Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Future singularities if the universe underwent Starobinsky inflation in
  the past   The effects which quantum fields and an $\alpha_0 R^2$ term in the
gravitational Lagrangian have on future singularities are investigated. While
all values of $\alpha_0$ are considered, an emphasis is placed on those values
which are compatible with the universe having undergone Starobinsky inflation
in the past. These are also values which lead to stable solutions to the
semiclassical backreaction equations in the present universe. The dark energy
is modeled as a perfect fluid, and the focus is on type I-IV singularities and
little rips which result when the classical Einstein equations are solved with
various types of dark energy as a source. First, evidence is provided that the
energy densities of massive conformally coupled scalar fields approach that of
the conformally invariant scalar field as a type III singularity is approached.
Then, solutions to the semiclassical backreaction equations are investigated
when conformally invariant fields and the $ \alpha_0 R^2$ term in the
gravitational Lagrangian are present. General proofs regarding the behaviors of
the solutions are given. The proofs are illustrated by analytic and numerical
calculations in specific cases.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an