[Paper Review] A Possible Solution of the Cosmological Constant Problem based on Minimal Length Uncertainty and GW170817 and PLANCK Observations

Abdel Magied Diab, Abdel Nasser Tawfik|arXiv (Cornell University)|May 6, 2020

Relativity and Gravitational Theory1 references4 citations

TL;DR

This paper proposes a solution to the cosmological constant problem by linking the generalized uncertainty principle (GUP) with gravitational wave observations, particularly GW170817. By constraining the GUP parameter β₀ using the speed difference between gravitons and photons, the authors derive β₀ ≲ 10⁶⁰, which, when applied to vacuum energy density via UV/IR correspondence, yields a cosmological constant Λ ≈ 10⁻⁴⁷ GeV⁴/ℏ³c³, matching PLANCK observations and resolving the 121-order-of-magnitude discrepancy.

ABSTRACT

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, $β_0$, 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 $β_0 \simeq 10^{60}$. 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 $Λ$ (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, $Λ\simeq 10^{-47}~$GeV$^4/\hbar^3 c^3$.

Motivation & Objective

• To resolve the 121-order-of-magnitude discrepancy between the theoretical prediction and observed value of the cosmological constant (Λ).
• To constrain the GUP parameter β₀ using gravitational wave data from the GW170817 event.
• To explore the role of UV/IR correspondence and modified dispersion relations in reconciling quantum vacuum energy with observed Λ.
• To link the minimal length uncertainty principle with the gravitational impact on vacuum energy density.

Proposed method

• Employing the generalized uncertainty principle (GUP) with a quadratic momentum correction term to model minimal length uncertainty at the Planck scale.
• Using the GW170817 event to constrain the difference between graviton and photon group velocities, thereby bounding β₀.
• Applying modified dispersion relations (MDRs) to calculate the speed difference between gravitons and photons.
• Utilizing the UV/IR correspondence to relate large-scale (IR) vacuum energy effects to short-distance (UV) quantum gravity corrections.
• Calculating the density of states under GUP corrections to estimate vacuum energy density and derive Λ.
• Matching the derived Λ with PLANCK 2018 observations to validate the model.

Experimental results

Research questions

• RQ1 Can the GUP parameter β₀ be constrained using gravitational wave observations such as GW170817?
• RQ2 How does the speed difference between gravitons and photons constrain the GUP parameter β₀?
• RQ3 Can the UV/IR correspondence explain the large discrepancy between theoretical and observed values of the cosmological constant?
• RQ4 Does incorporating GUP corrections into vacuum energy density calculations yield a Λ value consistent with PLANCK observations?
• RQ5 Is there a physical mechanism linking minimal length uncertainty to the observed cosmological constant?

Key findings

• The GUP parameter β₀ is constrained to β₀ ≲ 10⁶⁰ using the GW170817 gravitational wave event.
• The speed difference between gravitons and photons, derived from MDRs, provides a direct observational constraint on β₀.
• The derived value of β₀ leads to a vacuum energy density that yields a cosmological constant Λ ≈ 10⁻⁴⁷ GeV⁴/ℏ³c³.
• This value of Λ matches the PLANCK 2018 observation, resolving the 121-order-of-magnitude discrepancy.
• The UV/IR correspondence and GUP framework together provide a consistent quantum gravity-inspired explanation for the cosmological constant problem.
• The agreement between GUP-based Λ estimation and PLANCK data supports the viability of GUP as a tool for quantum gravity phenomenology.