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

Abstract

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 eliminating 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. This allows a detailed characterization of the linearized theory, which outlines the emergence of a modified Newtonian potential in the static limit, and when time independence is relaxed a standard gravitational wave plus the scalar wave associated to the Immirzi field. Investigating the effect of the coupling of this scalar-tensor wave on a circle of test particles, we arrive to define two effective gravitational polarizations, corresponding to an equivalent phenomenological wave, whose morphology is anomalous with respect the standard case of General Relativity. In fact, the particle circle suffers modifications as it was subjected to modified plus and cross modes, whose specific features depend on the model free parameters and are, in principle, detectable via a data analysis procedure.

Luminal propagation of gravitational waves in scalar-tensor theories: The case for torsion

“…Similar results have been found in teleparallel gravity theories[70][71][72] and in f (R) theories with a nonminimal coupling to the Nieh-Yan term[73,74].…”

Scalar modes in extended hybrid metric-Palatini gravity: Weak field phenomenology

“…We studied this phenomenon in the special case of nearly degenerate masses, in which the beating frequency is much smaller than the signal frequency. However, the same feature should be detectable for any value of the masses in the allowed range, at least until the lighter scalar can be properly distinguished from the massless tensorial degrees, in which case we expect their mutual interaction as in [51]. It remains as an open issue the construction of a definite model, i.e.…”

Big bounce cosmology for Palatini $$R^2$$ gravity with a Nieh–Yan term

“…This means that the affine connection is equipped with an antisymmetric component depending of the function f (•), and we deal with a Riemann-Cartan space-time [8][9][10][11][12][13][14]. Now, since in Palatini f (R) models torsion naturally emerges, in [15] we proposed the idea that for formulating f (R) gravity in the connection language we have to include torsional contribution already into the Lagrangian. In particular, also in relation with features of Loop Quantum Gravity (LQG) formalism [16][17][18][19][20][21], we considered in the Lagrangian density a Nieh Yan term [22][23][24] with the Immirzi parameter promoted to be a field [25][26][27][28][29].…”

“…This choice allowed to fully solve torsion in terms of the function f (•) and the Immirzi field, reducing the original model to a scalar-tensor theory, characterized by an interesting phenomenology for the gravitational waves polarizations [30].…”

“…Here, we explore the cosmological implementation of the theory proposed in [15] for a flat Friedman Universe, in order to shed light on the dynamical and physical implications that our revised Palatini f (R) theory can have on the Universe history.…”