Constraining inflationary models via de-Sitterization of Bianchi Cosmologies

Our Universe is isotropic and homogeneous when we observe it on $\gtrsim$ Mpc length scales. It is desirable that present state of the Universe has no dependence on its initial geometry. In case of Bianchi Universes, i.e., anisotropic but homogeneous Universe, this has already been demonstrated via cosmological constant in a process that we call \textit{de Sitterization}. In this letter, we show that for Bianchi Universe, the same state can be achieved by a homogeneous inflaton field with a general potential and satisfying a criterion without the need of a cosmological constant. More importantly, we show that the same condition can constrain models of inflation and explain our idea with examples.