In this talk, we will discuss constraints imposed by the symmetry of approximate conformal invariance during the inflationary phase of early universe cosmology. More specifically, with this symmetry-based approach, we will understand the possible signatures of the initial conditions of inflation on the non-Gaussianities (focussing on scalar fluctuations) in single-field slow-roll inflation. We will consider a generalized class of vacua, known as alpha−vacua, which is allowed by the symmetries of the de-Sitter space-time during inflation.