n-dimensional generalizations of the Friedmann-Robertson-Walker cosmology

Within the n-dimensional spatially flat Friedmann-Robertson-Walker cosmology, determined for a single scalar field minimally coupled to gravity, we derive the n-dimensional Lucchin-Mataresse (LM), Barrow-Burd-Lancaster-Madsen (BBLM), and Barrow-Saich (BS) cosmological solutions. No matter the dimensions one is dealing with, the potentials follow patterns similar to those ones of the corresponding standard 4-dimensional case; the self interacting potential for the n-LM inflationary model exhibits an exponential slow roll behavior as function of the scalar field, the potential of the n-BBLM model presents a Mexican-hat shape, while the potential for the n-BS cosmology, allowing for the simultaneous presence of a matter perfect fluid and a scalar field, follows a squared cosecant hyperbolic pattern.