On the thermodynamics of the cosmological apparent horizon
V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Ulitsa Gubkina 8, 119991, Moscow, Russia
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Accepted: 17 September 2015
Published online: 11 November 2015
It has been shown by Cai et al. that the apparent horizon of radius in the cosmological Friedmann space-time emits radiation at the temperature . Here, we derive this result from the Wheeler-DeWitt equation for the wave function of the Universe , starting from a classical gravitational Lagrangian L that contains a quadratic higher-derivative term , the scalar component of which is non-tachyonic, by application of the horizon hypothesis and definition of the physical three-space on the time-slice . We also extend our previous analysis of the Wheeler-DeWitt equation for the wave function of the apparent horizon of the de Sitter space-time to include the case of a more general energy-momentum source, that generates an arbitrary Friedmann space-time, confirming the expression for after application of the ADM formalism.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2015