Diving through the cosmic urobos' mouth

...to the dark matter quantum throat?

How far the famous cosmic uroboros bites its tail? Here is the most recent preprint daring at answering (in a quite  heuristical way) this pretty naive question:

If dark energy and dark matter would be such a case, i.e., the 21st century version of the blackbody radiation and the photoelectric effect, they would not be understood by simply modifying the general relativity and the quantum field theory. Another novel paradigm, a.k.a. quantum gravity, may be necessary to understand the nature of dark energy and dark matter [2]. 

... The emergent spacetime is a new fundamental paradigm that allows a background-independent formulation of quantum gravity and opens a new perspective to resolve the notorious problems in theoretical physics such as the cosmological constant problem, hierarchy problem, dark energy, and dark matter [3]. Moreover the emergent spacetime picture admits a background-independent description of the inflationary universe which has a sufficiently elegant and explanatory power to defend the integrity of physics against the multiverse hypothesis [4, 5]. We emphasize that noncommutative (NC) spacetime necessarily implies emergent spacetime if spacetime at microscopic scales should be viewed as NC [6]. We will elaborate the emergent gravity from a large N matrix model by considering a vacuum in the NC Coulomb branch satisfying the Heisenberg algebra and argue that dark energy and dark matter may arise as a cosmic ouroboros of quantum gravity due to the coherent vacuum structure of spacetime.

It was pointed out in [7, 8] that the emergent gravity from NC U(1) gauge fields resolves the cosmological constant problem in a surprising way and explains the nature of dark energy as arising from the UV/IR mixing of vacuum fluctuations over a coherent spacetime vacuum. However the possibility of dark matter has been overlooked in this approach partially due to the mainstream faction based on the particle model of dark matters. Recently there has been an encouraging mood from observations that the notion about the particle nature of dark matter may crumble. Moreover there are several suggestions to explain the dark matter based on the quantum condensate of light scalar fields [9, 10, 11], the emergent gravity from quantum entanglements [12, 13, 14] as well as the modified gravity [15, 16]... Since the theoretical structure of physics is always much bigger and richer than we thought, we should not be stuck only to fashionable ideas... 

Let us start with a zero-dimensional matrix model with four N×N Hermitian matrices, {φa ∈ AN |a = 1, · · · , 4}, whose action is given by S = − 1/4g²×Tr[φ_a, φ_b]². (2.1) Note that the matrix action (2.1) has the U(N) gauge symmetry as well as a global automorphism given by φ_a → φ'_a= Λ_a^bφ_b + ca (2.2) if Λ_a^b is a rotation in SO(4) and ca are constants proportional to the identity matrix. It will be shown later [4] that the global symmetry (2.2) is responsible for the Poincar´e symmetry of flat spacetime emergent from a vacuum in the Coulomb branch of matrix model and so will be called the Poincaré automorphism. The equations of motion for the matrix model (2.1) are given by [φ_b, [φ_a, φ_b]] = 0, (2.3) which must be supplemented with the Jacobi identity... 

We want to study the dynamics of fluctuations around a vacuum in the Coulomb branch of the matrix model. The conventional choice of vacuum in the Coulomb branch of U(N) Yang-Mills theory is given by  [φ_a, φ_b]|_vac = 0 ⇒ <φ_a>_vac = diag((α_a)₁,(α_a)₂,...,(α_a)_N ) for a = 1, ..., 4. In this case the U(N) gauge symmetry is broken to U(1)^N. If we consider the N → ∞ limit, the large N limit opens a new phase of the Coulomb branch given by [φ_a, φ_b]|_vac = −iB_ab ⇒ <φa>_vac = p_a ≡ B_aby^b (2.5) where the vacuum moduli y^a satisfy the Moyal-Heisenberg algebra [y_a, y_b]=iθ^ab with B_ab = (θ⁻¹)_ab. This vacuum will be called the NC Coulomb branch. Note that the NC Coulomb branch saves the NC nature of matrices while the conventional commutative vacuum dismisses the property.

 Dark Energy and Dark Matter in Emergent Gravity 

Jungjai Lee, Hyun Seok Yang(Submitted on 14 Sep 2017 (v1), last revised 18 Sep 2017 (this version, v2))

One part of dark matter for three parts of dark energy in a 3+1 fluctuating spacetime?

If the macroscopic scale L_H is identified with the size of cosmic horizon of our observable universe, L_H = 1.3×10²⁶m, the extended (nonlocal) energy in Eq. (3.22) or (3.23) is in good agreement with the observed value of current dark energy ρ_DE := δρ≈(10⁻³eV)⁴. Moreover one can determine the total energy within the hypersurface of radius L_H, which is given by δE=4πL_H/3L²_P . Thus the corresponding total entropy δS=δE/T_H  is determined as δS=A_H/4G since the de Sitter temperature of the cosmological horizon is given by T_H =1/2πL_H [25], where A_H=4πL²_H and 8πG=L²_P. Of course the numerical factor is a wishful thinking. This argument shows that the dark energy/matter in our Universe would be a holographic manifestation of a microscopic physics, a.k.a. quantum gravity. We showed before that space-like fluctuations give rise to the repulsive gravitational force while time-like fluctuations generate the attractive gravitational force. When considering the fact that the fluctuations are random in nature and we are living in the (3+1)-dimensional spacetime, the ratio of the repulsive and attractive components will end in 3/4 : 1/4 =75 : 25 and this ratio curiously coincides with the dark composition of our current Universe [8]. Note that the dark energy in (3.23) sets the current Hubble parameter H₀=cL_H and the Hubble parameter induces a characteristic acceleration scale a₀=cH₀=c²L_H. Since the dark matter is the fourth of the dark energy, the dark matter will give rise to the attractive acceleration scale a₀/4=c²/4L_H. This attractive force will compete with ordinary matters depending on their characteristic scales. The inclusion of ordinary matters definitely changes the previous ratio as 75↓ : 25↑, that will cause a better match with the current observation. Therefore it is expected that the emergent gravity can explain the dark sector of our Universe more precisely after including ordinary matters in this scheme.

The above spacetime picture in emergent gravity may bear some analogy with water waves in a swimming pool. Without water in the swimming pool, it is not possible to generater the water wave but instead sound waves can occur through air molecules in the pool. In order to generate the water wave, first it is necessary to fill up the swimming pool with water. Similarly there have been two phases of vacua in the Coulomb branch of a large N matrix model: the commutative vacuum and the NC vacuum. Unfortunately general relativity has no explanation about the dynamical origin of the Minkowski spacetime and there is a tangible difference about the origin of flat spacetime between general relativity and emergent gravity: the water in the swimming pool is regarded as a completely empty space in general relativity. This misconception for the dynamical origin of spacetime introduces several notorious puzzles in theoretical physics such as the cosmological constant problem and the hierarchy problem [8]. In particular, the correct identification of the dynamical origin of flat spacetime has been crucial to understand why dark energy and dark matter correspond to a cosmic ouroboros of quantum gravity due to the coherent vacuum structure of spacetime. A more meditation about emergent spacetime also reveals a remarkable picture [4, 5] that the cosmic inflation corresponds to the dynamical emergence of spacetime describing the dynamical process of Planck energy condensate in vacuum, i.e., the instant filling up the swimming pool with water.

Id.

The Cosmic Uroboros of quantum gravity represents the universe as a continuity of vastly different size scales. The diameter of the earth is about two orders of magnitude (10⁻²) smaller than that of the sun. About sixty orders of magnitude separate the very smallest from the very largest size. Traveling clockwise around the serpent from head to tail, we move from the maximum scale we can see, the size of the cosmic horizon (10²⁸ cm), down to that of a supercluster of galaxies, down to a single galaxy, to the distance from Earth to the Great Nebula in Orion, to the solar system, to the sun, the earth, a mountain, humans, an ant, a single-celled creature such as the E. coli bacterium, a strand of DNA, an atom, a nucleus, the scale of the weak interactions (carried by the W and Z particles) and the size of the last discovered elementary particle called Higgs boson (H). Contrary to the usual cosmic uroboros, the new perspective offered by quantum gravity (QG) does not require any massive dark matter particle lying at smaller scales to explain the anomalous galaxy rotation curves but reveals them as a "holographic" manifestation of microscopic physics, a.k.a. quantum gravity. Thus the tip of the tail might go through the snake's mouth to the galaxy scale where dark matter phenomenology occurs. (Adapted from The view from the center of the Universe )