https://doi.org/10.1140/epjp/i2015-15226-x
Regular Article
On the thermodynamics of the cosmological apparent horizon
V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Ulitsa Gubkina 8, 119991, Moscow, Russia
* e-mail: mdp30@cam.ac.uk
Received:
13
August
2015
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
