The dark matter content of the Universe is likely to be a mixture of matter and antimatter , perhaps comparable to the measured asymmetric mixture of baryons and antibaryons . During the early stages of the Universe , the dark matter particles are produced in a process similar to baryogenesis , and dark matter freeze-out depends on the dark matter asymmetry and the annihilation cross section ( s-wave and p-wave annihilation channels ) of particles and antiparticles . In these \eta - parametrised asymmetric dark matter models ( \eta ADM ) , the dark matter particles have an annihilation cross section close to the weak interaction cross section , and a value of dark matter asymmetry \eta close to the baryon asymmetry \eta _ { B } . Furthermore , we assume that dark matter scattering of baryons , namely , the spin-independent scattering cross section , is of the same order as the range of values suggested by several theoretical particle physics models used to explain the current unexplained events reported in the DAMA/LIBRA , CoGeNT and CRESST experiments . Here , we constrain \eta - parametrised asymmetric dark matter by investigating the impact of such a type of dark matter on the evolution of the Sun , namely , the flux of solar neutrinos and helioseismology . We find that dark matter particles with a mass smaller than 15 GeV , a spin-independent scattering cross section on baryons of the order of a picobarn , and an \eta - asymmetry with a value in the interval 10 ^ { -12 } -10 ^ { -10 } , would induce a change in solar neutrino fluxes in disagreement with current neutrino flux measurements . This result is also confirmed by helioseismology data . A natural consequence of this model is suppressed annihilation , thereby reducing the tension between indirect and direct dark matter detection experiments , but the model also allows a greatly enhanced annihilation cross section . All the cosmological \eta - asymmetric dark matter scenarios that we discuss have a relic dark matter density \Omega h ^ { 2 } and baryon asymmetry \eta _ { B } in agreement with the current WMAP measured values , \Omega _ { DM } h ^ { 2 } = 0.1109 \pm 0.0056 and \eta _ { B } = 0.88 \times 10 ^ { -10 } .