Minimum length uncertainty relations in the presence of dark energy

TL;DR

This paper proposes a dark energy-modified minimum length uncertainty relation (DE-MLUR) that incorporates the cosmological constant, leading to new insights into particle mass scales, cosmological implications, and potential experimental tests.

Contribution

It introduces a novel uncertainty relation incorporating dark energy effects, linking quantum mechanics with cosmology and deriving new mass scale estimates.

Findings

Charged particle limit near electron mass

Neutral particle limit consistent with neutrino bounds

Potential for experimental tests of dark energy effects in quantum regimes

Abstract

We introduce a dark energy-modified minimum length uncertainty relation (DE-MLUR) or dark energy uncertainty principle (DE-UP) for short. The new relation is structurally similar to the MLUR introduced by K{\' a}rolyh{\' a}zy (1968), and reproduced by Ng and van Dam (1994) using alternative arguments, but with a number of important differences. These include a dependence on the de Sitter horizon, which may be expressed in terms of the cosmological constant as $l_{\rm dS} \sim 1/\sqrt{\Lambda}$. Applying the DE-UP to both charged and neutral particles, we obtain estimates of two limiting mass scales, expressed in terms of the fundamental constants $\left\{G,c,\hbar,\Lambda, e\right\}$. Evaluated numerically, the charged particle limit corresponds to the order of magnitude value of the electron mass ($m_e$), while the neutral particle limit is consistent with current experimental bounds on the mass of the electron neutrino ($m_{\nu_e}$). Possible cosmological consequences of the DE-UP are considered and we note that these lead naturally to a holographic relation between the bulk and the boundary of the Universe. Low and high energy regimes in which dark energy effects may dominate canonical quantum behaviour are identified and the possibility of testing the model using near-future experiments is briefly discussed.