Restudy on Dark Matter Time-Evolution in the Littlest Higgs model with T-parity

Following previous study, in the Littlest Higgs model (LHM), the heavy photon is supposed to be a possible dark matter candidate and its relic abundance of the heavy photon is estimated in terms of the Boltzman-Lee-Weinberg time-evolution equation. The effects of the T-parity violation is also considered. Our calculations show that when Higgs mass $M_H$ taken to be 300 GeV and dont consider T-parity violation, only two narrow ranges $133<M_{A_{H}}<135$ GeV and $167<M_{A_{H}}<169$ GeV are tolerable with the current astrophysical observation and if $135<M_{A_{H}}<167$ GeV, there must at least exist another species of heavy particle contributing to the cold dark matter. As long as the T-parity can be violated, the heavy photon can decay into regular standard model particles and would affect the dark matter abundance in the universe, we discuss the constraint on the T-parity violation parameter based on the present data. Direct detection prospects are also discussed in some detail.