Exploring constraints of Dirac fields on gravitational wave dephasing

Abstract

Modern gravitational-wave (GW) parameter estimation greatly depends on highly precise vacuum templates framed in General Relativity which assume that compact binaries coalesce in an absolute vacuum. But actual astrophysical backgrounds possess dense matter distributions, including baryonic accretion disks, dark matter halos, and background cosmic Dirac fields. In this paper, the quantitative impact of external matter fields on the inspiral phase of compact binaries has been evaluated. Focus is specifically on a black hole binary (36 M_⊙ + 29 M_⊙) like GW150914. We model the dissipative corrections introduced by gravitational drag (dynamical friction) at the negative Post-Newtonian (-2PN) order in natural geometric units (G = c = 1).

Using standard analytical implementations and numerical simulations, the phase deviation ∆Ψ(ƒ) has been mapped across the ground-based (aLIGO) observation window (30 - 100 Hz). The indication of the findings is that for cosmic localized Dirac field configurations (ranging from ρ ∼ 10^-50 m^-2 to 10^-26 m^-2), the cumulative phase shifts at 30 Hz remain entirely suppressed (< 10^-15 rad). This validates the fact that current ground-based observing runs operating within the "Vacuum Limit," leave standard general relativity parameter estimations unperturbed while imposing the constraints will be necessary for future multi-band space missions.