Abstract
In this Letter, we describe how a spectrum of entropic perturbations generated during a period of slow contraction can source a nearly scale-invariant spectrum of curvature perturbations on length scales larger than the Hubble radius during the transition from slow contraction to a classical non-singular bounce (the `graceful exit' phase). The sourcing occurs naturally through higher-order scalar field kinetic terms common to classical (non-singular) bounce mechanisms. We present a concrete example in which, by the end of the graceful exit phase, the initial entropic fluctuations have become negligible and the curvature fluctuations have a nearly scale-invariant spectrum with an amplitude consistent with observations.
Highlights
Observational evidence [1,2,3] combined with theoretical reasoning [4,5] strongly indicate that the gravitationally bound structures that comprise our universe originate from quantum fluctuations of scalar fields generated on sub-Hubble wavelengths that evolve to induce classical curvature perturbations with a nearly scale-invariant and Gaussian spectrum on superHubble wavelengths
Two candidates for the smoothing phase are a period of accelerated expansion (a_; ä > 0) and a period of slow contraction (a_; ä < 0), where the spacetime geometry during the smoothing phase is well-described by the Friedmann-Robertson-Walker (FRW) metric with scale factor aðtÞ and the dot denotes differentiation with respect to the physical FRW time coordinate t
If our universe has undergone a phase of slow contraction that connects to the current expanding phase through a cosmological bounce, adiabatic and gravitational wave fluctuations from the smoothing phase decay and cannot contribute to the observed fluctuation spectra of the cosmic microwave background
Summary
Observational evidence [1,2,3] combined with theoretical reasoning [4,5] strongly indicate that the gravitationally bound structures (galaxies, galaxy clusters, etc.) that comprise our universe originate from quantum fluctuations of scalar fields generated on sub-Hubble wavelengths that evolve to induce classical curvature perturbations with a nearly scale-invariant and Gaussian spectrum on superHubble wavelengths. Adiabatic modes (as well as gravitational waves [13]) experience a growing antifriction due to the rapidly decreasing Hubble radius which leads to their decay This eliminates the quantum runaway problem, an important and distinctive advantage of the slow contraction scenario. We do not know of any other smoothing mechanism that could do the same It is well-known that, during smoothing slow contraction, a nonlinear sigma type kinetic interaction between two scalar fields naturally leads to a nearly scale-invariant and Gaussian spectrum of super-Hubble relative field fluctuations—purely entropic modes—which are quantum generated long before the modes leave the Hubble radius [14,15,16,17]. We present an example in which the only significant fluctuations at the beginning of the graceful exit phase are entropic but, by the end of the phase, the entropic fluctuations have become negligible and the curvature fluctuations have a nearly scale-invariant spectrum with an amplitude consistent with observations
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