FRW string cosmological solutions via Hojman symmetry

In this paper, we find exact string cosmological solutions for FRW cosmology, by using Hojman symmetry approach. The string cosmology under consideration includes a scalar field $\psi(t)$ with the potential $W(\psi)$, 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 $W(\psi)$ 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 $\psi(t)$ with variety of cosmological behaviors.