Challenging $Λ$CDM with Higher-Order GUP Corrections

TL;DR

This work investigates quantum corrections to the $Λ$CDM framework arising from a two-parameter, higher-order Generalized Uncertainty Principle. By deforming the canonical algebra and applying it to a flat FLRW cosmology, the authors derive a modified Raychaudhuri equation and a generalized evolution for the matter density parameter, introducing a dynamical dark energy sector characterized by parameters $β$ and $γ$. They analyze two specific realizations: the quadratic case ($f=H^2/ρ_m$) with a closed-form $Ω_m(a)$ and a correction to $H^2$, and a higher-order extension with $f=(H^2/ρ_m)^γ$ requiring numerical solutions for $H(z)$; observational constraints are obtained from Cosmic Chronometers, DESI DR2 BAO, PantheonPlus, and Union3 data. Although the $GUP$-modified model can achieve fits comparable to or slightly better than $Λ$CDM in some datasets, model selection via AIC generally favors $Λ$CDM due to its simplicity, while the best-fit values tend toward negative $β$ and $γ>1$, implying phantom-like effective dark energy. The study highlights the potential of late-time cosmological data to probe quantum gravity-inspired corrections and outlines future work including CMB data incorporation to sharpen constraints and address cosmological tensions.

Abstract

We study quantum corrections to the $Λ$CDM model model arising from a minimum measurable length in Heisenberg's uncertainty principle. We focus on a higher-order Generalized Uncertainty Principle, beyond the quadratic form. This generalized GUP introduces two free parameters, and we determine the modified Friedmann equation. This framework leads to a perturbative cosmological model that naturally reduces to $Λ$CDM in an appropriate limiting case of the deformation parameters. We construct the modified cosmological scenario, analyze its deviations from the standard case, and examine it as a mechanism for the description of dynamical dark energy. To constrain the model, we employ Cosmic Chronometers, the latest Baryon Acoustic Oscillations from the DESI DR2 release, and Supernova data from the PantheonPlus and Union3 catalogues. Our analysis indicates that the modified GUP model is statistically competitive with the $Λ$CDM scenario, providing comparable or even improved fits to some of the combined datasets. Moreover, the data constrain the deformation parameter of the GUP model, with the preferred value found to be negative, which corresponds to a phantom regime in the effective dynamical dark energy description.

Figures (2)

• Figure 1: Confidence regions of the posterior parameters for the GUP-modified model using the datasets PP&OHD and PP&OHD&BAO.
• Figure 2: Confidence space for the posterior parameters for the GUP-modified model with for the datasets U3&OHD and U3&OHD&BAO