Cosmological Inflation Based on the Uncertainty-Mediated Dark Energy

Abstract

It was suggested in our previous paper [Yu.V. Dumin, Grav. Cosmol. 25, 169 (2019)] that the cosmological Dark Energy might be mediated by the time–energy uncertainty relation in the Mandelstam–Tamm form, which is appropriate for the long-term evolution of quantum systems. The amount of such Dark Energy gradually decays with time, and the corresponding scale factor of the Universe increases by a “quasi-exponential” law (namely, the exponent is proportional to of the square root of time) throughout the entire cosmological evolution. While such a universal behavior looks quite appealing, an important question arises: Does the quasi-exponential expansion resolve the major problems of the early Universe in the same way as the standard inflationary scenario? In the present paper, we elucidate this issue by analyzing the causal structure of the space–time following from this model. It is found that the observed region of the Universe (the past light cone) covers a single causally connected domain developing from the Planck times (the future light cone). Consequently, there should be no appreciable inhomogeneity and anisotropy in the early Universe, creation of the topological defects will be suppressed, etc. From this point of view, the uncertainty-mediated Dark Energy can serve as a reasonable alternative to the standard (exponential) inflationary scenario.