Reconstructing inflationary potential from NANOGrav 15-year data: A robust study using Non-Bunch Davies initial condition

We discuss the theoretical framework behind reconstruction of a generic class of inflationary potentials for canonical single-field slow-roll inflation in a model-independent fashion. The Non-Bunch Davies (NBD) initial condition is an essential choice to determine the structure of potential and to accommodate the blue-tilted tensor power spectrum feature recently observed in NANOGrav. Using the reconstruction technique we found the favoured parameter space which supports blue tilted tensor power spectrum. The validity of the EFT prescription in inflation is also maintained through the use of a new field excursion formula while keeping the necessary and sufficient conditions on the sub-Planckian field values in check. We find that the reconstructed potential display inflection point behaviour, which has deeper connection with high energy physics.