Note on the dynamical features for the extended <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>P</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> cubic gravity
Mihai Marciu
Abstract
The paper studies the physical characteristics for the extended $f(P)$ cubic gravity from a transitive perspective based on dynamical system analysis, by considering the linear stability theory in two specific cases, corresponding to power--law $f(P)={f}_{0}{P}^{\ensuremath{\alpha}}$ and exponential $f(P)={f}_{0}{e}^{\ensuremath{\alpha}P}$ gravity types, where ${f}_{0}$ and $\ensuremath{\alpha}$ are constant parameters. In these cases we have analyzed the effects in the phase space complexity, revealing the cosmological solutions attached to the critical points. For the power--law and exponential gravity types, we have noticed the presence of two cosmological epochs associated to the critical points involved, corresponding to de Sitter eras and quintessencelike epochs, described by a constant effective equation of state. For all of these solutions we have studied the dynamical characteristics which are associated to the stability properties, determining possible constraints to various parameters from a transient perspective. The dynamical prospects asserted that the extended $f(P)$ cubic gravity can represent a promising modified theory of gravitation, leading to the manifestation of the accelerated expansion at late time evolution.