Quantum Theory at Planck Scale, Dynamical Cosmological Term and Deformed Gravity

The dark energy problem is analyzed from the viewpoint of the time-varying cosmological term. It is demonstrated that, at least within the scope of the holographic principle, an experimental value of the vacuum energy density may be derived and may be tested quite well with a new small parameter arising in a quantum theory with the fundamental length on the order of Planck’s length. Besides, within a theory proclaiming the existence of such fundamental length a high-energy deformation of the General Relativity for the space with horizon has been constructed. The obtained results have been applied to solving of the dark energy problem, making it possible to frame the following hypothesis: a dynamic cosmological term is a measure of deviation from a thermodynamic identity (the first law of thermodynamics) of the high-energy (Planck’s) deformation of Einstein equations for horizon spaces in their thermodynamic interpretation.