Implications on the cosmic coincidence by a dynamical extrinsic curvature

TL;DR

This paper explores how a dynamical extrinsic curvature can modify Friedmann equations, potentially alleviating the cosmic coincidence problem by matching observational data and explaining the transition from deceleration to acceleration.

Contribution

It introduces a novel approach using smooth deformation to incorporate dynamical extrinsic curvature into cosmological models, addressing the cosmic coincidence issue.

Findings

The ratio of matter to extrinsic energy density varies minimally during key cosmic epochs.

The calculated redshift for equivalence aligns with the observed transition from deceleration to acceleration.

The model's predictions are consistent with BAO, CMBR, and SNIa observational data.

Abstract

In this work, we apply the smooth deformation concept in order to obtain a modification of Friedmann equations. It is shown that the cosmic coincidence can be at least alleviated using the dynamical properties of the extrinsic curvature. We investigate the transition from nucleosynthesis to the coincidence era obtaining a very small variation of the ratio $r=\frac{\rho_{m}}{\rho_{ext}}$, that compares the matter energy density to extrinsic energy density, compatible with the known behavior of the deceleration parameter. We also show that the calculated "equivalence" redshift matches the transition redshift from a deceleration to accelerated phase and the coincidence ceases to be. The dynamics on $r$ is also studied based on Hubble parameter observations as the latest Baryons Acoustic Oscillations/Cosmic Microwave Background Radiation (BAO/CMBR) + SNIa.