A Unified Framework for Analyzing Gravitational Wave Effects in Modified Gravity Theories Based on the Isaacson Picture
Sep 18, 2024
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Abstract: (arXiv)
The Isaacson picture is established on two sets of basic equations and provides a necessary foundation for discussing gravitational wave effects without ambiguity. It is typically derived by expanding the field equations to second-order perturbations. In addition to the above method, the perturbation action method can also serve as an alternative derivation method. In this paper, we elaborate on this method, establishing its foundations more rigorously. Especially, the second-order perturbation action in the Minkowski background encapsulates all the required information for constructing the Isaacson picture far from the source. This approach provides a method that, in principle, allows for the construction of a model-independent parametric framework, encompassing the vast majority of modified gravitational theories. It enables a unified and generalized analysis of various gravitational wave effects across these theories, including the polarization modes, velocity dispersion relations, effective energy-momentum tensor, and memory effects. These properties have garnered significant attention due to their close connection with observable effects and are expected to be identified by the next generation of gravitational wave detectors, which aim to test potential modifications to gravity theory. We demonstrate this method using the most general second-order vector-tensor theory, including parity-violation terms, as an example, and specifically analyze the polarization modes of gravitational waves in this theory.Note:
- 51 pages + 4 appendices, 1 figure, improved readability
References(88)
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