Perspectives on constraining a cosmological constant-type parameter with pulsar timing in the Galactic Center

TL;DR

This paper explores how pulsar timing near the Galactic Center could significantly improve constraints on the cosmological constant, surpassing current Solar System bounds by several orders of magnitude.

Contribution

It proposes using pulsar timing measurements in the Galactic Center to set tighter bounds on the cosmological constant, extending to modified gravity models.

Findings

Potential to improve bounds on Λ by several orders of magnitude.

A specific orbital configuration (like S2) could constrain |Λ| to ~9×10⁻⁴⁷ m⁻².

Method applicable to Λ-type parameters in modified gravity theories.

Abstract

Independent tests aiming to constrain the value of the cosmological constant $\Lambda$ are usually difficult because of its extreme smallness $\left(\Lambda \simeq 1\times 10^{-52}~\textrm{m}^{-2},~\textrm{or}~2.89\times 10^{-122}~\textrm{in Planck units}\right)$. Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the $\simeq 10^{-43}-10^{-44}~\textrm{m}^{-2}~\left(5-1\times 10^{-113}~\textrm{in Planck units}\right)$ level, but they may turn out to be somewhat optimistic since $\Lambda$ has not yet been explicitly modeled in the planetary data reductions. Accurate $\left(\sigma_{\tau_\textrm{p}}\simeq 1-10~\mu\textrm{s}\right)$ timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By looking at the average time shift per orbit $\overline{\Delta\delta\tau}^\Lambda_\textrm{p}$, a S2-like orbital configuration with $e=0.8839,~P_\textrm{b}=16~\textrm{yr}$ would allow to obtain preliminarily an upper bound of the order of $\left|\Lambda\right|\lesssim 9\times 10^{-47}~\textrm{m}^{-2}~\left(\lesssim 2\times 10^{-116}~\textrm{in Planck units}\right)$ if only $\sigma_{\tau_\textrm{p}}$ were to be considered. Our results can be easily extended to modified models of gravity using $\Lambda-$type parameters.