Higher-Derivative $f(R,\square R,T)$ Theories of Gravity

Abstract

In literature there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress-energy momentum tensor $T=T_{\mu }^{\mu }$. This type of modified gravity is called as $f(R,T)$ in which $R$ is Ricci scalar $R=R_{\mu }^{\mu }$. We extend manifestly this model to include the higher derivative term $\square R$. We derived equation of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter solution is unstable for a generic type of $f(R,\square R,T)$ model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.

arXiv comment14 pages, revtex4 format. arXiv admin note: text overlap with arXiv:1104.2669 by other authors

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• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Charged Gravastars in Modified Gravity
• Definition of Complexity Factor for Self-Gravitating Systems in Palatini $f(R)$ Gravity
• Construction of Charged Cylindrical Gravastar-like Structures
• Constraining Anisotropic Cosmological Model in $f(\mathcal{R},{\mathcal{L}}_m)$ Gravity
• Energy Conditions in Higher Derivative $f(R,\square R,T)$ Gravity
• New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas
• Geometric structures of Morris-Thorne wormhole metric in $f(R,L_m)$ gravity and energy conditions
• Charged gravastar model in Rastall theory of gravity
• Bounds on Higher Derivative $f(R,\square R,T)$ Models from Energy Conditions