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Dark Matter, Parallel Universe and Multiple Higgs Signals at the ILC

The existence of dark matter is now well established by several indirect experiments. Several candidates for dark matter has also been proposed. However, the dark matter can just be like our ordinary matter in a parallel Universe with both Universes being described by their own non-abelian gauge symmetries forbidding any kinetic mixing. However, the quartic Higgs interactions involving Higgs fields between the two Universes are allowed by the symmetries of the model. The ensuing mixing between the two lightest Standard Model like Higgses gives rise to interesting signatures at the proposed international electron-positron collider (ILC) specially in the case when mass splitting between the two surviving light Higgs bosons are small ($\sim$ 100 MeV) so that they can not be resolved at the LHC.