Energy Conditions in $f(P)$ Gravity

$f(P)$ gravity is a novel extension of ECG in which the Ricci scalar action replaced by function curvature invariant $P$ represents contractions Riemann tensor at cubic order \cite{p}. The present work concentrated on bounding some models using concept energy conditions where functional forms are represented as \textbf{a)} $f(P) = \alpha \sqrt{P}$, and \textbf{b)} \exp (P)$, $\alpha$ sole model parameter. Energy interesting linear relationships between pressure density have been extensively employed to derive results Einstein's gravity, also an excellent tool impose constraints any cosmological model. To place bounds, we ensured that must remain positive, negative, EoS parameter attain value close $-1$ make sure bounds respect accelerated expansion Universe harmony with latest observational data. We report for both models, suitable spaces exist satisfy aforementioned therefore posit theory be promising modified gravitation.