We derive a special scalar field potential using the anisotropic Bianchi type I cosmological model from canonical quantum cosmology under determined conditions in the evolution to anisotropic variables ${\beta }_{\pm }$. In the process, we obtain a family of potentials that has been introduced by hand in the literature to explain cosmological data. Considering supersymmetric quantum cosmology, this family is scanned, fixing the exponential potential as more viable in the inflation scenario $V(\varphi )=V_0{e}^{-\sqrt{3}\varphi }$.

• Received 26 March 2010

DOI:https://doi.org/10.1103/PhysRevD.82.044008