The equivalence theorem in the generalized gravity of f(R)-type and canonical quantization II

Details The equivalence theorem in the generalized gravity of f(R)-type and canonical quantization II The equivalence theorem in the generalized gravity of f(R)-type and canonical quantization II

2012-04-11

arxiv.org/abs/1204.2396v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages. Ecept for the change of style from {book} to {article} and related changes, e.g., addition of abstract and the form

Scientific paper

We first review the equivalence theorem of the f(R)-type gravity to Einstein gravity with a scalar field by deriving it in a self-contained and pedagogical way. Then we describe the problem of to what extent the equivalence holds. Main problems are (i) Is the surface term given by Gibbons and Hawking which is necessary in Einstein gravity also necessary in the f(R)-type gravity? (ii) Does the equivalence hold also in quantum theory? (iii) Which metric is physical, i.e., which metric should be identified with the observed one? In this work, we clarify the problem (i) and review the problem (ii) in a canonical formalism which is the generalization of the Ostrogradski one. We briefly comment on the problem (iii). Some discussions are given on one of the results of (ii) concerning the general relativity in non-commutative spacetime.

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