Gibbons–Hawking temperature corrected by quantum cosmology

Abstract

We explore a quantum cosmology description of the de Sitter (dS) radiation and its back-reaction to a dS space, inherent in the wave function of the Wheeler–DeWitt equation for pure gravity with a cosmological constant. We first investigate the quantum Friedmann–Lemaitre–Robertson–Walker cosmological model and then consider the possible effects of inhomogeneities of the universe on the dS radiation. In both the cases we obtain the modified Friedmann equation, including the back-reaction from spacetime fluctuations, and the quantum-corrected Gibbons–Hawking (GH) temperature. It is shown that the quantum correction increases the GH temperature with the increment characterized by the ratio of the dS scale to the Planck scale.