Post-Newtonian Gravitational Waves with cosmological constant $\Lambda$ from the Einstein-Hilbert theory

Abstract

We study the Post-Newtonian approach implemented to the Einstein-Hilbert action adding the cosmological constant $\Lambda$ at 1PN order. We consider very small values of $\Lambda$ to derive the Lagrangian of a two body compact system at the center of mass frame at 1PN. Furthermore, the phase function $\varphi (t)$ is obtained from the balance equation and the two polarizations $h_{+}$ and $h_{\times }$ are also calculated. We observe changes due to $\Lambda$ only at very low frequencies and we notice that it plays the role of "stretch" the spacetime such that both amplitudes become smaller; however, given its nearly negligible value, $\Lambda$ has no relevance at higher frequencies whatsoever.

arXiv comment20 pages, 7 figures

References in corpus (28)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order
• Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order
• Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations
• The Case for an Accelerating Universe from Supernovae
• Post-Newtonian Gravitational and Scalar Waves in Scalar-Gauss-Bonnet Gravity
• Scales Set by the Cosmological Constant
• Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time
• Solar and stellar system tests of the cosmological constant
• Asymptotics with a positive cosmological constant: III. The quadrupole formula
• Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order
• Gravitational waves from isolated systems: Surprising consequences of a positive cosmological constant
• The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection Experiment
• Gravitational form factors of a baryon with spin-3/2
• Gravitational Wave Memory In dS${}_{4+2n}$ and 4D Cosmology
• Gravitational waves in the presence of a cosmological constant
• Cosmological Horizon and the Quadrupole Formula in de Sitter Background
• Cosmological Constant and Local Gravity
• Gravitational waves in Brans-Dicke Theory with a cosmological constant
• A generalization of the quadruple formula for the energy of gravitational radiation in de Sitter spacetime
• The effect of the cosmological constant on gravitational wave quadrupole signal

Cited by in corpus (1)

• Exploring Scalarized Einstein-Gauss-Bonnet Theories Through the Lens of Parametrized Post-Newtonian Formalism