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Galaxies 2019, 7(1), 11;

Minimum Length Uncertainty Relations in the Presence of Dark Energy

School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
Received: 13 December 2018 / Revised: 31 December 2018 / Accepted: 4 January 2019 / Published: 8 January 2019
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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 Károlyházy (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 dS 1 / Λ . 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 G , c , , Λ , e . 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 ν 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. View Full-Text
Keywords: dark energy; minimum length uncertainty relations; quantum gravity dark energy; minimum length uncertainty relations; quantum gravity

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Lake, M.J. Minimum Length Uncertainty Relations in the Presence of Dark Energy. Galaxies 2019, 7, 11.

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