  Global symmetry can guarantee the stability of dark matter particles (DMps).
However, the nonminimal coupling between dark matter (DM) and gravity can
destroy the global symmetry of DMps, which in turn leads to their decay. Under
the framework of nonminimal coupling between scalar singlet dark matter (ssDM)
and gravity, it is worth exploring to what extent the symmetry of ssDM is
broken. It is suggested that the total amount of decay products of ssDM cannot
exceed current observational constraints. Along these lines, the data obtained
with satellites such as Fermi-LAT and AMS-02 can limit the strength of the
global symmetry breaking of ssDM. Since the mass of many well--motivated DM
candidates may be in the GeV--TeV range, we determine a reasonable parameter
range for the lifetime in this range. We find that when the mass of the ssDM is
around the electroweak scale (246 GeV), the corresponding 3--$\sigma$ lower
limits of the lifetime of ssDM is $5.3\times10^{26}$ s. Our analysis of ssDM
around the typical electroweak scale contains the most abundant decay channels
of all mass range, so the analysis of the behaviour of ssDM under the influence
of gravity is more comprehensive.
