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

TL;DR

This work investigates $α$-attractor inflation under a minimal length induced by the Generalized Uncertainty Principle (GUP). It modifies the Friedmann equations and perturbation spectra, focusing on the α-attractor T-model with $V(φ)=Λ^4 \tanh^2(φ/\sqrt{6α}M_p)$, and derives the GUP-influenced observables $n_s$ and $r$ that reduce to the standard results when $β=0$. By confronting the predictions with the joint ACT DR6 Planck DESI BK18 data, the study shows that $β \gtrsim 10^{13}$ shifts the model into the 68% CL region, while larger $β$ tightens the allowed range of $α$ (maximum near $α ≈ 0.74$ at $β ≈ 1.4×10^{13}$). The results demonstrate that quantum gravity motivated minimal length effects can reconcile inflationary models with high-precision cosmological observations and place cosmological constraints on the GUP parameter $β$.

Abstract

Here, the $α$-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 $α$-attractor model ($β=0$) lies near the $2σ$ boundary of joint observations. More interestingly enough is that in the presence of GUP effect, the predictions of the model for the GUP parameter $β\gtrsim O(10^{13})$ shifts into the $68\%$ CL interval. This value for $β$ is in well agreement with upper bounds on the GUP parameter deduced from cosmological analysis as well as quantum and gravitational experiments.

Figures (6)

• Figure 1: Field value of the scalar field at the pivot scale $\phi_*/M_{\rm p}$ versus the GUP parameter $\beta$ for different values of $\alpha$. Here, $N_*=60$ is assumed for the horizon exit of the pivot scale.
• Figure 2: Evolution of the scalar field $\phi/M_p$ as a function of $e$-folds number $N$ for (a) $\alpha=1$ and (b) $\alpha=10$. Each panel displays six curves corresponding to different values of the GUP parameter $\beta=(0, 10^{10}, 10^{11}, 10^{12}, 10^{13}, 10^{14})$. The case of $\beta=0$ refers to the standard model of inflation.
• Figure 3: Evolution of the Hubble parameter $H$ as a function of $e$-folds number $N$ for (a) $\alpha=1$ and (b) $\alpha=10$. Each panel displays six curves corresponding to different values of the GUP parameter $\beta=(0, 10^{10}, 10^{11}, 10^{12}, 10^{13},10^{14})$.
• Figure 4: The $r-n_s$ plane showing predictions for the $\alpha$-attractor T-model modified by GUP. The $r-n_s$ curves correspond to fixed GUP parameter values: $\beta=0$ (black), $\beta=10^{12}$ (purple), $\beta=10^{13}$ (blue), $\beta=10^{14}$ (green), and $\beta=10^{15}$ (red). Along each curve, $\alpha$ varies from $0.001$ at the bottom to $10$ at the top.
• Figure 5: The inflationary observables as a function of the GUP parameter $\beta$ for several fixed values of $\alpha$. (a) The scalar spectral index $n_s$ versus $\beta$. (b) The tensor-to-scalar ratio $r$ versus $\beta$ on a logarithmic scale. The dark and light purple shaded regions show the 68% and 95% CL constraints from the combined P-ACT-LB-BK18 dataset, respectively.