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In this paper, we study a class of higher derivative, non-local gravity which admits homogeneous and isotropic non-singular, bouncing universes in the absence of matter. At the linearized level, the theory propagates only a scalar degree of freedom, and no vector or tensor modes. The scalar can be made free from perturbative ghost instabilities, and has oscillatory and bounded evolution across the bounce.
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We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmological perturbations during the contracting, bouncing and inflationary phases. We derive an expression for the Mukhanov-Sasaki perturbation variable at the onset of the inflationary phase that follows the bounce. Rather than being in the Bunch-Davies vacuum, it is found to be in an excited state that depends on the time scale of the bounce. We then show that this induces oscillations superimposed on the nearly scale-invariant primordial spectra for scalar and tensor perturbations. We discuss the effects of these oscillations in the cosmic microwave background and in the matter power spectrum. We propose a new way to indirectly measure the spatial curvature energy density parameter in the context of this model.
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We study Kaluza-Klein cosmology in cuscuton gravity and find an exact solution describing an accelerating 4-dimensional universe with a stable extra dimension. A cuscuton which is a non-dynamical scalar field is responsible for the accelerating expansion and a vector field makes the extra dimensional space stable. Remarkably, the accelerating universe in our model is not exactly de Sitter.
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