# Nonlinear Field Space Cosmology

## TL;DR

This paper explores a novel nonlinear scalar field with a compact phase space in cosmology, revealing effects like recollapse, bounces, and modifications to perturbation amplitudes, bridging cosmology and condensed matter physics.

## Contribution

It introduces a nonlinear scalar field model with a spherical phase space in cosmology, analyzing its effects on universe dynamics and perturbations, connecting condensed matter concepts with cosmological models.

## Key findings

- Nonlinearity leads to recollapse and bounce scenarios.
- Perturbation amplitude receives corrections, while spectral index remains unchanged.
- The approach links cosmology with condensed matter physics, opening new research avenues.

## Abstract

We consider the FRW cosmological model in which the matter content of universe (playing a role of inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced Nonlinear Field Space Theory (NFST), where physical phase space of a given field is assumed to be compactified at large energies. For our analysis we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector we find that nonlinearity of the field phase space is becoming relevant for large volumes of universe and then it can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where nontrivial nature of its phase space can be neglected, while there is a non-vanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.