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 } { \color { black } ,~ { } % \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 } ~ { } { \color { black } \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 ~ { } { \mathchoice { \mbox { } } { \mbox { } } { % \mbox { } } { \mbox { } } } \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 _ { 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 } ~ { } { \color { % black } \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 .