Corrections to the gravitational wave phasing

Abstract

The gravitational wave, traveling a long cosmological distance to reach interferometers, interacts with the (homogeneous and isotropic) cosmological background, so generally speaking, its amplitude and phase are modified in some nontrivial way. As the sensitivity of interferometers is improved, one may detect corrections to the short-wavelength approximation, which naturally includes the information of cosmological evolution. In this work, the Newman-Penrose variable ${\Psi }_4$ has been calculated to show that there are two new corrections to the short-wavelength approximation. One formally occurs at the first post-Newtonian order but is highly suppressed by the Hubble parameters; the other occurs at the fifth post-Newtonian order, which is due to the variation of the amplitude. The first correction contains the evolution of the Universe, but it may not be easily detected. The second one indicates that the short-wavelength approximation has to be corrected, when the more accurate waveforms with the higher-order post-Newtonian terms are calculated.

12 pages, 2 figures. Match the published version

References in corpus (24)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The Confrontation between General Relativity and Experiment
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• GW190425: Observation of a Compact Binary Coalescence with Total Mass $\sim 3.4M_{\odot }$
• An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A
• GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
• Exploring the Sensitivity of Next Generation Gravitational Wave Detectors
• A gravitational-wave standard siren measurement of the Hubble constant
• Dark Energy after GW170817: dead ends and the road ahead
• INTEGRAL Detection of the First Prompt Gamma-Ray Signal Coincident with the Gravitational Wave Event GW170817
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• The Invar tensor package: Differential invariants of Riemann
• The effect of matter structure on the gravitational waveform
• Propagation of the gravitational waves in a cosmological background
• Gravitational Wave Interference via Gravitational Lensing: Measurements of Luminosity Distance, Lens Mass, and Cosmological Parameters
• The wave nature of continuous gravitational waves from microlensing
• Gravitational wave propagation beyond geometric optics
• Gravitational Lensing of Gravitational Waves: Rotation of Polarization Plane
• Gravitational lensing beyond geometric optics: II. Metric independence

Cited by in corpus (4)

• Lensing rates of gravitational wave signals displaying beat patterns detectable by DECIGO and B-DECIGO
• Constraining cosmological parameters from strong lensing with DECIGO and B-DECIGO sources
• Dark photon bursts from compact binary systems and constraints
• Rotations of the polarization of a gravitational wave propagating in Universe