Abstract.
It has been shown by Cai et al. that the apparent horizon of radius \(r_{0}\) in the cosmological Friedmann space-time emits radiation at the temperature \(T_{0} = 1/2\pi r_{0}\). Here, we derive this result from the Wheeler-DeWitt equation for the wave function of the Universe \(\Psi\), starting from a classical gravitational Lagrangian L that contains a quadratic higher-derivative term \(R^{2}\) , 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 \(dx_{0} = 0\). We also extend our previous analysis of the Wheeler-DeWitt equation for the wave function \( \Phi\) 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 \( T_{0}\) after application of the ADM formalism.
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Pollock, M.D. On the thermodynamics of the cosmological apparent horizon. Eur. Phys. J. Plus 130, 226 (2015). https://doi.org/10.1140/epjp/i2015-15226-x
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DOI: https://doi.org/10.1140/epjp/i2015-15226-x