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.
