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Register a new userA minimal Length Uncertainty Approach to Cosmological Constant Problem
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Added by
Abdel Nasser Tawfik
Publication date
2020
fields
Physics
and research's language is
English
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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.
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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$^4/hbar^3 c^3$.
In an earlier paper, it is proposed that, due to resonance tunneling effect, tunneling from a large cosmological constant $Lambda$ site in the stringy comic landscape can be fast, while tunneling from a small $Lambda$ site may take exponentially long time. Borrowing the renormalization group analysis of the conductance in the Anderson localization transition, we treat the landscape as a multi-dimensional random potential and find that the vastness of the landscape leads to a sharp transition at a small critical value $Lambda_{c}$ from fast tunneling for $Lambda > Lambda_{c} $ to suppressed tunneling for $Lambda_{c} > Lambda >0$. Mobility in the landscape makes eternal inflation highly unlikely. As an illustration, we find that $Lambda_{c}$ can easily be exponentially small compared to the string/Planck scale. These properties may help us in finding a qualitative understanding why todays dark energy is so small.
One brief idea on the extended uncertainty relation and the dynamical quantization of space-time at the Planck scale is presented. The extended uncertainty relation could be a guiding principle toward the renormalizable quantum gravity. Cosmological constant in the Universe as a quantum effect is also roughly estimated.
We consider the Kepler two-body problem in presence of the cosmological constant $Lambda$. Contrary to the classical case, where finite solutions exist for any angular momentum of the system $L$, in presence of $Lambda$ finite solutions exist only in the interval $0<L< L_{lim}(Lambda)$. The qualitative picture of the two-body motion is described, and critical parameters of the problem are found. Application are made to the relative motion of the Local Group and Virgo cluster.
We consider a non singular origin for the Universe starting from an Einstein static Universe in the framework of a theory which uses two volume elements $sqrt{-{g}}d^{4}x$ and $Phi d^{4}x$, where $Phi $ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field $phi$ are considered in the action. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for $phi rightarrow infty$ relevant for the non singular origin of the Universe and $phi rightarrow -infty$, describing our present Universe. Surprisingly, avoidance of singularities and stability as $phi rightarrow infty$ imply a positive but small vacuum energy as $phi rightarrow -infty$. Zero vacuum energy density for the present universe is the threshold for universe creation. This requires a modified emergent universe scenario, where the universe although very old, it does have a beginning.
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