Cosmological Bounds on the Generalized Uncertainty Principle from the CMB

Abstract

We constrain the deformation parameter $\beta$ of the Generalized Uncertainty Principle with cosmological observations. A quadratic deformation of the Heisenberg uncertainty principle modifies the Friedmann equations of $\Lambda$CDM and gives rise to a phenomenological dynamical dark energy with a single free parameter, $\beta$. To avoid a singular behaviour for the effective dark energy equation of state parameter, we restrict the prior to non-negative values of $\beta$. Using Planck 2018 CMB temperature and polarization data together with DESI DR2 BAO and Pantheon+SH0ES supernovae, we find the upper limit $\beta <0.00728$ at $68\%$ confidence interval. The resulting cosmological model fits the data slightly better than $\Lambda$CDM, providing smaller value for the ${\chi }_{min}^2$, such that the Akaike Information Criterion to suggest statistical equivalency between the two models, although the Bayesian evidence favours the $\Lambda$CDM. Finally, the quadratic Generalized Uncertainty Principle does not alleviate the $H_0$ tension, it reduces the tension to $4.8\sigma$, that is, due to the small correlation between the $H_0-\beta$ parameters.

arXiv comment9 pages, 3 figures