Cosmological perturbations through a simple bounce

Abstract

We present a detailed study of a simple scalar field model that yields non-singular cosmological solutions. We study both the qualitative dynamics of the homogeneous and isotropic background and the evolution of inhomogeneous linear perturbations. We calculate the spectrum of perturbations generated on super-Hubble scales during the collapse phase from initial vacuum fluctuations on small scales and then evolve these numerically through the bounce. We show there is a gauge in which perturbations remain well-defined and small throughout the bounce, even though perturbations in other commonly used gauges become large or ill-defined. We show that the comoving curvature perturbation calculated during the collapse phase provides a good estimate of the resulting large scale adiabatic perturbation in the expanding phase while the Bardeen metric potential is dominated by what becomes a decaying mode after the bounce. We show that a power-law collapse phase with scale factor proportional to $(-t)^{2/3}$ can yield a scale-invariant spectrum of adiabatic scalar perturbations in the expanding phase, but the amplitude of tensor perturbations places important constraints on the allowed initial conditions.Comment: 25 pages, 15 figures, latex with revtex. v2: missing factor of 2 included in tensor-scalar ratio, other minor changes and references added. v3: version to appear in PR

A critical review of classical bouncing cosmologies

“…The current lore in the literature is that linear perturbation theory fails in some gauges, such as the longitudinal [126,395] and comoving ones [398], while it remains valid in others, for example, in the uniform χ field gauge [285]. As shown in [50,371], the curvature perturbation and anisotropy grow rapidly during contraction, casting doubt on the viability of perturbation theory, see Sec.…”

“…The same idea was applied to the special situation in which, instead of radiation, the positive energy fluid is a scalar field whose dynamics is driven by an exponential potential [285], providing a model for the matter bounce. Contrary to many other bouncing models, the amplitude of tensor modes can be large, of order r ∼ O(30) [284,285], with a scale-invariant spectrum, in excess of current measurements, see Sec.…”

“…Contrary to many other bouncing models, the amplitude of tensor modes can be large, of order r ∼ O(30) [284,285], with a scale-invariant spectrum, in excess of current measurements, see Sec. IV C.…”

Bouncing Models With a Cosmological Constant

“…11, 13-15 can still be considered to be valid at the bounce. This should also be valid for other bouncing models, [7][8][9][10][11] as long as any bounce should take place at very short length scales, where the cosmological constant has no role.…”

“…If the contracting phase of a regular bouncing model is dominated by a perfect fluid, it has been shown by many authors, in different frameworks, [7][8][9][10][11][12] that this fluid must be dust, in order to reproduce a scale invariant spectrum of scalar and tensor cosmological perturbations.…”