$\mathcal{H}$olographic $\mathcal{N}$aturalness and Pre-Geometric Gravity

TL;DR

This paper proposes a unified framework combining holographic naturalness and pre-geometric gravity to explain the smallness and stability of the cosmological constant through entropy and quantum information considerations.

Contribution

It introduces a model where spacetime geometry emerges from symmetry breaking and links the de Sitter entropy to a fundamental Higgs-like field, offering a novel solution to the cosmological constant problem.

Findings

De Sitter entropy is proportional to the Higgs field VEV v.

The small cosmological constant results from the largeness of de Sitter entropy.

Quantum transitions are exponentially suppressed in high-entropy states.

Abstract

The cosmological constant (CC, $\Lambda$) problem represents a remarkable discrepancy of about 120 orders of magnitude between the observed dark energy and its natural expectation from quantum field theory. This paper synthesizes two paradigms - holographic naturalness ($\mathcal{HN}$) and pre-geometric gravity (PGG) - to propose a unified resolution. The $\mathcal{HN}$ framework posits that CC stability is not a matter of radiative corrections but of quantum information and entropy. The large entropy $S_\text{dS}\sim M_\text{P}^2/\Lambda$ of the de Sitter (dS) vacuum acts as an entropic barrier, exponentially suppressing destabilizing quantum transitions. This explains why the universe remains in a high-entropy, low-CC state. We embed this within PGG, where spacetime geometry and the Einstein-Hilbert action emerge dynamically from the spontaneous symmetry breaking SO($1,4$)$\rightarrow$SO($1,3$), driven by a Higgs-like field $\phi^A$. Both $M_\text{P}$ and $\Lambda$ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the VEV $v$ of the pre-geometric Higgs field and the de Sitter entropy: $S_\text{dS}\sim v$ (or $v^3$). Thus, the field generating spacetime also encodes its information content. The smallness of $\Lambda$ follows directly from the largeness of $S_\text{dS}$, a manifestation of a large $v$. The CC is stable because a large-entropy state's decay is exponentially suppressed. Our study shows new semi-classical quantum gravity effects dynamically generate "hairons", particles whose mass is tied to the CC. The instability of the dS space, driven by a condensate evolution, points to a dynamical origin for dark energy. This framework inextricably links the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime, providing a novel path toward solving the CC problem.