Multi-Dimensional Cosmology and DSR-GUP

TL;DR

This paper explores multidimensional cosmology under DSR-GUP, revealing that unlike GUP, DSR-GUP prevents eternal acceleration, leading to a future decelerating phase and a big crunch.

Contribution

It introduces the application of DSR-GUP to multidimensional cosmology and compares its effects with GUP, highlighting key differences in late-time cosmic behavior.

Findings

DSR-GUP leads to deceleration after initial acceleration.

Unlike GUP, DSR-GUP prevents eternal acceleration.

Both internal and external spaces eventually decelerate and collapse.

Abstract

A multidimensional cosmology with FRW type metric having 4-dimensional space-time and $d$-dimensional Ricci-flat internal space is considered with a higher dimensional cosmological constant. The classical cosmology in commutative and DSR-GUP contexts is studied and the corresponding exact solutions for negative and positive cosmological constants are obtained. In the positive cosmological constant case, it is shown that unlike the commutative as well as GUP cases, in DSR-GUP case both scale factors of internal and external spaces after accelerating phase will inevitably experience decelerating phase leading simultaneously to a big crunch. This demarcation from GUP originates from the difference between the GUP and DSR-GUP algebras. The important result is that unlike GUP which results in eternal acceleration, DSR-GUP at first generates acceleration but prevents the eternal acceleration at late times and turns it into deceleration.