From Geometry to Observation: Gravitational Waves and the Raychaudhuri Equation

Abstract

Gravitational waves (GWs) are independent of any particular theory of gravity. The universality of this notion is highlighted by the Raychaudhuri equation (RE), which is independent of any theory of gravity and contains the Ricci tensor $R_{\mu \nu }$ as a key ingredient, thereby connecting spacetime geometry with matter-energy content. Under small metric perturbations, $R_{\mu \nu }\propto \square h_{\mu \nu }$, where $h_{\mu \nu }$ is the perturbation, indicating that various gravity theories, via their corresponding $R_{\mu \nu }$, produce different gravitational wave equations. In the framework of Einstein's gravity, this leads to the standard wave equation. This study analyzes a modified form, {\it GW-inspired RE}, within the homogeneous and isotropic FLRW background to investigate late-time cosmic acceleration and structure formation. We employ {\it Pantheon+ SNe Ia, Hubble, and BAO} datasets to constrain model parameters through Bayesian inference utilizing NUTS in {\it NumPyro}. A nuisance parameter ${\mu }_0$ is introduced to address residual systematics. This facilitates a robust estimation of $H_0$, ${\Omega }_{DE,0}$, and $r_d$, which addresses the resolution of the Hubble tension. We analyze the redshift evolution of the deceleration parameter, $q(z)$, both with and without ${\mu }_0$, emphasizing its influence on cosmic dynamics. The GW-inspired RE is reformulated as a harmonic oscillator, providing insight into expansion and geodesic focusing. A graphical comparison demonstrates the relationship $d_L^{GW}(z)=d_L^{EM}(z)$ utilizing GWOSC data. Thus, the RE in the context of small perturbation of the metric opens up whole new vistas of {\it observational astronomy.}

19 pages, 10 figures, 6 tables, Accepted from Physics of the Dark Universe

References in corpus (21)

• f(R,T) gravity
• The Pantheon+ Analysis: Cosmological Constraints
• Bayes in the sky: Bayesian inference and model selection in cosmology
• A gravitational-wave standard siren measurement of the Hubble constant
• The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space
• The 1965 Penrose singularity theorem
• Data analysis recipes: Fitting a model to data
• The Raychaudhuri equations: a brief review
• Testing the interaction between dark energy and dark matter via latest observations
• Data Analysis of three parameter models of deceleration parameter in FRW Universe
• Reconstruction of $f(R)$ gravity models for an accelerated universe using Raychaudhuri equation
• Reconstruction of $f(R,T)$ gravity model via the Raychaudhuri equation
• Raychaudhuri equation in $k$-essence geometry: conditional singular and non-singular cosmological models
• Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory
• Self Similar Collapse and the Raychaudhuri equation
• Form Invariance of Raychaudhuri equation in the presence of Inflaton-type fields
• NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation
• Modified $f(R,T)$ theory in light of gravitational wave standard sirens
• Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework