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

Martin Drobczyk

doi:10.1088/1361-6382/ae1ac1

paper

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

arXiv:2506.12464 · doi:10.1088/1361-6382/ae1ac1

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 $X \equiv u_{α} u_{β} T_{matter}^{α β}$ , ensuring manifest covariance. The resulting density-responsive scalar energy $ρ_{Φ}$ exhibits dual behavior: (i) in high-density regimes, it saturates at $ρ_{Φ} \leq A M_{P}^{4} /2$ , providing a Planck-scale upper bound on the total energy density that regularizes classical singularities; (ii) in low-density regimes, it approaches a constant $ρ_{Φ} \to A M_{U}^{4}$ , driving cosmic acceleration as dynamical dark energy. A natural renormalization group evolution with an anomalous dimension $γ \approx 0.501$ connects the Planck scale to the meV dark energy scale without fine-tuning. The model makes distinctive, testable predictions: $w_{0} \approx - 0.99$ and $w_{a} \approx + 0.03$ , where the positive $w_{a}$ distinguishes it from $Λ$ CDM and standard quintessence models. Despite the novel interaction terms, the fifth forces are suppressed by $β_{eff} \propto 1/ ρ_{m}^{2}$ , yielding factors below $1 0^{- 58}$ 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.

arXiv commentRevised per referee reports; resubmitted to Classical and Quantum Gravity. Title and Abstract updated, Structure clarified and updated; updated figures; expanded appendices

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

Abstract

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