Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Friedmann integrals and physical vacuum in the framework of
  macroscopic extra dimensions   The structure and origin of the Friedmann integrals are analyzed within the
framework of large extra dimensions proposed by Arkani-Hamed et all. (1998). It
is demonstrated that the integrals might emerge from extra-dimension physics
and reveal its signature. In the case of two extra dimensions, the integrals
are expressed via the product $M_* R$ of the only fundamental energy $M_*$ and
the size $R $ of the extra dimensions. The cosmic vacuum density turns out to
be $\sim R^4$, in this case. The effective cut-off in the spectrum of the
quantum zero-point oscillations at the frequency $\omega_V \sim 1/R$ is assumed
to be associated with the epoch when the Hubble radius becomes larger than $R$.
This occurs at temperatures $ \sim M_*$ in the first three picoseconds of the
cosmic expansion.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat