Bouncing Galileon Cosmologies

TL;DR

The work investigates nonsingular bouncing solutions within the conformal Galileon framework, revealing a sequence of radiation-dominated contraction, quintom crossing, a bounce, and a late-time Galilean Genesis. It demonstrates that adiabatic perturbations are blue-tilted and that a kinetically coupled curvaton can yield a scale-invariant curvature spectrum, with two viable couplings (one stable, one requiring fine-tuning). Tensor perturbations inherit a blue spectrum with $n_T=2$, implying suppressed amplitudes on observable scales. The study also discusses backreaction, EFT validity near Genesis, and potential observational signatures through non-Gaussianities and reheating scenarios, highlighting the model’s viability and limitations as a NEC-violating cosmology.

Abstract

We present nonsingular, homogeneous and isotropic bouncing solutions of the conformal Galileon model. We show that such solutions necessarily begin with a radiation-dominated contracting phase. This is followed by a quintom scenario in which the background equation of state crosses the cosmological constant boundary allowing for a nonsingular bounce which in turn is followed by Galilean Genesis. We analyze the spectrum of cosmological perturbations in this background. Our results show that the fluctuations evolve smoothly and without any pathology, but the adiabatic modes form a blue tilted spectrum. In order to achieve a scale-invariant primordial power spectrum as required by current observations, we introduce a light scalar field coupling to the Galileon kinetically. We find two couplings which yield a scale-invariant spectrum, one of which requires a fine tuning of the initial conditions. This model also predicts a blue tilted spectrum of gravitational waves stemming from quantum vacuum fluctuations in the contracting phase.

Figures (7)

• Figure 1: The Hubble parameter in a bouncing solution first shrinks as in a radiation dominated phase, then crosses zero during the nonsingular bounce and eventually evolves to the moment of Galilean Genesis. In the numerical calculation, the values of parameters are listed in (\ref{['parameter']}).
• Figure 2: The scale factor $a(t)$ in a bouncing solution first shrinks as in a radiation dominated phase, then arrives at a nonzero minimal value at the bouncing point and after that enters an expanding phase. In the numerical calculation, the values of parameters are listed in (\ref{['parameter']}).
• Figure 3: The Galileon $\Pi$ monotonically increases throughout the whole cosmological evolution in the model of Galileon bounce. In the numerical calculation, the values of parameters are listed in (\ref{['parameter']}).
• Figure 4: The ratio of the pressure to the density of the Galileon field begins at $1/3$, which is the same as that of normal radiation. It steadily decreases and crosses $w=-1$ just before the bounce. In the numerical calculation, the values of parameters are listed in (\ref{['parameter']}).
• Figure 5: Plot of the parameter $D$ in the context of Galileon bounce. The background parameters are chosen to be the same as the values provided in Eq. (\ref{['parameter']}).