Dark matter particles with properties identical to dark matter candidates that are hinted at by several international collaborations dedicated to experimental detection of dark matter (DAMA, CO-GENT, CRESST and CDMS-II, although not, most notably, by LUX), and which also have a dark matter asymmetry identical to the observed baryon asymmetry (Planck and Wilkinson Microwave Anisotropy Probe), may produce a significant impact on the evolution of the first generation of lowmetallicity stars. The lifetimes of these stars in different phases of stellar evolution are significantly extended, namely, in the pre-main sequence, main sequence, and red giant phases. In particular, intermediate-mass stars in the red giant phase experience significant changes in their luminosity and chemical composition. The annihilations of dark matter particles affect the interior of the star in such a way that the 3α−reaction becomes less efficient in the production of carbon and oxygen. This dark matter effect contradicts the excess of carbon and other metals observed today in stars of low mass and low metallicity. Hence, we can impose an upper limit on the dark matter halo density, and therefore on the redshift, at which the first generation of low-metallicity stars formed.