Cosmological constraints on GUP from modified Friedmann equations

Abstract

The Generalized Uncertainty Principle (GUP) has emerged in numerous attempts to a theory of quantum gravity and predicts the existence of a minimum length in Nature. In this work, we consider two cosmological models arising from Friedmann equations modified by the GUP (in its linear and quadratic formulations) and compare them with observational data. Our aim is to derive constraints on the GUP parameter and discuss the viability and physical implications of such models. We find for the parameter in the quadratic formulation the constraint $$\alpha ^{2}_{Q}<10^{59}$$ α Q 2 < 10 59 (tighter than most of those obtained in an astrophysical context) while the linear formulation does not appear compatible with present cosmological data. Our analysis highlights the powerful role of high-precision cosmological probes in the realm of quantum gravity phenomenology.

Interacting quintessence in light of generalized uncertainty principle: cosmological perturbations and dynamics

“…The deformation parameter can be positive or negative [77,78]. Moreover, there are various proposed theoretical constraints in the literature from quantum systems [79,80] and also from gravitational systems [81,82].…”

“…Hence, by writing in Fourier form and setting δu i = 0, for the exponential potential, the perturbative equations ( 80)- (82) are written as follows…”

Quantum cosmology with dynamical vacuum in a minimal-length scenario

“…The quantization process takes place in the framework of mini-superspace and according with the Wheeler-DeWitt quantization scheme, p a −→p a (42) and…”

“…Although the most common modified or deformed commutation relation (MCR) associated with a GUP (KMM GUP [37]) is quadratic in the momentum operator, effects of a MCR with a linear term in the momentum operator, which leads to a minimal length and a maximum momentum [38], have been studied in contexts of cosmological models [10,11,[39][40][41]. Nevertheless, apparently this GUP leads to non-unitary theories [40] and it is not compatible with current data available [42].…”

“…This modified uncertainty principle has terms proportional to even powers in the position uncertainty [58]. Cosmological observational data have been used to obtain constraints for GUP parameters [21,42,48,56,59]. 2 The 3rd quantization consists of initially considering the Wheeler-DeWitt equation as a classical equation of a classical field (the wave function of the Universe in the 2nd quantization) which then is turned an operator.…”