We approach the cosmological inflation thought symmetries of differential equations. We consider the general inflaton field in a homogeneous Friedmann--Lema\^{ \i}tre--Robertson--Walker spacetime and with the use of conformal transformations we are able to write the generic algebraic solution for the field equations. We put emphasis on the inflationary models and we show how we can construct new inflationary models from already known models by using symmetry transformations.
Categories: gr-qc math-ph math.MP