure cannot be captured by a single FRW description due to superhorizon perturbations, though each horizon-sized patch behaves FRW-like. Altogether, the paper argues for a non-inflationary resolution to the horizon and flatness problems and offers a coherent mechanism for perturbation generation and transfer through successive cycles.

Abstract

We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle are generated by the quantum fluctuations in the preceding cycle without interference from perturbations or structure generated in earlier cycles and without interfering with structure generated in later cycles; (2) the ekpyrotic phase, an epoch of gentle contraction with equation of state $w\gg 1$ preceding the hot big bang, makes the universe homogeneous, isotropic and flat within any given observer's horizon; and, (3) although the universe is uniform within each observer's horizon, the global structure of the cyclic universe is more complex, owing to the effects of superhorizon length perturbations, and cannot be described in a uniform Friedmann-Robertson-Walker picture. In particular, we show that the ekpyrotic phase is so effective in smoothing, flattening and isotropizing the universe within the horizon that this phase alone suffices to solve the horizon and flatness problems even without an extended period of dark energy domination (a kind of low energy inflation). Instead, the cyclic model rests on a genuinely novel, non-inflationary mechanism (ekpyrotic contraction) for resolving the classic cosmological conundrums.

Cosmic Perturbations Through the Cyclic Ages

TL;DR

This work shows that in the cyclic universe, ekpyrotic contraction with can render the observable patch homogeneous, isotropic, and flat without any inflationary phase. It demonstrates that galaxies and large-scale structure in a cycle originate from quantum fluctuations in the preceding cycle and that a five-dimensional bounce matching preserves the perturbation spectrum across cycles. The global structure cannot be captured by a single FRW description due to superhorizon perturbations, though each horizon-sized patch behaves FRW-like. Altogether, the paper argues for a non-inflationary resolution to the horizon and flatness problems and offers a coherent mechanism for perturbation generation and transfer through successive cycles.

Abstract

We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle are generated by the quantum fluctuations in the preceding cycle without interference from perturbations or structure generated in earlier cycles and without interfering with structure generated in later cycles; (2) the ekpyrotic phase, an epoch of gentle contraction with equation of state preceding the hot big bang, makes the universe homogeneous, isotropic and flat within any given observer's horizon; and, (3) although the universe is uniform within each observer's horizon, the global structure of the cyclic universe is more complex, owing to the effects of superhorizon length perturbations, and cannot be described in a uniform Friedmann-Robertson-Walker picture. In particular, we show that the ekpyrotic phase is so effective in smoothing, flattening and isotropizing the universe within the horizon that this phase alone suffices to solve the horizon and flatness problems even without an extended period of dark energy domination (a kind of low energy inflation). Instead, the cyclic model rests on a genuinely novel, non-inflationary mechanism (ekpyrotic contraction) for resolving the classic cosmological conundrums.

Paper Structure

This paper contains 9 sections, 26 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Overview of the Cyclic Model and its Perturbations
  3. Quantum Generation of Perturbations
  4. Matching Perturbations through the Bounce
  5. Classical Evolution of Perturbations
  6. Interference of perturbations from different cycles
  7. Global Structure of the Cyclic Universe
  8. Homogeneity, Isotropy and Flatness without Inflation
  9. Conclusions

Figures (5)

  • Figure 1: An example potential $V(\phi)$. This plot shows where $\phi$ is on its potential at each stage in a cycle. The equation of state parameter of the background solution is denoted by $w$.
  • Figure 2: A "wheel" diagram indicating the behavior of both the background solution (inner, solid, line) and perturbations (outer, dashed and dotted, lines) in the cyclic model. "Start" marks the point in the cycle at which our perturbation analysis in Sec. \ref{['sec:quantum']} begins.
  • Figure 3:
  • Figure 4: A timeline of the cyclic universe showing the behavior of key quantities over the course of a cycle. The labels "$k_\text{tran}$ exits" and "$k_\text{end}$ exits" show the times where these two modes start to follow ultralocal evolution (i.e. when spatial gradients become negligible).
  • Figure 5: A plot of the power spectrum $P_\Phi$ of the Newtonian potential $\Phi$ (in arbitrary units) at various points in a cosmic cycle. $k=1$ corresponds to the horizon at the start of the simulation in the radiation era, and $\ln k \approx -6.6$ corresponds to the horizon at matter-radiation equality. A horizontal line corresponds to scale invariance. The curve A indicates the power at the end of the matter epoch. Curve B indicates the power at turnaround ($H=0$). Curve C indicates the power some way into ekpyrotic contraction, and curve D indicates the power further into the ekpyrotic phase.