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arXiv:2604.10519

Energy-momentum and dark energy in $\boldsymbol{SU(\infty)}$-QGR quantum gravity

Houri Ziaeepour

gr-qcastro-ph.COquant-phSubmitted Apr 12, 2026• Announced Apr 14, 2026• Revised Jun 6, 2026 (v2)
v1 · Apr 12, 2026v2 · Jun 6, 2026
arXivHTMLPDF

Abstract

$SU(\infty)$ Quantum GRavity (QGR) is a recently proposed fundamentally quantum approach to gravity and cosmology. In this model the Hilbert space of the Universe represents $SU(\infty)$ symmetry. Its fragmentation generates approximately isolated subsystems (particles) representing, in addition to $SU(\infty)$, finite-rank local symmetries. The common $SU(\infty)$ is associated to quantum gravity, and at lowest quantum order the effective action for all symmetries is Yang-Mills on a 4D parameter space $Ξ$. Nonetheless, physical processes and measurables must be independent of the geometry of $Ξ$. In previous works we demonstrated that diffeomorphism of $Ξ$ can be neutralized by $SU(\infty)$ gauge transformation. In this work we show that the invariance of action under variation of $Ξ$'s metric leads to a constraint resembling Einstein equation. It consists of energy-momentum tensors for all components of the model, including the spin-1 gravitons. In addition, through calculation of quantum information measures we study the effect of Hilbert Space Fragmentation (HSF) on the emergent classical spacetime and different cosmological era, such as inflation, reheating, and late time accelerating expansion. The results of this preliminary and approximate investigation show that HSF may be classically interpreted as these phenomena. Consequently, inflaton, quintessence, and similar fields associated to these processes may be order parameters that phenomenologically present them.

Comments
32 pages, no figure. v2: minor changes in the text

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SU(∞)SU(\infty)SU(∞) Quantum GRavity (QGR) is a recently proposed fundamentally quantum approach to gravity and cosmology. In this model the Hilbert space of the Universe represents SU(∞)SU(\infty)SU(∞) symmetry. Its fragmentation generates approximately isolated subsystems (particles) representing, in addition to SU(∞)SU(\infty)SU(∞), finite-rank local symmetries. The common SU(∞)SU(\infty)SU(∞) is associated to quantum gravity, and at lowest quantum order the effective action for all symmetries is Yang-Mills on a 4D parameter space ΞΞΞ. Nonetheless, physical processes and measurables must be independent of the geometry of ΞΞΞ. In previous works we demonstrated that diffeomorphism of ΞΞΞ can be neutralized by SU(∞)SU(\infty)SU(∞) gauge transformation. In this work we show that the invariance of action under variation of ΞΞΞ's metric leads to a constraint resembling Einstein equation. It consists of energy-momentum tensors for all components of the model, including the spin-1 gravitons. In addition, through calculation of quantum information measures we study the effect of Hilbert Space Fragmentation (HSF) on the emergent classical spacetime and different cosmological era, such as inflation, reheating, and late time accelerating expansion. The results of this preliminary and approximate investigation show that HSF may be classically interpreted as these phenomena. Consequently, inflaton, quintessence, and similar fields associated to these processes may be order parameters that phenomenologically present them.
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In this thesis we shall apply techniques from quantum information theory to the problem of measuring the structure of spacetime or equivalently measuring the gravitational field. In turn we will also look at how acceleration may effect quantum information techniques for processing and transmitting information. Measuring the structure of spacetime is a slight abuse of terminology as spacetime structure is not directly observable. We will be investigating the estimation of spacetime structure by making measurements on quantum systems which depend on the spacetime background. The structure of spacetime and the gravitational field will be treated in accordance with Einstein's general theory of relativity. This is currently the most accurately tested classical theory for gravity. It is widely believed that fundamentally, gravity should be treated within the framework of quantum mechanics, just like the other forces of nature. This is yet to be seen experimentally and a theory capable of falsifiable predictions is yet to be found. In this thesis we shall focus on the effects of gravity at the classical level, however we shall treat matter and non-gravitational energy using quantum mechanics. When looking at how gravity effects quantum information we will specifically be focusing on the simple case of acceleration, yet we shall treat it in this relativistic spacetime context. Knowing the structure of spacetime in general relativity amounts to knowing an object called the metric tensor. This object contains all the information about a spacetime. This may include local curvature, for instance around a star or black hole, gravitational radiation coming from a binary pulsar and even the large scale structure of the universe such as the rate of expansion. By performing local experiments one may attempt to extract this information. Fundamentally these experiments will be governed by quantum mechanics, hence the accuracy of the estimation will be fundamentally limited by the statistical nature of quantum theory. In this thesis we shall develop an equation which states just what accuracy one can ultimately achieve when attempting to measure the structure of spacetime. This equation will be shown to be a generalisation of known results for the accuracy to which one can ultimately measure position and momentum as well as time and energy. The result will be applied to a range of relativistic phenomena including acceleration in flat spacetime, the local curvature around a black hole, the amplitude of a gravitational wave and the expansion of the universe in a cosmological model. Following the use of quantum information theory to investigate gravity we shall look at how acceleration can effect quantum information. Firstly we shall see how quantum entanglement can be created and stored between two optical cavities when one is uniformly accelerating. This is in contrast to a number of results which predict that entanglement will be lost in the presence of acceleration. This loss of entanglement is predicted due to an as yet unobserved phenomena known as the Unruh effect. The Unruh effect states that an observer uniformly accelerating will see a thermal distribution of particles even if an inertial observer will see no particles at all. We will show how the use of optical cavities can prevent this effect from causing problems both for the storage and creation of entanglement. Finally we shall look at how a particular quantum detection scheme can be employed in the presence of acceleration. Our technique will emphasis the importance of locality, that is the localisation of physics in spacetime. We will also show how some commonly used approximations used to study the Unruh effect, can be avoided with our new formulation.
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