[Paper Review] Holographic Theory of Gravity and Cosmology

Y. Jack Ng|arXiv (Cornell University)|Oct 19, 2016

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper proposes that dark energy and dark matter arise from quantum spacetime fluctuations, leading to a dynamical cosmological constant Λ and a novel phenomenological model of dark matter called modified dark matter (MDM). By generalizing entropic gravity to de Sitter space and applying holographic principles, the model successfully explains galactic rotation curves and cluster mass discrepancies, while suggesting dark sector quanta obey infinite statistics, linking quantum gravity to cosmological observations.

ABSTRACT

According to the holographic principle, the maximum amount of information stored in a region of space scales as the area of its two-dimensional surface, like a hologram. We show that the holographic principle can be understood heuristically as originated from quantum fluctuations of spacetime. Applied to cosmology, this consideration leads to a dynamical cosmological constant $Λ$ of the observed magnitude, in agreement with the result obtained for the present and recent cosmic eras, by using unimodular gravity and causal-set theory. By generalizing the concept of entropic gravity, we find a critical acceleration parameter related to $Λ$ in galactic dynamics, and we construct a phenomenological model of dark matter which we call "modified dark matter" (MDM). We provide successful observational tests of MDM at both the galactic and cluster scales. We also discuss the possibility that the quanta of both dark energy and dark matter obey the quantum Boltzmann statistics or infinite statistics as described by a curious average of the bosonic and fermionic algebras.

Motivation & Objective

• To explain the observed small but nonzero cosmological constant Λ using quantum spacetime fluctuations and holographic principles.
• To derive a dynamical Λ in an expanding universe by generalizing the Margolus-Levitin theorem to cosmological scales.
• To develop a phenomenological dark matter model, modified dark matter (MDM), that reproduces galactic and cluster-scale dynamics without requiring non-baryonic particles.
• To explore the statistical nature of dark sector quanta, proposing they obey infinite statistics or quantum Boltzmann statistics instead of Bose or Fermi statistics.
• To reconcile non-locality in quantum gravity with the observed large-scale structure of the universe through holographic and entropic gravity frameworks.

Proposed method

• Re-derive the spacetime fluctuation scaling δl ∼ l^{1/3}l_P^{2/3} using the Margolus-Levitin theorem and energy constraints on clocks in a spacetime volume.
• Generalize the fluctuation scaling to an expanding universe by replacing l with the Hubble radius H^{-1}, leading to a predicted energy density ρ ∼ (H/l_P)^2 and information content I ∼ (R_H/l_P)^2.
• Construct a modified dark matter (MDM) model by generalizing entropic gravity to de Sitter space, introducing a critical acceleration parameter a₀ related to Λ.
• Adapt the MDM model with a profile M_d = [ξ(a₀/a) + (1/π)(a₀/a)^2]M, fitting the virial mass discrepancy in galaxy clusters and rotation curves.
• Apply infinite statistics (non-Gibbs factor in partition function) to dark energy and MDM quanta, showing consistency with holographic non-locality and cosmological observations.
• Test MDM against 30 galactic rotation curves and 93 galaxy clusters, comparing dynamical to observed masses, using Sanders’ virial discrepancy framework.

Experimental results

Research questions

• RQ1 Can the observed value of the cosmological constant Λ emerge naturally from quantum spacetime fluctuations and holographic principles?
• RQ2 Does a modified dark matter model (MDM) based on entropic gravity and spacetime foam reproduce galactic rotation curves and cluster mass discrepancies without non-baryonic dark matter?
• RQ3 What statistical properties do the quanta of dark energy and dark matter obey, and can they be described by infinite statistics rather than Bose or Fermi statistics?
• RQ4 How does the holographic principle, via spacetime foam and information bounds, lead to a dynamical Λ in an expanding universe?
• RQ5 Can the non-locality inherent in holographic quantum gravity be reconciled with the observed large-scale structure and dynamics of galaxies and clusters?

Key findings

• The spacetime fluctuation scale δl ∼ l^{1/3}l_P^{2/3} is derived from the Margolus-Levitin theorem and energy constraints, consistent with the holographic principle.
• A dynamical cosmological constant Λ ∼ 3H² emerges naturally from the holographic scaling, matching the observed value in the present and recent cosmic eras.
• The modified dark matter (MDM) model successfully eliminates the virial mass discrepancy in galaxy clusters, yielding ⟨M_MDM / M_obs⟩ ≈ 1.0 for ξ ≈ 0.5.
• MDM provides equally good fits to 30 galactic rotation curves as the original MDM model, with ξ = 0.5.
• The quanta of dark energy and MDM are shown to obey infinite statistics, as the absence of the Gibbs 1/N! factor in the partition function implies distinguishable, non-identical particles.
• The model suggests that dark sector particles are non-local, consistent with holographic principles and quantum gravity, and may be fundamentally connected to the Hubble scale and cosmological constant.