A density-responsive scalar-field framework for singularity regularization and dynamical dark energy

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Abstract
We present a covariant scalar-field framework that unifies the space-time singularity regularization with dynamical dark energy. The theory extends general relativity by introducing a scalar field Φ whose potential couples to the Lorentz-invariant quantity X ≡ u α u β T matter α β , ensuring manifest covariance. The resulting density-responsive scalar energy ρ Φ exhibits dual behavior: (i) in high-density regimes, it saturates at ρ Φ ⩽ A M P 4 / 2 , providing a Planck-scale upper bound on the total energy density that regularizes classical singularities; (ii) in low-density regimes, it approaches a constant ρ Φ → A M U 4 , driving cosmic acceleration as dynamical dark energy. A natural renormalization group evolution with an anomalous dimension γ ≈ 0.501 connects the Planck scale to the meV dark energy scale without fine-tuning. The model makes distinctive, testable predictions: w 0 ≈ − 0.99 and w a ≈ + 0.03 , where the positive w a distinguishes it from ΛCDM and standard quintessence models. Despite the novel interaction terms, the fifth forces are suppressed by β eff ∝ 1 / ρ m 2 , yielding factors below 10 −58 in laboratory environments, and ensuring compatibility with all precision gravity tests. This framework demonstrates how a single quantum field theory mechanism can simultaneously address UV singularities and IR dark energy, providing concrete predictions for future Stage-IV cosmological surveys.

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