What question did this study set out to answer?

To address the cosmological coincidence problem by proposing a new scalar-tensor theory, Inward Fixed-Point Gravity (IFG).

April 26, 2026Open Access

Inward Fixed-Point Gravity: A Natural Solution to the Cosmological Coincidence Problem

Key Points

To address the cosmological coincidence problem by proposing a new scalar-tensor theory, Inward Fixed-Point Gravity (IFG).
Developed a volume-normalized scalar field within a scalar-tensor framework.
Conducted numerical simulations of cosmic evolution with varying initial conditions.
Analyzed experimental constraints using existing gravitational data from Cassini and MICROSCOPE.
IFG naturally transitions to dark-energy domination without fine-tuning, achieving w₀ ≈ −0.85 and wₐ ≈ −0.21.
Satisfies all local gravity constraints, providing a self-consistent model of dynamical dark energy.
Phenomenologically predicts finite-range Yukawa corrections within experimental limits.

Abstract

Inward Fixed-Point Gravity (IFG) is a new scalar–tensor extension of general relativity in which the scalar field is volume-normalized: \ (/ -g\). This geometric construction automatically produces an exact tracker solution in cosmology: the scalar tracks the dominant background (radiation → matter) and naturally transitions to dark-energy domination today, solving the long-standing cosmological coincidence problem without fine-tuning of potential parameters or initial conditions. Key breakthroughs: • Automatic tracker mechanism induced purely by volume normalization (no ad-hoc potential tuning required) • Smooth combined experimental constraint envelope using soft-min p-norm (Cassini PPN + MICROSCOPE EP + Eöt-Wash torsion balance) • Realistic numerical FLRW background evolution with wide initial-condition scans yielding w₀ ≈ −0. 85 and wₐ ≈ −0. 21• Benchmark point at m ∼ 10⁻³ eV, ℓ ∼ 0. 2 mm, β² ∼ 10⁻⁶ lying inside the sub-millimeter sensitivity window The theory recovers Einstein gravity with an emergent cosmological constant in the static limit, predicts finite-range Yukawa corrections, and satisfies all current local gravity constraints while naturally producing dynamical dark energy. Figures: • Figure 1: Smooth combined exclusion envelope (black curve β²ₘax (m) ) • Figure 2: Numerical cosmological evolution (Ω_μ (a), w (a) with CPL fit, \ (\) (a) ) IFG is fully falsifiable with current sub-millimeter gravity experiments (Eöt-Wash, MICROSCOPE) and upcoming cosmological surveys (DESI, Euclid, CMB-S4). The volume-normalization mechanism offers a novel geometric route to dynamical dark energy that simultaneously satisfies all local tests. Keywords: Inward Fixed-Point Gravity, IFG, volume-normalized scalar, cosmological coincidence problem, tracker quintessence, dynamical dark energy, scalar-tensor gravity, modified gravity, cosmological constant problem, Yukawa corrections, post-Newtonian constraints, equivalence principle, torsion balance, Cassini, MICROSCOPE, Eöt-Wash

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