Newtonian cosmology and Evolution of kappa-deformed universe

TL;DR

This paper explores how non-commutative space--time modifies the evolution of the universe using Newtonian cosmology, deriving altered Friedmann equations and analyzing effects on the scale factor in different cosmological eras.

Contribution

It generalizes Newtonian cosmology to $ppa$-deformed space--time, deriving first-order modified Friedmann equations and analyzing their implications for universe evolution.

Findings

Deformation affects the rate of change of the scale factor.

Modified equations suggest a possible resolution to the Hubble tension.

Existence of a bounce in universe evolution is supported.

Abstract

Considering space--time to be non-commutative, we study the evolution of the universe employing the approach of Newtonian cosmology. Generalizing the conservation of energy and the first law of thermodynamics to $\kappa$-deformed space--time, we derive the modified Friedmann equations, valid up to the first order, in the deformation parameter. Analyzing these deformed equations, we derive the time evolution of the scale factor in cases of radiation-dominated, matter-dominated, and vacuum (energy)-dominated universes. We show that the rate of change of the scale factor in all three situations is modified by the non-commutativity of space--time, and this rate depends on the sign of the deformation parameter, indicating a possible explanation for the observed Hubble tension. We undertake this investigation for two different realizations of non-commutative space--time coordinates. In both cases, we also argue for the existence of bounce in the evolution of the universe.