observational status of zero-point length cosmic inflation

We examine observational status of cosmological inflation with a zeropoint length. by considering the zero-point length correction to the geometric part of the field equations, specially the hubble parameter, we derive modified background equations, slow-roll parameters and inflation observables including scalar spectral index and tensor-to-scalar ratio in this setup. we conduct numerical analysis on a power-law inflation as a toy model and also some other inflation potentials to assess the impact of a minimum length on the inflationary cosmology. in this regard, we compare our results with recent data from planck 2018 tt, te, ee +lowe +lensing, planck 2018 tt, te, ee +lowe +lensing+bk15, and planck 2018 tt, te, ee +lowe +lensing+ bk15+ bao at the %68 and %95 levels of confidence. we find that the impact of the zeropoint length varies across different potentials and its characteristic value is of different orders of magnitude (in units of the planck length), determined based on the varioustypes of the potentials. we show that, while some inflation potentials fall outside the mentioned datasets’ confidence levels in the absence of the zero-point length, they are in good agreement with the same datasets in the presence of the zero-point length. in this comparison, we obtain a range of consistency for the zero-point length with the mentioned observational data.