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Register a new userA Possible Solution of the Cosmological Constant Problem based on Minimal Length Uncertainty and GW170817 and PLANCK Observations
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Added by
Abdel Nasser Tawfik
Publication date
2020
fields
Physics
and research's language is
English
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We propose the generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics as a quantum mechanical framework for the minimal length uncertainty at the Planck scale. We demonstrate that the GUP parameter, $beta_0$, could be best constrained by the the gravitational waves observations; GW170817 event. Also, we suggest another proposal based on the modified dispersion relations (MDRs) in order to calculate the difference between the group velocity of gravitons and that of photons. We conclude that the upper bound reads $beta_0 simeq 10^{60}$. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non-gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant $Lambda$ (apparently manifesting gravitational influences on the vacuum energy density), known as {it catastrophe of non-gravitating vacuum}, we suggest a possible solution for this long-standing physical problem, $Lambda simeq 10^{-47}~$GeV$^4/hbar^3 c^3$.
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Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On other hand this suggests modified dispersion relations (MDRs) enabling an estimation for the difference between the group velocity of gravitons and that of photons. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non-gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant (apparently manifesting gravitational influences on the vacuum energy density), we suggest a possible solution for the cosmological constant problem.
A quantum equation of gravity is proposed using the geometrical quantization of general relativity. The quantum equation for a black hole is solved using the Wentzel-Kramers-Brillouin (WKB) method. Quantum effects of a Schwarzschild black hole are demonstrated by solving the quantum equation while requiring a stationary phase and also by using the Einstein-Brillouin-Keller (EBK) quantization condition, and two approaches shows a consistent result. The WKB method is also applied to the McVittie-Thakurta metric, which describes a system consisting of Schwarzschild black holes and a scalar field. A possible interplay between quantum black holes and a scalar field is investigated in detail. The number density of black holes in the universe is obtained by applying statistical mechanics to a system consisting of black holes and a scalar field. A possible solution to the cosmological constant problem is proposed from a statistical perspective.
In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form the infinite-dimensional representation of the deformed SU(1,1) algebra. Our construction is independent of prior knowledge of the exact solution of the Schrodinger equation of the model. The approach can be generalized to the $D$-dimensional oscillator with non-commuting coordinates.
We consider a model with two parallel (positive tension) 3-branes separated by a distance $L$ in 5-dimensional spacetime. If the interbrane space is anti-deSitter, or is not precisely anti-deSitter but contains no event horizons, the effective 4-dimensional cosmological constant seen by observers on one of the branes (chosen to be the visible brane) becomes exponentially small as $L$ grows large.
Modifications of Heisenbergs uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change in the quantum mechanical commutation relations involving position and momenta. In particular, the modifications to the spectrum of the hydrogen atom can be naturally interpreted as a varying (with energy) fine structure constant. From the data on the energy levels we attempt to constrain the scale of the new physics and find that it must be close to or larger than the weak scale. Experiments in the near future are expected to change this bound by at least an additional order of magnitude.
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