Search for possible signals of space-time non-commutativity from ACT DR6

TL;DR

This work probes quantum gravity phenomenology by modeling inflation in a κ-deformed non-commutative space-time, deriving a κ-Poincaré invariant scalar field theory and its κ-deformed oscillator algebra, which yield scale-dependent corrections to the scalar and tensor primordial power spectra. The authors derive closed-form expressions for the deformed spectra and spectral indices, showing that κ-deformation can raise the scalar index and potentially reconcile ACT DR6 with Planck results. A comprehensive Bayesian analysis using ACT DR6 data constrains the non-commutative length scale to around $λ\sim10^{-30}$ m, implying that precision cosmology can probe Planck-scale physics. The results, while not definitive, point to a consistent framework where early-universe quantum-gravity effects leave detectable imprints in CMB observables, motivating further theoretical development and data-driven tests.

Abstract

The non-commutative geometry offers an effective framework for describing physics at the Planck scale, incorporating generic quantum-gravitational effects through an intrinsic minimal length and the $κ$-deformed space-time stands out as a particularly well-developed model based on a Lie-algebraic type non-commutative space-time structure. We investigate the inflationary paradigm and the associated primordial perturbations within the framework of $κ$-deformed non-commutative space-time. By constructing a scalar field theory invariant under the $κ$-Poincaré algebra, we derive the deformed oscillator algebra for the field modes of the primordial perturbations resulting in the non-trivial scale dependent modification of both the scalar and tensor power spectra. Further, we compute the corresponding $κ$-deformed corrections to the scalar spectral index and its running, finding that the $κ$-deformation naturally provides a higher value for spectral index which offers a potential resolution to the discrepancy between the values reported by PLANCK and ACT. Finally we perform a comprehensive Bayesian analysis using the latest ACT DR6 data, constraining the $κ$-deformed non-commutative length scale to $λ=2.17^{+2.33}_{-1.53}\times 10^{-30}m$ at the $1σ$ confidence level, suggesting the precision cosmology as a powerful probe of quantum gravity phenomenology.

Figures (1)

• Figure 1: The marginalised posterior distribution of the slow-roll parameters and $\kappa$-deformation scale derived using the latest ACT DR6 measurements of scalar spectral index and its running