Holographic complexity and the Hubble tension: a quantum gravity portrayal for the large scale structure of the cosmos

TL;DR

This work links the Hubble tension to a quantum gravity framework in which spacetime emerges from holographic quantum correlations and a second law of holographic complexity. By embedding an IR/UV regularization via the universe’s causal diamond and a quantum of area $\Delta$, the authors derive $H_{0}^{2} = D C_{h}^{\gamma}$ with $\gamma = \frac{3+3\varepsilon-4\alpha\varepsilon}{3\alpha\varepsilon}$ and show that $\alpha<\tfrac{3}{2}$ and $\varepsilon>1$, ensuring a consistent holographic picture. Fixing $N^{\gamma}=e$ yields a simple model $H_{0} = D e^{\alpha}$, enabling an $S$-shaped evolution of $H_{0}$ that can reproduce early, middle, and late-time measurements, as the quantum-complexity budget evolves (via a superstatistics construction) and saturates. The framework offers a observer-independent microscopic account of the varying $H_{0}$ and proposes gravitational-wave and other cosmological probes as potential tests of holographic complexity as a fundamental cosmological driver.

Abstract

In this letter, we propose a relationship between the so-called Hubble-Lemaître constant $H_{0}$ and holographic complexity related to the emergence of spacetime in quantum gravity. Such a result can represent an important step to understanding the Hubble tension by introducing a quantum gravity perspective for cosmological observations: regarding the degree of quantum complexity we measure around us.

Figures (3)

• Figure 1: Schematic illustration of the universe’s causal diamond: the overlap between the past and future light cones of an observer’s worldline. It shows the region of spacetime that can both influence and be influenced by an observer.
• Figure 2: The exponent $\alpha$, and $H_{0}(k)$ are plotted against the quantum number $k$, by considering $C' = 0.5\; ln (\frac{73.04}{67.4}))$, $D = 67.4$, $a = 1.0$, $b = 0.0$, and $\Delta = 0.1$. Large positive $k$ values strongly suppress larger area eigenvalues corresponding to a more sharply-localized, fine-grained behavior. On the other hand, large $k$ negative values favor larger area eigenvalues, implying a coarse-grained surface structure.
• Figure 3: The plot shows the $S$-shaped behavior of $H_{0}$ given by our results with $k_{0} = 20$, and $z_{c} = 0.4$. The plot also shows the key early, middle, and late-time measured values for $H_{0}$ against the effective redshift related to the measurement: Planck Planck:2018vyg, Standard BAOs eBOSS:2020yzd, Ly$\alpha$ forest + BAOs eBOSS:2020tmo, SHOES + TRGB Riess:2021jrx, and Megamasers Pesce:2020xfe.