α-attractor inflation modified by GUP in light of ACT observations

Abstract

Here, the $\alpha$-attractor inflation is investigated within a framework incorporating a minimal measurable length, as implemented by the Generalized Uncertainty Principle (GUP). The GUP modifications to the Friedmann equations and cosmological perturbation parameters are employed to assess the model observational viability against the Atacama Cosmology Telescope (ACT) data. Our results indicate that in the $r-n_s$ plane, the predictions of the standard $\alpha$-attractor model ($\beta =0$) lies near the $2\sigma$ boundary of joint observations. More interestingly enough is that in the presence of GUP effect, the predictions of the model for the GUP parameter $\beta \gtrsim O\left({10}^{13}\right)$ shifts into the $68\%$ CL interval. This value for $\beta$ is in well agreement with upper bounds on the GUP parameter deduced from cosmological analysis as well as quantum and gravitational experiments.