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

Abstract

Independent tests aiming to constrain the value of the cosmological constant $\Lambda$ are usually difficult because of its extreme smallness $\left(\Lambda \simeq 1\times 10^{-52}{\text{m}}^{-2},\text{or}2.89\times 10^{-122}\text{in Planck units}\right)$. Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the $\simeq 10^{-43}-10^{-44}{\text{m}}^{-2}\left(5-1\times 10^{-113}\text{in Planck units}\right)$ level, but they may turn out to be somewhat optimistic since $\Lambda$ has not yet been explicitly modeled in the planetary data reductions. Accurate $\left({\sigma }_{{\tau }_{\text{p}}}\simeq 1-10\mu \text{s}\right)$ 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 ${\overline{\Delta \delta \tau }}_{\text{p}}^{\Lambda }$, a S2-like orbital configuration with $e=0.8839,P_{\text{b}}=16\text{yr}$ would allow to obtain preliminarily an upper bound of the order of $\left|\Lambda \right|\lesssim 9\times 10^{-47}{\text{m}}^{-2}\left(\lesssim 2\times 10^{-116}\text{in Planck units}\right)$ if only ${\sigma }_{{\tau }_{\text{p}}}$ were to be considered. Our results can be easily extended to modified models of gravity using $\Lambda -$type parameters.

Latex2e, 12 pages, 1 table, 1 figure, 79 references

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Cited by in corpus (9)

• Test-particle dynamics in general spherically symmetric black hole spacetimes
• Pulsar timing in extreme mass ratio binaries: a general relativistic approach
• Cosmic censorship conjecture in a general Kerr-Newman black hole
• Dark Energy as a Critical Period in Binary Motion: Bounds from Multi-scale Binaries
• Lense-Thirring precession and modified gravity constraints
• Gravitational Burst Radiation from Pulsars in the Galactic centre and stellar clusters
• Anti-de Sitter neutron stars in the theory of gravity with nonminimal derivative coupling
• Two body problem in presence of cosmological constant
• Orbital precession and other properties of two-body motion in the presence of dark energy