Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory

Abstract

A generalized Brans-Dicke (GBD) theory in the framework of Palatini formalism are proposed in this paper. We derive the field equations by using the variational approach and obtain the linearized equations by using the weak-field approximation method. We show various properties of the geometrical scalar field in the Palatini-formalism of GBD theory: it is massless and source-free, which are different from the results given in the metric-formalism of GBD theory. Also, we investigate the polarization modes of gravitational waves (GWs) by using the the geodesic deviation method and the Newman-Penrose method in the Palatini-GBD theory. It is observed that there are three polarizations modes and four oscillation in the Palatini-GBD theory. Concretely, they are the two transverse tensor ($+$) and ($\times$) standard polarization modes, and one breathing mode (with two oscillation). The results of GWs polarization in the Palatini-GBD theory are different from that in the metric-GBD theory, where there are four polarizations modes: the two standard tensorial modes ($+$ and $\times$), a scalar breathing mode, and a massive scalar mode that is a mix of the longitudinal and the breathing polarization. Comparing with the Palatini-$f(\tilde{R})$ theory and the General Relativity, we can see that the extra breathing mode of GWs polarization can be found in the Palatini-GBD theory. At last, the expression of the parameterized post Newton (PPN) parameter is derived, which could pass through the experimental test.

12 pages, no figure

References in corpus (22)

• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Cosmological Evolution of a Quintom Model of Dark Energy
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• Solar System constraints to general f(R) gravity
• Limit to General Relativity in f(R) theories of gravity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Higgs-Palatini Inflation and Unitarity
• Holographic Dark Energy in Brans-Dicke Theory
• Dynamical symmetries in Brans-Dicke cosmology
• Scalar-tensor cosmology with R^{-1} curvature correction by Noether Symmetry
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• Matter Power Spectra in Viable $f(R)$ Gravity Models with Massive Neutrinos
• Exact cosmological solution of a Scalar-Tensor Gravity theory compatible with the $\Lambda CDM$ model
• Palatini f(R) gravity as a fixed point
• CMB Polarization and Theories of Gravitation with Massive Gravitons
• Linearized modified gravity theories and gravitational waves physics in the GBD theory
• An analytic calculation of the growth index for $f(R)$ dark energy model
• Gravitational Waves in Scalar-Tensor-Vector Gravity Theory