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We study the decay of 125 GeV Higgs boson to light LSP neutralino in thephenomenological minimal supersymmetric standard model in the context ofcollider searches and astrophysical experiments. We consider the parameterspace for light neutralinos that can be probed via the invisible Higgs decaysand higgsino searches at the ILC. We consider the cases where the lightneutralino is compatible with the observed relic density or where the thermalrelic is over-abundant, pointing to non-standard cosmology. In the former case,when the neutralino properties give rise to under-abundant relic density, thecorrect amount of relic abundance is assumed to be guaranteed by eitheradditional DM particles or by non-thermal cosmology. We contrast thesedifferent cases. We assess what astrophysical measurements can be made, inaddition to the measurements made at the ILC, which can provide a clue to thenature of the light neutralino. We find that a number of experiments, includingXenon-nT, PICO-250, LZ in conjunction with measurements made at the ILC oninvisible Higgs width can pin down the nature of this neutralino, along withits cosmological implications. Additionally, we also point out potential LHCsignatures that could be complementary in this region of parameter space.

The invisible decay of Higgs boson in the context of a thermal and non-thermal relic in MSSM