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

The principal objective of this paper is to show that deformation of the General Relativity within the scope of both the Generalized Uncertainty Principle (UV-cutoff) and the Extended Uncertainty Principle (IR-cutoff) in the cases when the corresponding gravitational equations have a thermodynamic interpretation may be studied in terms of a small parameter introduced in previous works of the author. From this viewpoint the parameter is though to be universal. 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. This paper is devoted to the 70-th Anniversary of Professor Nikolai Maksimovich Shumeiko, Director of the Belarusian Particles and High Energy Physics National Centre.