Spacetime Origin Solves Universe Energy Puzzle

Scientists are tackling one of cosmology’s most enduring puzzles, the cosmological constant problem, with a novel approach that avoids the need for speculative fine-tuning or anthropic principles. Andrea Addazi from the Center for Theoretical Physics, College of Physics Science and Technology, Sichuan University, and Laboratori Nazionali di Frascati INFN, working in collaboration with Giuseppe Meluccio from Scuola Superiore Meridionale and INFN Sezione di Napoli, propose a solution rooted in pre-geometric gravity, where spacetime itself emerges from a fundamental symmetry breaking. Their research demonstrates a crucial link between the topological Gauss-Bonnet coupling and the de Sitter entropy, effectively quantising the cosmological constant into discrete sectors and dynamically selecting the observed vacuum energy. This framework, detailed in their paper, offers a compelling explanation for the observed smallness of the cosmological constant by unifying gravity and topology, potentially representing a significant step towards a more complete understanding of the universe.

By understanding the universe’s expansion may soon move beyond guesswork, offering a precise value for dark energy — this advance stems from a theory where spacetime itself arises from fundamental symmetries, not pre-existing dimensions. Elegantly explaining the observed vacuum energy without needing to invoke chance or multiple universes, and scientists are tackling one of cosmology’s most persistent puzzles: the cosmological constant problem. A discrepancy between theoretical predictions and observed values for the energy density of empty space, while current models predict a vacuum energy density some 60 orders of magnitude larger than what astronomers actually measure.

Emergent gravity links Planck mass, cosmological constant and de Sitter entropy via topological quantization

Initial analysis of this pre-geometric gravity model reveals a striking relationship between emergent gravitational scales and the de Sitter entropy, quantified by a ratio of approximately 10 120. This value, denoted as M 2 P /Λ, directly links the Planck mass and the cosmological constant, where the vacuum expectation value of the gravitational Higgs field, φ, governs the scale.

This ratio is proportional to the Gauss-Bonnet coupling, α GB, which scales with the de Sitter entropy, S dS, establishing a holographic connection between ultraviolet and infrared gravity scales. The project further demonstrates topological quantization of the cosmological constant, as recognition of the Gauss-Bonnet term as a gravitational θ-term within the path integral forces its coupling, α GB, and as a result Λ, to become discrete.

The quantization condition, Λ ∝ 1/(kG), ties the observed cosmological constant value to an integer topological quantum number, k, transforming a continuous fine-tuning problem into a mechanism of discrete vacuum selection via spontaneous symmetry breaking. As a result, the observed value of dark energy isn’t a result of precise tuning, but a selection from a set of allowed topological states.

Here, the project details deterministic selection of our universe, with the spontaneous symmetry breaking potential for the pre-geometric Higgs field being periodic. In turn, this periodicity leads to a discrete field of topologically distinct vacua, each corresponding to a different value of k and, therefore, Λ. Meanwhile, the dynamics of symmetry breaking naturally selects the vacuum with k ∼ 10 120. Uniquely reproducing the observed hierarchy between the Planck scale and the cosmological constant.

Also, the selected vacuum state is dynamically stabilised by an enormous entropic barrier — suppressing quantum tunneling transitions to other topological sectors by a factor of approximately e −10120. Radiative corrections are controlled within this framework, as they cannot alter the fundamentally topological and quantized nature of Λ, and the potential barrier between different vacua is Planckian, effectively stabilising the cosmological constant over time. By linking gravity, topology, and information, this pre-geometric approach offers a potential resolution to the cosmological constant problem without requiring fine-tuning or anthropic reasoning.

Emergent gravity from de Sitter gauge symmetry and scalar field condensation

At the same time, this effort is underpinned by a gauge theory defined on a four-dimensional manifold, initially lacking a metric structure. Here, the gauge group employed is the de Sitter group SO(1, 4), utilising a connection denoted as AABμ and its corresponding curvature FABμν. In turn, the theory is constructed to be generally covariant without introducing a spacetime metric or tetrads at the fundamental level. Instead relying on an internal metric η with a signature of (−, +, +, +, +).

Spacetime geometry emerges dynamically through the condensation of a scalar field φA, transforming under the fundamental representation of SO(1, 4). Once a ‘sombrero’ potential for φ is implemented, this gravitational Higgs field acquires a nonzero vacuum expectation value, spontaneously breaking the gauge symmetry down to the Lorentz subgroup SO(1, 3).

As a result, the low-energy effective theory reproduces general relativity, with the pre-geometric fields AABμ and φA becoming gravitational degrees of freedom — since no inverse metric exists prior to symmetry breaking, the Levi-Civita symbol εμνρσ, possessing weight −1. Serves as the sole available contravariant density on the manifold, and the MacDowell, Mansouri Lagrangian, a key component of the methodology. Is constructed using this symbol and the curvature and scalar fields, incorporating a coupling constant YMM.

After spontaneous symmetry breaking, achieved by fixing one internal direction with the vacuum expectation value ⟨φA⟩= vδA5, the SO(1 — 4) connection decomposes into tetrads eaμ and a spin connection ωabμ. Through identifying these components, an emergent pseudo-Riemannian geometry arises, effectively reducing the framework to a gravitational theory, and by substituting the vacuum expectation value into the MacDowell, Mansouri Lagrangian yields terms corresponding to the Einstein, Hilbert action. A cosmological constant, and a Gauss, Bonnet density.

Through matching these coefficients to the standard gravitational action establishes the emergent Planck mass and cosmological constant, linking them to the coupling constant YMM and the vacuum expectation value v. This approach differs from previous attempts by providing a deterministic vacuum selection, where the symmetry-breaking potential possesses numerous degenerate minima, each corresponding to a distinct value of Λ.

Emergent spacetime topology and a resolution to the cosmological constant problem

For decades, the cosmological constant problem has haunted theoretical physics, a discrepancy between predicted and observed vacuum energy so vast it strains the foundations of our understanding. A pre-geometric approach offers a potential resolution, not through fine-tuning or speculative multiverse arguments, but by reimagining the very origin of spacetime itself.

Rather than treating spacetime as a fixed background, this effort proposes it emerges from a broken symmetry — a concept with implications extending beyond cosmology and into the structure of gravity. Pre-geometric models are gaining traction as avenues for addressing long-standing issues, and by linking the cosmological constant to topological properties of spacetime is a bold step. A quantization of vacuum energy previously thought unattainable.

By connecting the observed universe’s scale to a specific topological sector, the framework provides a natural explanation for its smallness. Sidestepping the need for improbable coincidences. Establishing a definitive link between these abstract mathematical structures and physical reality remains a considerable challenge — the potential barrier protecting the vacuum state is dependent on the Higgs field. This requires further investigation to confirm its stability and behaviour.

The significance extends beyond simply solving a cosmological puzzle. A deeper understanding of vacuum energy could influence our comprehension of dark energy and the universe’s accelerating expansion. Unlike many theoretical proposals, this effort suggests testable predictions related to the distribution of topological defects in the early universe. Potentially observable through future cosmological surveys.

The framework’s reliance on fundamental symmetries and emergent spacetime could offer insights into quantum gravity, a field desperately seeking a consistent theoretical foundation — a complete Hamiltonian analysis is needed to confirm the stability of the proposed pre-geometric spacetime. The broader effort to understand the cosmological constant is likely to involve a combination of theoretical innovation and increasingly precise cosmological observations, and the focus may shift towards exploring the interaction between pre-geometric models and other promising avenues, such as modified gravity theories and holographic principles. In the search for a truly complete picture of the universe.