Perspectives on Constraining a Cosmological Constant-Type Parameter with Pulsar Timing in the Galactic Center

Independent tests aiming to constrain the value of the cosmological constant A are usually difficult because of its extreme smallness (Lambda similar or equal to 1 x 10(-52) m(-2), or 2.89 x 10(-122) in Planck units). Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the similar or equal to 10(-43)-10(-44) m(-2) (5-1 x 10(-113) in Planck units) level, but they may turn out to be optimistic since A has not yet been explicitly modeled in the planetary data reductions. Accurate (sigma(tau p) similar or equal to 1-10 mu s) 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 (Delta delta(tau p)) over bar (Lambda), an S2 -like orbital configuration with e = 0.8839, P-b = 16 yr would permit a preliminarily upper bound of the order of vertical bar Lambda vertical bar less than or similar to 9 x 10(-47) m(-2) (less than or similar to 2 x 10(-116) in Planck units) if only sigma(tau p) were to be considered. Our results can be easily extended to modified models of gravity using Lambda-type parameters.