Cosmological perturbations through a non-singular ghost-condensate/Galileon bounce

Abstract

We study the propagation of super-horizon cosmological perturbations in a non-singular bounce spacetime. The model we consider combines a ghost condensate with a Galileon term in order to induce a ghost-free bounce. Our calculation is performed in harmonic gauge, which ensures that the linearized equations of motion remain well-defined and nonsingular throughout. We find that, despite the fact that near the bounce the speed of sound becomes imaginary, super-horizon curvature perturbations remain essentially constant across the bounce. In fact, we show that there is a time close to the bounce where curvature perturbations of all wavelengths are required to be momentarily exactly constant. We relate our calculations to those performed in other gauges, and comment on the relation to previous results in the literature. a lorenzo.battarra@aei.mpg.de b

A critical review of classical bouncing cosmologies

“…If the spectrum is generated in a matter phase, non-Gaussianities result due to the growth of fluctuations after Hubble radius crossing in the contracting phase, see Sec. IV E. Observables in the super bounce model are in line with other ekpyrotic models according to [72].…”

“…IV, since curvature perturbations stay frozen on super Hubble scales during the bounce, as shown in [72]: here, the computation was per- formed in the harmonic gauge with a detailed discussion of the validity of linear perturbation theory, see Sec. IV A.…”

“…For more details on the use of the harmonic gauge see [72], which makes contact to other commonly used gauges and provides another application to the superbounce, see Sec. III C 4: the validity of linear perturbation theory was tested and it was confirmed that the equations of motion for certain variables, such as the curvature perturbation R in (84), contain singularities.…”

G-bounce inflation: towards nonsingular inflation cosmology with galileon field

“…We will see in the following that kinetic part of this form is useful in matching bounce with inflation, which was first proposed for ghost-free bounce by Cai et al [49], and later connected with Supergravity in [50,51]. Following the Lagrangian (2.1), one can get the equation of motion for φ as:…”

“…We also show the shape functions and potential explicitly by numerics in figure 1 and 2. For pioneer works of using this shape functions to model building, see [49][50][51] for ghost-free bounce and see [59] for dark energy models. Now let's go to a little bit more detail about the field evolution both before and after the bounce, which actually become very simple.…”