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 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. 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.

8 pages, 4 figures, accepted for publication in Physical Review D

References in corpus (15)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Solar System constraints to general f(R) gravity
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Fourth order gravity: equations, history, and applications to cosmology
• Solar system constraints on R${}^n$ gravity
• Is exponential gravity a viable description for the whole cosmological history?
• Barbero-Immirzi field in canonical formalism of pure gravity
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• Perihelion precession for modified Newtonian gravity
• Remarks on Barbero-Immirzi parameter as a field
• Big-Bounce cosmology in the presence of Immirzi field
• The Immirzi parameter from an external scalar field
• Exponential Lagrangian for the Gravitational Field and the problem of Vacuum Energy

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• Luminal Propagation of Gravitational Waves in Scalar-tensor Theories: The Case for Torsion
• Generalized Ashtekar variables for Palatini f(R) models
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• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Barbero-Immirzi Value from Experiment