Cosmological models in scale-independent energy-momentum squared gravity

TL;DR

This paper explores a scale-independent energy-momentum squared gravity model, analyzing its effects on various cosmological solutions, including static, steady state, and accelerated universes, revealing novel behaviors and extensions of classical cosmologies.

Contribution

It introduces and investigates a scale-independent EMSG model that permits matter creation, modifies cosmological dynamics, and extends classical solutions with new features and behaviors.

Findings

Reproduces static and de Sitter universes within the model.

Identifies conditions for accelerated or decelerated expansion depending on the parameter α.

Extends cosmological solutions to include steady state and anisotropic universes with novel properties.

Abstract

Scale-independent EMSG is a particular model of energy-momentum squared gravity (EMSG) in which the new terms in the Einstein field equations arising from the EMSG theory enter with the same power as the usual terms from Einstein-Hilbert part of the action. However, the model violates the local energy-momentum conservation and matter-current conservation in general and hence, permits a process of matter creation/annihilation in an expanding universe. Consequently, the scale factor dependencies of the energy densities are modified by the dimensionless model parameter $\alpha$. We revisit some nostalgias such as static universes and de Sitter/steady state universes. We reproduce the original ones, moreover, present some novelties, e.g., a spatially flat static universe, de Sitter expansion by negative vacuum energy, steady state universes in the presence of arbitrary fluids with constant equation of state (EoS) parameter other than dust, etc. We also investigate the possible dynamics of dust dominated and radiation dominated universes. Depending on the value of $\alpha$, dust/radiation dominated universe exhibits power-law accelerated/decelerated expansion, corresponds to a steady state model or may end in a big rip. In the framework of anisotropic cosmology, we reproduce Barrow's quiescent universe in the presence of stiff fluid and extend it to fluids with arbitrary constant EoS parameter. We also relax the condition for isotropic initial singularity (big bang) owing to that EMSG effectively allows ultra-stiff EoS parameters.