10th International Conference on Gravitation and Cosmology: New Horizons and Singularities in Gravity (ICGC 2023)

Evolution of Universe in $\kappa$-deformed Non-commutative space-time

Not scheduled

15m

IIT Guwahati

Poster Classical & Quantum Gravity Classical & Quantum Gravity

Speaker

Mr Suman Kumar Panja (School of Physics, University of Hyderabad)

Description

Quantum gravity has been studied using various approaches and all of these approaches introduce a fundamental length scale in the theory. Non-commutative space-time is an approach which incorporates this fundamental minimum length scale naturally and provides a testing ground to build quantum gravity models. Thus, it is of paramount interest to study how non-commutative space-time will affect the cosmological models.

In this work, we investigate the evolution of the universe in $\kappa$-deformed space-time, a non-commutative space-time which is the underlying space-time associated with doubly special relativity as well as that of certain quantum gravity models.
This is done by adapting the Newtonian cosmological framework to $\kappa$-space-time. We obtain the modified Friedmann equations, valid up to the first order in the deformation parameter, using generalized energy conservation equation and generalized first law of thermodynamics to $\kappa$-deformed space-time. We find the temporal evolution of the scale factor in the cases of radiation-dominated, matter-dominated, and vacuum (energy) dominated worlds by analyzing these deformed equations. We illustrate that the non-commutativity of space-time modifies the rate of change of the scale factor in each of the three cases and that this rate depends on the sign of the deformation parameter. We take out this research for two distinct realizations of
non-commutative space-time. We also argue in both cases for the presence of bounce in the evolution of the universe.

References
1. W. H. McCrea and E. A. Milne, Quart. J. Math. Oxf. 5 (1934) 73.
2. T. F. Jordan, Am. J. Phys. 73 (2005) 653.
3. P. Bargueño, S. B. Medina, M. Nowakowski and D. Batic, Eur. Phys. J. 76 (2016) 543.
4. A. Connes, Non-Commutative Geometry; Academic Press: London, UK, 1994.
5. S. Meljanac and M. Stojic, Eur. Phys. J. 47 (2006) 531.
6. E. Harikumar, H. Sreekumar and Suman Kumar Panja, Universe 9 (2023) 343.