A $\Lambda$CDM bounce scenario

TL;DR

This paper explores a bouncing cosmological model within loop quantum cosmology, showing it can produce nearly scale-invariant perturbations with observable features that distinguish it from inflationary scenarios.

Contribution

It demonstrates that a contracting universe with a bounce can generate nearly scale-invariant perturbations, incorporating quantum gravity effects via loop quantum cosmology.

Findings

Perturbations remain nearly scale-invariant through the bounce.

The scalar spectral index exhibits a positive running, differentiating from inflation.

Predicts a small tensor-to-scalar ratio for low sound speed of dark matter.

Abstract

We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt, in agreement with observations. We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly scale-invariant. We also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter, the Hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation, and the curvature scale that the loop quantum cosmology bounce occurs at. Importantly, as this scenario predicts a positive running of the scalar index, observations can potentially differentiate between it and inflationary models. Finally, for a small sound speed of cold dark matter, this scenario predicts a small tensor-to-scalar ratio.