# Minisuperspace model of compact phase space gravity

## TL;DR

This paper explores the compactification of phase space in a minisuperspace gravity model, revealing effects like re-collapse and analyzing quantum transitions, thus addressing singularity issues in classical gravity.

## Contribution

It introduces a novel approach of phase space compactification in a minisuperspace model, connecting classical and quantum gravity regimes with new dynamical insights.

## Key findings

- Compact phase space leads to re-collapse phenomena.
- Quantum analysis shows transition probabilities peaked at zero cosmological constant.
- Model unifies features of de Sitter and loop quantum cosmology.

## Abstract

The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The purpose of this article is to study the idea of generalizing the theory of gravity by compactification of the phase space. We investigate the procedure of compactification of the phase space on a minisuperspace gravitational model with two dimensional phase space. In the affine limit, the model reduces to the flat de Sitter cosmology. The phase space is generalized to the spherical case, and the case of loop quantum cosmology is recovered in the cylindrical phase space limit. Analysis of the dynamics reveals that the compactness of the phase space leads to both UV and IR effects. In particular, the phase of re-collapse appears, preventing the universe from expanding to infinite volume. Furthermore, the quantum version of the model is investigated and the quantum constraint is solved. As an example, we analyze the case with the spin quantum number $s=2$, for which we determine transition amplitude between initial and final state of the classical trajectory. The probability of the transition is peaked at $\Lambda=0$.