Gravitational-wave polarizations in generic linear massive gravity and generic higher-curvature gravity

Abstract

We study the polarizations of gravitational waves (GWs) in two classes of extended gravity theories. First, we formulate the polarizations in linear massive gravity (MG) with generic mass terms of non-Fierz-Pauli type by identifying all the independent variables that obey Klein-Gordon-type equations. The dynamical degrees of freedom (dofs) in the generic MG consist of spin-2 and spin-0 modes, the former breaking down into two tensor (helicity-2), two vector (helicity-1) and one scalar (helicity-0) components, while the latter just corresponding to a scalar. We find convenient ways of decomposing the two scalar modes of each spin into distinct linear combinations of the transverse and longitudinal polarizations with coefficients directly expressed by the mass parameters, thereby serving as a useful tool in measuring the masses of GWs. Then we analyze the linear perturbations of generic higher-curvature gravity (HCG) whose Lagrangian is an arbitrary polynomial of the Riemann tensor. On a flat background, the linear dynamical dofs in this theory are identified as massless spin-2, massive spin-2, and massive spin-0 modes. As its massive part encompasses the identical structure to the generic MG, GWs in the generic HCG provide six massive polarizations on top of the ordinary two massless modes. In parallel to MG, we find convenient representations for the scalar-polarization modes directly connected to the parameters of HCG. In this analysis, we employ two distinct methods; One takes full advantage of the partial equivalence between the generic HCG and MG at the linear level, whereas the other relies upon a gauge-invariant formalism. We confirm that the two results agree. We also discuss methods to determine the theory parameters by GW-polarization measurements. Our method does not require measuring the propagation speeds or the details of the waveforms of the GWs. [Abridged]

arXiv comment19 pages, no figures, references added, published in Phys. Rev. D

References in corpus (24)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Theoretical Aspects of Massive Gravity
• Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
• Probing non-tensorial polarizations of stochastic gravitational-wave backgrounds with ground-based laser interferometers
• Massive, massless and ghost modes of gravitational waves from higher-order gravity
• First search for nontensorial gravitational waves from known pulsars
• Hamiltonian formulation of f(Riemann) theories of gravity
• Probing Dynamical Gravity with the Polarization of Continuous Gravitational Waves
• Detecting massive gravitons using pulsar timing arrays
• Detecting Beyond-Einstein Polarizations of Continuous Gravitational Waves
• Polarization test of gravitational waves from compact binary coalescences
• Model-independent test of gravity with a network of ground-based gravitational-wave detectors
• Constraining extra gravitational wave polarizations with Advanced LIGO, Advanced Virgo and KAGRA and upper bounds from GW170817
• Subluminal stochastic gravitational waves in pulsar-timing arrays and astrometry
• Gauge invariant formulation of gravitational waves in metric $f(R)$ gravity
• Polarization states of gravitational waves with a massive graviton
• A longitudinal component in massive gravitational waves arising from a bimetric theory of gravity
• Probing gravitational wave polarizations with Advanced LIGO, Advanced Virgo and KAGRA
• Inflation with a Weyl term, or ghosts at work
• Condition for directly testing scalar modes of gravitational waves by four detectors
• On the longitudinal response function of interferometers for massive gravitational waves from a bimetric theory of gravity
• Non-Fierz-Pauli bimetric theory from quadratic curvature gravity on Einstein manifolds

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