Modified Dispersion Relations lead to a finite Zero Point Gravitational Energy

Details Modified Dispersion Relations lead to a finite Zero Point Gravitational Energy Modified Dispersion Relations lead to a finite Zero Point Gravitational Energy

2011-02-18

arxiv.org/abs/1102.3803v1

Phys.Rev.D83:084021,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTex 16 pages, 6 figures

Scientific paper

10.1103/PhysRevD.83.084021

We compute the Zero Point Energy in a spherically symmetric background distorted at high energy as predicted by \textit{Gravity's Rainbow}. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation. With the help of a canonical decomposition, we find that the relevant contribution to one loop is given by the graviton quantum fluctuations around the given background. By means of a variational approach based on gaussian trial functionals, we find that the ordinary divergences can here be handled by an appropriate choice of the rainbow's functions, in contrast to what happens in other conventional approaches. A final discussion on the connection of our result with the observed cosmological constant is also reported.

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