Implications of minimum and maximum length scales in cosmology

Abstract

We investigate the cosmological implications of the generalized and extended uncertainty principle (GEUP), and whether it could provide an explanation for the dark energy. The consequence of the GEUP is the existence of a minimum and a maximum length, which can in turn modify the entropy area law and also modify the Friedmann equation. The cosmological consequences are studied by paying particular attention to the role of these lengths. We find that the theory allows a cosmological evolution where the radiation-and matter-dominated epochs are followed by a long period of virtually constant dark energy, that closely mimics the ΛCDM model. The main cause of the current acceleration arises from the maximum length scale β, governed by the relation Λ ∼ −β −1 W (−β −1 ). Using recent observational data (the Hubble parameters, type Ia supernovae, and baryon acoustic oscillations, together with the Planck or WMAP 9-year data of the cosmic microwave background radiation), we estimate constraints to the minimum length scale α 10 81 and the maximum length scale β ∼ −10 −2 .

Cosmological constraints on GUP from modified Friedmann equations

“…Nonetheless, a negative GUP parameter has interesting implications, see e.g. [28,[38][39][40][41]. For the purposes of this work, we found that allowing α L to be negative leads to the unphysical result H (z) < 0.…”

“…To the best of our knowledge, there are very few studies that aim to constrain the GUP parameter with cosmological observations. One of them is [28], which makes use of the apparent horizon formalism to inquire whether the GUP effects could account for dark energy. However, the author mostly deals with an alternative formulation of the GUP, the General Extended Uncertainty Principle (GEUP), which predicts the existence of a maximum length as well as a minimum one.…”

“…However, the instances in which theoretical studies are complemented by comparison with experimental data, especially in a cosmological setting, are, to the best of our knowledge, scarce (exceptions are e.g. [28,29]).…”

Quantum cosmology with dynamical vacuum in a minimal-length scenario

“…In [4] the authors use GEUP to show that a non-zero cosmological constant can restore the Chandrasekhar limit. Effects of GEUP in cosmology has been studied in [56]. Modified uncertainty principles that induce a maximum length have been employed in order to describe the cosmological particle horizon [57].…”

“…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.…”