Relativistic Bose-Einstein condensate in the rainbow gravity

TL;DR

This paper investigates how rainbow gravity modifies the properties and critical temperature of relativistic Bose-Einstein condensates, providing bounds on model parameters and analyzing the impact on particle condensation.

Contribution

It introduces a formal framework to compute rainbow gravity corrections to relativistic BECs and derives the modified critical temperature and phenomenological bounds.

Findings

Derived the corrected critical temperature $T_c$ under rainbow gravity.

Established upper bounds for rainbow gravity parameters.

Showed that rainbow gravity makes particle condensation harder at $T<T_c$.

Abstract

In this paper, we study the effects of a modified theory of gravity - the rainbow gravity - on the relativistic Bose-Einstein condensate (BEC). We initially discuss some formal aspects of the model in order to compute the corrections to the relevant quantities of the condensate. Following, we evaluate the generating functional from which obtain some thermodynamic parameters. Then we calculate the corrected critical temperature $T_c$ that sets the relativistic Bose-Einstein condensate considering the three principal rainbow functions, finding, in addition, a phenomenological upper bound for the parameters involved in the model. Finally, we discuss how harder is for the particles at an arbitrary temperature $T<T_c$ to enter the condensed state compared to the usual scenario, {\it i.e.}, without rainbow gravity.