Implications of the Holst term in a $f(R)$ theory with torsion

Understand

We analyze a modified $f(R)$ theory of gravity in the Palatini formulation, when an Holst term endowed with a dynamical Immirzi field is included.

• We study the basic features of the model, especially in view of liminating the torsion field via the Immirzi field and the scalar-tensor degrees of freedom of the $f(R)$ model.
• The main task of this study is the investigation of the morphology of the gravitational wave polarization when their coupling to a circle of test particles is considered.
• We first observe that the dynamics of the scalar mode of the $f(R)$ Lagrangian is frozen out, since its first order term identically vanishes.