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

Martin Drobczyk

TL;DR

The paper develops a covariant, environment-dependent scalar field framework in which a single scalar Φ interacts with the local matter density X through a covariant potential U(Φ,X). A renormalization-group driven running scale M_U(μ) connects Planck-scale physics to the meV dark-energy scale via an anomalous dimension γ ≈ 0.501, yielding a density-dependent energy ρ_Φ that regularizes ultraviolet singularities at high density and drives infrared cosmic acceleration at low density. The model predicts a distinctive dark-energy equation of state evolution with w_0 ≈ -0.99 and w_a ≈ +0.03, and features automatic fifth-force screening β_eff ∝ 1/ρ_m^2, ensuring compatibility with precision gravity tests. It also implies Planck-scale black-hole cores, Planckian remnants, and a potential unified dark sector with self-interacting dark matter and gravitational-wave signals from hidden-sector dynamics, all testable by upcoming Stage-IV cosmological surveys and gravitational-wave experiments.

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 $X \equiv u_α u_β T^{αβ}_{\mathrm{matter}}$, ensuring manifest covariance. The resulting density-responsive scalar energy $ρ_Φ$ exhibits dual behavior: (i) in high-density regimes, it saturates at $ρ_Φ\leq AM_P^4/2$, providing a Planck-scale upper bound on the total energy density that regularizes classical singularities; (ii) in low-density regimes, it approaches a constant $ρ_Φ\to AM_U^4$, 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 $β_{\rm eff} \propto 1/ρ_m^2$, 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.

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

TL;DR

The paper develops a covariant, environment-dependent scalar field framework in which a single scalar Φ interacts with the local matter density X through a covariant potential U(Φ,X). A renormalization-group driven running scale M_U(μ) connects Planck-scale physics to the meV dark-energy scale via an anomalous dimension γ ≈ 0.501, yielding a density-dependent energy ρ_Φ that regularizes ultraviolet singularities at high density and drives infrared cosmic acceleration at low density. The model predicts a distinctive dark-energy equation of state evolution with w_0 ≈ -0.99 and w_a ≈ +0.03, and features automatic fifth-force screening β_eff ∝ 1/ρ_m^2, ensuring compatibility with precision gravity tests. It also implies Planck-scale black-hole cores, Planckian remnants, and a potential unified dark sector with self-interacting dark matter and gravitational-wave signals from hidden-sector dynamics, all testable by upcoming Stage-IV cosmological surveys and gravitational-wave experiments.

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 whose potential couples to the Lorentz-invariant quantity , ensuring manifest covariance. The resulting density-responsive scalar energy exhibits dual behavior: (i) in high-density regimes, it saturates at , providing a Planck-scale upper bound on the total energy density that regularizes classical singularities; (ii) in low-density regimes, it approaches a constant , driving cosmic acceleration as dynamical dark energy. A natural renormalization group evolution with an anomalous dimension connects the Planck scale to the meV dark energy scale without fine-tuning. The model makes distinctive, testable predictions: and , where the positive distinguishes it from CDM and standard quintessence models. Despite the novel interaction terms, the fifth forces are suppressed by , yielding factors below 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.

Paper Structure

This paper contains 91 sections, 105 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. The covariant scalar field framework
  3. Action and the covariant potential
  4. Equilibrium dynamics and the density-responsive energy
  5. Validity of the quasi-static approximation.
  6. The full stress-energy tensor $T_\Phi^{\mu\nu}$
  7. Key assumptions and their implications.
  8. Effective equation of state and background cosmology
  9. Scale hierarchy from renormalization group evolution
  10. The RG equation for $M_U$
  11. Connecting the Planck and dark energy scales
  12. Microphysical Origin and Phenomenological Viability
  13. From RG to cosmology: $\mu(a)$, IR freezeout, and background dynamics
  14. IR freezeout (baseline).
  15. Continuous RG improvement.
  16. ...and 76 more sections

Figures (4)

  • Figure 1: Cosmological predictions of the model. (a) The equation of state $w_\Phi^{\rm eff}(z)$ evolves from $w \approx -1/2$ at high redshift towards $w \to -1$ today, with a distinctive positive slope $w_a \approx +0.03$. (b) The expansion rate $H(z)$ shows a characteristic deviation of 0.29% from the $\Lambda$CDM model, providing an observational target for upcoming surveys.
  • Figure 2: Hidden-sector contribution to $\Delta N_{\rm eff}$ versus fermion flavours $N_f$. Solid (dashed) curves correspond to $SU(2)$ ($SU(3)$); colours denote $T_{\rm dec}=10$ GeV (purple), $100$ GeV (orange) and $1000$ GeV (green). The horizontal band shows the Planck +BBN $2\sigma$ bound $\Delta N_{\rm eff}<0.15$. The red circle and blu square mark the two benchmark models quoted in the text.
  • Figure 3: Forecasted 1$\sigma$ and 2$\sigma$ constraints on the dark energy equation of state parameters ($w_0, w_a$) for a Stage-IV spectroscopic survey. The red point marks the prediction of our model ($w_0=-0.99, w_a=+0.03$), while the black cross indicates the $\Lambda$CDM model. The forecast shows that these two models are distinguishable at the $\sim 1.1\sigma$ level.
  • Figure 4: Modified Oppenheimer–Snyder collapse for observational ($A = 0.024$, top) and theoretical ($A \approx 0.0016$, bottom) coupling values, simulated using the full LQC-like dynamics. Left: Scale factor evolution showing a non-singular bounce (blue) versus the classical singularity (red dashed). Right: Energy densities, with the total effective density (blue) peaking as the system bounces. The bounce occurs at 139.2% (99.0%) of the GR singularity time for the observational (theoretical) values, respectively.