Application of the form invariance transformations of the scalar cosmological model in inflation theory

Abstract

In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a forminvariance symmetry, which is arising from the form invariance transformation. Form invariance transformation is defined by linear function ¯ρ = n 2 ρ in general case. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at exponent of the scale factor α > 1, but stability of the transformation model depends on index n. Slow roll parameters and spectral induces is obtained and at large α they agree with Planck observation data.