Solution to the Cosmological Constant Problem from Pre-geometric Gravity

Abstract: We present a novel solution to the cosmological constant (CC) problem that requires no fine-tunings nor anthropic reasoning. In pre-geometric gravity (PGG), spacetime emerges from the spontaneous breaking of a fundamental gauge symmetry. This mechanism dynamically generates general relativity while also revealing a deep connection: the topological Gauss-Bonnet coupling of the theory scales precisely as the de Sitter entropy, an enormous number which reflects the information content of our universe. This coupling acts as a gravitational $θ$-angle parameter, forcing the CC to become quantized into discrete topological sectors. The symmetry-breaking dynamics naturally selects the sector corresponding to the observed vacuum energy. The selected vacuum state is stabilized by the extremely large potential barrier of the pre-geometric Higgs field, which effectively seals it off from quantum tunneling transitions to other topological sectors. The PGG framework thus provides a dynamical explanation for the smallness of the CC, linking gravity, topology and quantum information in a unified picture.

• The paper proposes a non-anthropic mechanism where spontaneous symmetry breaking and topological quantization naturally select a small cosmological constant.
• The paper demonstrates that the condensation of a gravitational Higgs field gives rise to emergent spacetime and links the Planck mass with the cosmological constant.
• The paper shows that discrete, topologically ordered vacuum sectors and an entropic barrier ensure radiative stability and suppress quantum fluctuations.

Pre-geometric Gravity as a Solution to the Cosmological Constant Problem

Overview and Motivation

The cosmological constant (CC) problem is a central issue in modern theoretical physics, characterized by an extreme discrepancy between quantum predictions of vacuum energy and its observed value in cosmology. Quantum fluctuations in the Standard Model, with contributions on the order of $(10^{3}\ \text{GeV})^4$, vastly exceed the empirically measured dark energy density; Planck-scale corrections amplify the mismatch by $120$ orders of magnitude. Notably, the ratio $M_\text{P}^{2}/\Lambda$ scales as the de Sitter (dS) entropy $S_\text{dS}\sim 10^{120}$, suggesting an underlying information-theoretic structure that is not captured by effective field theory.

This paper proposes a non-anthropic, non-fine-tuned mechanism for resolving the CC problem within the pre-geometric gravity (PGG) framework. PGG describes spacetime as an emergent phenomenon arising from the spontaneous symmetry breaking (SSB) of a fundamental gauge symmetry, specifically the $SO(1,4)$ (de Sitter) group, mediated by a gravitational Higgs field. The mechanism dynamically generates general relativity, quantizes the cosmological constant, and locks its small observed value via topological and entropic arguments.

Emergence of Geometry and Gravitational Scales

The fundamental PGG theory is formulated as an $SO(1,4)$ gauge theory on a manifold devoid of metric structure. All geometric attributes arise from the condensation of a gravitational Higgs field $\phi^A$. The SSB mechanism breaks $SO(1,4)$ to $SO(1,3)$, with $\phi^A$ acquiring a vacuum expectation value (VEV) $v$. The MacDowell–Mansouri action leverages this structure, leading to the emergence of tetrads and spin connections that define pseudo-Riemannian geometry.

Post-SSB, the MacDowell–Mansouri (MM) Lagrangian yields the Einstein–Hilbert term, a cosmological constant term, and the Gauss–Bonnet (GB) topological invariant. The Planck mass and cosmological constant are determined by

$$M_\text{P}^2 \sim Y_\text{MM} v m^2,\quad \Lambda\sim \frac{M_\text{P}^2}{Y_\text{MM} v}$$

where $Y_\text{MM}$ is the MM coupling. The GB coupling is fixed by the relation

$$\alpha_\text{GB} = -\frac{3 M_\text{P}^2}{8\Lambda} \sim -S_\text{dS}$$

Importantly, $\alpha_\text{GB}$ scales as the de Sitter entropy, introducing an entropic see-saw mechanism: the enormous hierarchy between $M_\text{P}$ and $\Lambda$ is mapped to the large VEV of the gravitational Higgs field and to holographic information theoretic content.

Topological Quantization and Vacuum Structure

The four-dimensional GB term is strictly topological, proportional to the Euler characteristic $\chi(M)$ of the manifold. Within the gravitational path integral, the GB coupling behaves as a $\theta$-angle, with periodicity

$$\theta = 32\pi^2 \alpha_\text{GB}\ \ (\text{mod}\ 2\pi)$$

This periodicity and its interplay with the SSB of the Higgs field $\phi$ imply the existence of discrete, topologically ordered vacuum sectors. The periodic potential for $\phi$ is structured to allow an infinite tower of minima, each characterized by a distinct value of $k\in\mathbb{Z}$, corresponding to different $\Lambda$ values:

$M_\text{P}^2/\Lambda^{(k)} \sim k$

The observed CC corresponds to the sector with $k \sim 10^{120}$, matching the de Sitter entropy and establishing a deterministic selection of the vacuum.

Transitions between sectors are exponentially suppressed by a Planckian potential barrier. The tunneling amplitude between sectors scales as $e^{-S_\text{dS}}\sim e^{-10^{120}}$, rendering such processes physically implausible and dynamically stabilizing the selected vacuum.

Dynamical Protection and Radiative Stability

Fluctuations of the Higgs field about its VEV are characterized by a super-Planckian mass $\mu_\rho\sim M_\text{P}$, ensuring that quantum corrections and radiative instabilities cannot perturb the vacuum unless the $SO(1,4)$ symmetry is fully restored. Hence, radiative corrections are dynamically controlled; the quantized, topological nature of the CC is preserved regardless of the details of the UV-completion of gravity.

The entropic barrier perspective, aligned with the Holographic Naturalness paradigm, further substantiates the irreversibility of transitions to vacua with lower entropy (larger $\Lambda$). Any such transition would involve a violation of the second law of thermodynamics, again suppressed at the level of $e^{-S_\text{dS}}$.

Implications and Prospects

The deterministic, quantized mechanism for selecting and protecting a small CC addressed in this paper reveals several theoretical and practical implications:

• UV-IR Connection: The holographic relation between the Planck scale, CC, and GB coupling indicates that quantum gravity and information theory are intimately linked, potentially informing quantum gravity models at the Planck scale.
• Landscape Structure: The discrete vacuum landscape provides a non-anthropic explanation for the hierarchy problem, obviating the necessity for fine-tuning or anthropic selection typically invoked in string theory.
• Quantum Gravity and Topology: The identification of the CC with a topological quantum number highlights the central role of topology in gravitational dynamics.
• Cosmological Applications: The stability mechanism may influence models of inflation, dark energy, and late-time cosmic acceleration. The extension to higher-dimensional operators could naturally explain evolving dark energy phenomena and remain stable under quantum corrections, with ramifications for cosmological observations (e.g., DESI).

As a direction for future research, the PGG framework might be extended to elucidate UV-complete gravitational theories, probe the quantum information content of spacetime, and connect quantum gravity with cosmological data.

Conclusion

This paper provides a mathematically rigorous and physically robust solution to the cosmological constant problem in the context of pre-geometric gravity. By leveraging spontaneous symmetry breaking, topological quantization of the cosmological constant, and an entropic protection mechanism, the model achieves deterministic vacuum selection, dynamic stabilization, and radiative robustness. The approach synthesizes gravitational topology, quantum information, and vacuum dynamics into a unified theoretical framework, with potential ramifications for both quantum gravity phenomenology and cosmological modeling (2602.16840).