Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy-momentum squared symmetric Teleparallel gravity:
  $f(Q,T_{\mu\nu}T^{\mu\nu})$ gravity   In this work we propose the $f(Q,T_{\mu\nu}T^{\mu\nu})$ gravity as a further
extension of the $f(Q)$ and $f(Q,T)$ gravity theories. The action involves an
arbitrary function of the non-metricity $Q$ and $T_{\mu\nu}T^{\mu\nu}$ in the
gravity Lagrangian. The field equations for the theory are derived in the
metric formalism by varying the action with respect to the metric. The theory
involves a non-minimal coupling between the geometric and the matter sectors,
and hence the covariant divergence of the energy momentum tensor is non-zero,
thus implying the non-conservation of the same. The vacuum solutions of the
theory are investigated and it is found that the theory perfectly admits a
de-Sitter like evolution of the universe. The cosmological equations are
derived and it is found that there are two correction terms arising as
modification of the gravity. Two specific toy models of the form $Q+\eta
\left(\textbf{T}^2\right)^{n}$ and $f_{0}Q^{m} \left(\textbf{T}^2\right)^{n}$
are explored to gain further insights into the dynamics of the theory. It is
seen that the field equations of both the models have terms similar to those
arising from the quantum gravity effects and are thus responsible for the
avoidance of the singularity. One striking feature of the model is that the
non-linear correction terms dominate in the early universe and gradually fade
away at later times giving standard FLRW universe. Solutions for the FLRW
equations are found wherever possible and the evolution of the scale factor and
the matter energy density are plotted. Finally the energy conditions are
explored in the background of the theory. Using these conditions and some
observational data the theory is considerably constrained.

22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys