  Inspired by String T-duality and taking into account the zero-point length
correction, $l_0$, to the gravitational potential, we construct modified
Friedmann equations by applying the first law of thermodynamics on the apparent
horizon of the Friedmann-Robertson-Walker (FRW) Universe. The cosmological
viability of this extended scenario is investigated by studying influences on
the evolution of the early Universe and performing the cosmographic analysis.
Furthermore, we explore the inflationary paradigm under the slow-roll
condition. By testing the model against observational data, the zero-point
length is constrained around the Planck scale, in compliance with the original
assumption from String T-duality. We also study the growth of density
perturbations in the linear regime. It is shown that the zero-point length
stands out as an alternative characterization for the broken-power-law
spectrum, which provides a better fitting for the experimental measurements
comparing to the simple power-law potential. Finally, we focus on implications
for the primordial gravitational waves (PGWs) spectrum. Should the zero-point
length be running over energy scales, as is the case for all parameters and
coupling constants in quantum gravity under renormalization group
considerations, deviations from General Relativity (GR) might be potentially
tested through upcoming PGW observatories.
