Deformed Quantum Field Theory, Thermodynamics at Low and High Energies, and Gravity. II. Deformation Parameter

TL;DR

This paper explores how a single deformation parameter can unify various gravitational theories within the framework of generalized uncertainty principles, revealing a common thermodynamic interpretation and potential for broader generalizations.

Contribution

It demonstrates that one deformation parameter can describe multiple cases of General Relativity under different uncertainty principles, linking them through thermodynamic interpretations.

Findings

Unified description of gravitational equations via deformation parameter

Thermodynamic interpretation of gravitational equations

Potential extension to dynamic cosmological constant

Abstract

This work is a continuation of studies presented in the papers arXiv:0911.5597, arXiv:1003.4523. In the work it is demonstrated that with the use of one and the same parameter deformation may be described for several cases of the General Relativity within the scope of both the Generalized Uncertainty Principle (UV-cutoff) and the Extended Uncertainty Principle (IR-cutoff). All these cases have a common thermodynamic interpretation of the corresponding gravitational equations. Consideration is given to the possibility for extension of the obtained results to more general cases. Possible generalization of the uncertainty relation for the pair (cosmological constant, "space-time volume"), where the cosmological constant is regarded as a dynamic quantity at high and low energies is analyzed.