The symmetron is a scalar field associated with the dark sector whose coupling to matter depends on the ambient matter density. The symmetron is decoupled and screened in regions of high density, thereby satisfying local constraints from tests of gravity, but couples with gravitational strength in regions of low density, such as the cosmos. In this paper we derive the cosmological expansion history in the presence of a symmetron field, tracking the evolution through the inflationary, radiation-and matter-dominated epochs, using a combination of analytical approximations and numerical integration. For a broad range of initial conditions at the onset of inflation, the scalar field reaches its symmetry-breaking vacuum by the present epoch, as assumed in the local analysis of spherically symmetric solutions and tests of gravity. For the simplest form of the potential, the energy scale is too small for the symmetron to act as dark energy, hence we must add a cosmological constant to drive late-time cosmic acceleration. We briefly discuss a class of generalized, nonrenormalizable potentials that can have a greater impact on the late-time cosmology, though cosmic acceleration requires a delicate tuning of parameters in this case.

Ekpyrotic bouncing cosmologies have been proposed as alternatives to inflation. In these scenarios, the universe is smoothed and flattened during a period of slow contraction preceding the bounce while quantum fluctuations generate nearly scale-invariant super-horizon perturbations that seed structure in the post-bounce universe. An analysis by Tolley and Wesley (2007) showed that, for a wide range of ekpyrotic models, generating a scale-invariant spectrum of adiabatic or entropic fluctuations is only possible if the cosmological background is unstable, in which case the scenario is highly sensitive to initial conditions. In this paper, we analyze an important counterexample: a simple action that generates a Gaussian, scale-invariant spectrum of entropic perturbations during ekpyrotic contraction without requiring fine-tuned initial conditions. Based on this example, we discuss some generalizations.

A bouncing universe with a long period of contraction during which the average density is pressureless (the same equation of state as matter) as cosmologically observable scales exit the Hubble horizon has been proposed as an explanation for producing a nearly scale-invariant spectrum of adiabatic scalar perturbations. A well-known problem with this scenario is that, unless suppressed, the energy density associated with anisotropy grows faster than that of the pressureless matter, so the matter-like phase is unstable. Previous models introduce an ekpyrotic phase after the matter-like phase to prevent the anisotropy from generating chaotic mixmaster behavior. In this work, though, we point out that, unless the anisotropy is suppressed first, the matter-like phase will never start and that suppressing the anisotropy requires extraordinary, exponential fine-tuning.

We propose a mechanism to generate a nearly scale-invariant spectrum of adiabatic scalar perturbations about a stable, ekpyrotic background. The key ingredient is a coupling between a single ekpyrotic field and a perfect fluid of ultra-relativistic matter. This coupling introduces a friction term into the equation of motion for the field, opposing the Hubble anti-friction, which can be chosen such that an exactly scale-invariant (or nearly scale-invariant) spectrum of adiabatic density perturbations is continuously produced throughout the ekpyrotic phase. This mechanism eliminates the need for a second (entropic) scalar field and hence any need for introducing a second phase for converting entropic into curvature fluctuations. It also reduces the constraints on the equation of state during the ekpyrotic phase and, thereby, the need for parametric fine-tuning. arXiv:1603.06608v2 [gr-qc]

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