Inflation in Energy-Momentum Squared Gravity in Light of Planck2018
  We study cosmological dynamics of the energy-momentum squared gravity. By
adding the squared of the matter field's energy-momentum tensor ($\zeta\,
\textbf{T}^{2}$) to the Einstein Hilbert action, we obtain the Einstein's field
equations and study the conservation law. We show that the presence of $\zeta\,
\textbf{T}^{2}$ term, breaks the conservation of the energy-momentum tensor of
the matter fields. However, an effective energy-momentum tensor in this model
is conserved in time. By considering the FRW metric as the background, we find
the Friedmann equations and by which we explore the cosmological inflation in
$\zeta\,\textbf{T}^{2}$ model. We perform numerical analysis on the
perturbation parameters and compare the results with Planck2018 different data
sets at $68\%$ and $95\%$ CL, to obtain some constraints on the coupling
parameter $\zeta$. We show that \textbf{ for $0< \zeta \leq 2.1\times 10^{-5}$,
the $\zeta\, \textbf{T}^{2}$ gravity is an observationally viable model of
inflation.
