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For the inflaton field we determine a new exact solution by using the Liesymmetry analysis. Specifically, we construct a second-order differentialmaster equation for arbitrary scalar field potential by assuming that thespectral index for the density perturbations $n_{s}$ and the scalar to tensorratio $r$ are related as $n_{s}-1=h\left( r\right) $. Function $h\left(r\right) $ is classified according to the admitted Lie symmetries for themaster equation. The possible admitted Lie symmetries form the $A_{2}$,$A_{3,2}$, $A_{3,3}$ and $sl\left( 3,R\right) $ Lie algebras. The newinflationary solution is recovered by the Lie symmetries of the $A_{3,3}$algebra. Scalar field potential is derived explicitly, while we compare theresulting spectral indices with the observations.

New inflationary exact solution from Lie symmetries