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Global symmetry can guarantee the stability of dark matter particles (DMps).However, the nonminimal coupling between dark matter (DM) and gravity candestroy the global symmetry of DMps, which in turn leads to their decay. Underthe framework of nonminimal coupling between scalar singlet dark matter (ssDM)and gravity, it is worth exploring to what extent the symmetry of ssDM isbroken. It is suggested that the total amount of decay products of ssDM cannotexceed current observational constraints. Along these lines, the data obtainedwith satellites such as Fermi-LAT and AMS-02 can limit the strength of theglobal symmetry breaking of ssDM. Since the mass of many well--motivated DMcandidates may be in the GeV--TeV range, we determine a reasonable parameterrange for the lifetime in this range. We find that when the mass of the ssDM isaround the electroweak scale (246 GeV), the corresponding 3--$\sigma$ lowerlimits of the lifetime of ssDM is $5.3\times10^{26}$ s. Our analysis of ssDMaround the typical electroweak scale contains the most abundant decay channelsof all mass range, so the analysis of the behaviour of ssDM under the influenceof gravity is more comprehensive.

Observational constraints on dark matter decaying via gravity portals