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

TL;DR

This paper investigates the third quantization of general $f(R)$-type gravity, showing that the universe transitions from quantum-dominated behavior at early times to classical behavior at late times, avoiding tachyonic states.

Contribution

It extends previous work by analyzing the Heisenberg uncertainty relation in general $f(R)$ gravity, demonstrating the universe's quantum-to-classical transition without tachyonic states.

Findings

Quantum effects dominate at early universe times.

Spacetime becomes classical at late times.

Tachyonic states are avoided in the 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.