We re-examine the non-singular Matter Bounce scenario first developed in [20], which starts with a matter-dominated period of contraction and transitions into an Ekpyrotic phase of contraction. We consider both matter fields, the first of which plays the role of regular matter, and the second of which is responsible for the non-singular bounce. Since the dominant matter field is massive, the induced curvature fluctuations are initially not scale-invariant, whereas the fluctuations of the second scalar field (which are initially entropy fluctuations) are scale-invariant. We study the transfer of the initial entropy perturbations into curvature fluctuations in the matter-dominated phase of contraction and show that the latter become nearly scale invariant on large scales but are blue tilted on small scales. We study the evolution of both curvature and entropy fluctuations through the bounce, and show that both have a scale-invariant spectrum which is blue-tilted on small scales. However, we find that the entropy fluctuations have an amplitude that is much smaller than that of the curvature perturbations, due to gravitational amplification of curvature perturbations during the bounce phase.
We propose a nonlinear massive gravitational theory which includes F (R) modifications. This construction inherits the benefits of the de Rham-Gabadadze-Tolley model and is free of the Boulware-Deser ghost due to the existence of a Hamiltonian constraint accompanied by a nontrivial secondary one. The scalar perturbations in a cosmological background can be stabilized at the linear level for a wide class of the F (R) models. The linear scalar mode arisen from the F (R) sector can absorb the nonlinear longitudinal graviton, and hence, our scenario demonstrates the possibility of a gravitational Goldstone theorem. Finally, due to the combined contribution of the F (R) and graviton-mass sectors, the proposed theory allows for a large class of cosmological evolutions, such as the simultaneous and unified description of inflation and late-time acceleration.
We present new traversable wormhole and non-singular black hole solutions in pure, scale-free R 2 gravity. These exotic solutions require no null energy condition violating or "exotic" matter and are supported only by the vacuum of the theory. It is well known that f (R) theories of gravity may be recast as dual theories in the Einstein frame. The solutions we present are found when the conformal transformation required to move to the dual frame is singular. For quadratic R 2 gravity, the required conformal factor is identically zero for spacetimes with R = 0. Solutions in this case are argued to arise in the strong coupling limit of General Relativity.
The matter bounce scenario allows for a sizable parameter space where cosmological fluctuations originally exited the Hubble radius when the background energy density was small. In this scenario and its extended versions, the low energy degrees of freedom are likely responsible for the statistical properties of the cosmic microwave background power spectrum at large length scales. An interesting consequence is that these modes might be observable only at relatively late times. Therefore low redshift observations could provide evidence for, or even falsify, various bouncing models. We provide an example where a recently hinted potential deviation from Λ-cold-dark-matter cosmology results from a dark matter and dark energy interaction. The same interaction allows matter bounce models to generate a red tilt for the primordial curvature perturbations in corroboration with cosmic microwave background experiments.
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