Inflation without Inflaton: A Model for Dark Energy

TL;DR

This paper proposes a novel cosmological model where non-commutative quantum mechanics induces interactions between causally disconnected regions, leading to inflationary or oscillating solutions that explain dark energy without an inflaton.

Contribution

It introduces a new approach using deformed Poisson brackets to model interactions between disconnected universe regions, providing a fresh perspective on dark energy and cosmic acceleration.

Findings

Solutions exhibit inflationary or oscillating behavior depending on parameters

The model demonstrates the presence of dark energy through the equation of state

Perturbative analysis confirms the robustness of the solutions

Abstract

The interaction between two initially causally disconnected regions of the universe is studied using analogies of non-commutative quantum mechanics and deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metrics with scale factors $a$ and $b$ and cosmological constants $\Lambda_a$ and $\Lambda_b$, respectively. The causality is turned on by positing a non-trivial Poisson bracket $[ {\cal P}_{\alpha}, {\cal P}_{\beta} ] =\epsilon_{\alpha \beta}\frac{\kappa}{G}$, where $G$ is Newton's gravitational constant and $\kappa $ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of $\kappa$. In this model the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for $\kappa \ll1 $ is also studied.