Third quantization of $f(R)$-type gravity II - General $f(R)$ case -

Abstract

In the previous paper we examined the third quantization of the $f(R)$-type gravity and studied the Heisenberg uncertainty relation of the universe in the example of $f(R)=R^2$. In this work the Heisenberg uncertainty relation of the universe is investigated in the general $f(R)$-type gravity where tachyonic states are avoided. It is shown that, at late times namely the scale factor of the universe is large, the spacetime becomes classical, and, at early times namely the scale factor of the universe is small, the quantum effects dominate.

9 pages. Subtitle and a reference are added with some minor changes. arXiv admin note: text overlap with arXiv:1203.1361

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Cited by in corpus (6)

• Constraints on Operator Ordering from Third Quantization
• On the canonical formalism of $f(R)$-type gravity using Lie derivatives
• Can quantum gravity be both consistent and complete?
• Virtual Black Holes in a Third Quantized Formalism
• Operator Ordering Ambiguity and Third Quantization
• A Quantum Informational Approach to the Problem of Time