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.

arXiv comment8 pages, 4 figures, accepted for publication in Physical Review D

References in corpus (37)

• The Cosmological Constant and Dark Energy
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Tests of general relativity with GW150914
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Physical Aspects of the Space-Time Torsion
• Unifying inflation with LambdaCDM epoch in modified f(R) gravity consistent with Solar System tests
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Real and complex connections for canonical gravity
• Post-Newtonian constraints on f(R) cosmologies in metric formalism
• Post-Newtonian constraints on f(R) cosmologies in Palatini formalism
• Solar System constraints to general f(R) gravity
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• The role of energy conditions in $f(R)$ cosmology
• Linearized f(R) Gravity: Gravitational Radiation & Solar System Tests
• Fourth order gravity: equations, history, and applications to cosmology
• The Immirzi parameter in quantum general relativity
• Experimental Tests of General Relativity
• Black hole entropy and isolated horizons thermodynamics
• A Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background
• An improved estimate of black hole entropy in the quantum geometry approach
• First search for nontensorial gravitational waves from known pulsars
• 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
• Gravitational Wave Polarization Modes in $f(R)$ Theories
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• Massive relic gravitational waves from f(R) theories of gravity: production and potential detection
• 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
• $f(R)$ gravity with Torsion and the Immirzi field: signature for GW detection
• Exponential Lagrangian for the Gravitational Field and the problem of Vacuum Energy

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• Super-entropic black hole with Immirzi hair
• Modified Gravitational Waves Across Galaxies from Macroscopic Gravity
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
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