Third quantization of $f(R)$-type gravity

Details Third quantization of $f(R)$-type gravity Third quantization of $f(R)$-type gravity

2012-03-07

arxiv.org/abs/1203.1361v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, Arbitrary constants in (4.19) are changed to arbitrary functions of $\varphi$. Conclusions are not changed. Reference

Scientific paper

We examine the third quantization of $f(R)$-type gravity, based on its effective Lagrangian in the case of a flat Friedmann-Lemaitre-Robertson-Walker metric. Starting from the effective Lagrangian, we execute a suitable change of variable and the second quantization, and we obtain the Wheeler-DeWitt equation. The third quantization of this theory is considered. And the uncertainty relation of the universe is investigated in the example of $f(R)$-type gravity, where $f(R)=R^2$. It is shown, when the time is late namely the scale factor of the universe is large, the spacetime does not contradict to become classical, and, when the time is early namely the scale factor of the universe is small, the quantum effects are dominating.

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