FRW string cosmological solutions via Hojman symmetry

In this paper, we find exact string cosmological solutions for FRW cosmology, by using the Hojman symmetry approach. The string cosmology under consideration includes a scalar field phi(t) with the potential W(phi), and a totally antisymmetric field strength H mu nu rho which is specifically defined in terms of the scale factor a(t). We show that for this string cosmology, Hojman conserved quantities exist using which new exact solutions for the scale factor and the scalar field are obtained for specific potentials W(phi) with some free parameters. The presence of these parameters, together with those of arising from Hojman symmetry, is an important advantage using which one can construct the solutions a(t) and phi(t) with variety of cosmological behaviors.