Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields

TL;DR

This paper uses numerical relativity to study slowly contracting spacetimes with kinetically coupled scalar fields, showing they evolve towards homogeneous FRW geometry but can eventually approach a Kasner-like state, with implications for early universe models.

Contribution

It provides the first non-perturbative simulations of kinetically coupled scalar fields in contracting spacetimes, revealing their dynamical attractors and late-time behavior.

Findings

Homogeneous, isotropic, flat FRW geometry emerges from diverse initial conditions.

Kinetic coupling causes evolution to deviate towards a Kasner-like stationary point.

Deviations from flat FRW occur on timescales too long to impact observations.

Abstract

We present non-perturbative numerical relativity simulations of slowly contracting spacetimes in which the scalar field driving slow contraction is coupled to a second scalar field through an exponential non-linear sigma model-type kinetic interaction. These models are important because they can generate a nearly scale-invariant spectrum of super-Hubble density fluctuations fully consistent with cosmic microwave background observations. We show that the non-linear evolution rapidly approaches a homogeneous, isotropic and flat Friedmann- Robertson-Walker (FRW) geometry for a wide range of inhomogeneous and anisotropic initial conditions. Ultimately, we find, the kinetic coupling causes the evolution to deflect away from flat FRW and towards a novel Kasner-like stationary point, but in general this occurs on time scales that are too long to be observationally relevant.