Form Invariance of Raychaudhuri equation in the presence of Inflaton-type fields

We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fields $\phi$ whose Lagrangian is non-canonical and of the form $\mathcal{L}(X,\phi )=-V(\phi )F(X)$, with $X=\frac{1}{2}{g}_{\mu \nu }{\mathrm{\nabla }}^{\mu }\phi {\mathrm{\nabla }}^{\nu }\phi$ and $V(\phi )$ the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus our results are in sync with the latest observations. So the Raychaudhuri equation can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios.