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

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 ($\mathcal{H}\mathcal{N}$) and pre-geometric gravity (PGG) - to propose a unified resolution. The $\mathcal{H}\mathcal{N}$ 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($1,4$)$\to$SO($1,3$), driven by a Higgs-like field ${\varphi }^A$. 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.

Version accepted in Physics (1 figure)

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Cited by in corpus (1)

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