Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third quantization of $f(R)$-type gravity II - General $f(R)$ case -   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.

11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
2
The categories of this paper are: math
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph