  We propose a dark-matter (DM) admixed density-dependent equation of state
where the fermionic DM interacts with the nucleons via Higgs portal. Presence
of DM can hardly influence the particle distribution inside neutron star (NS)
but can significantly affect the structure as well as equation of state (EOS)
of NS. Introduction of DM inside NS softens the equation of state. We explored
the effect of variation of DM mass and DM Fermi momentum on the NS EOS.
Moreover, DM-Higgs coupling is constrained using dark matter direct detection
experiments. Then, we studied cooling of normal NSs using APR and DD2 EOSs and
DM admixed NSs using dark-matter modified DD2 with varying DM mass and Fermi
momentum. We have done our analysis by considering different NS masses. Also DM
mass and DM Fermi momentum are varied for fixed NS mass and DM-Higgs coupling.
We calculated the variations of luminosity and temperature of NS with time for
all EOSs considered in our work and then compared our calculations with the
observed astronomical cooling data of pulsars namely Cas A, RX J0822-43, 1E
1207-52, RX J0002+62, XMMU J17328, PSR B1706-44, Vela, PSR B2334+61, PSR
B0656+14, Geminga, PSR B1055-52 and RX J0720.4-3125. It is found that APR EOS
agrees well with the pulsar data for lighter and medium mass NSs but cooling is
very fast for heavier NS. For DM admixed DD2 EOS, it is found that for all
considered NS masses, all chosen DM masses and Fermi momenta agree well with
the observational data of PSR B0656+14, Geminga, Vela, PSR B1706-44 and PSR
B2334+61. Cooling becomes faster as compared to normal NSs in case of
increasing DM mass and Fermi momenta. It is infered from the calculations that
if low mass super cold NSs are observed in future that may support the fact
that heavier WIMP can be present inside neutron stars.
