Inverse Time Limit Theory (ITLT)

We present Inverse Time Limit Theory (ITLT), a geometric framework based on the principle that spacetime curvature saturates at a fundamental density scale:

 ρ* = βMₚ⁴

This principle provides a minimal extension of Einstein gravity without modifying the Einstein–Hilbert action or introducing additional fields. In the static, spherically symmetric sector, it yields a regular black hole solution described by the metric function

f(r) = 1 − (2Mr²)/(r³ + a),

where a = M/ρ*

This spacetime is free of curvature singularities, contains a finite-curvature core, and asymptotically recovers the Schwarzschild solution. 

All curvature invariants remain finite, and the spacetime is geodesically complete.
The same curvature saturation principle extends naturally to homogeneous cosmology, leading to a modified Friedmann equation in which the Hubble parameter remains finite at arbitrarily high densities. This eliminates the classical Big Bang curvature divergence while preserving standard cosmological evolution in the low-density limit. The theory predicts the existence of a universal curvature bound, nonsingular black hole interiors, and Planck-scale remnant formation.
ITLT provides a unified and purely geometric mechanism for singularity resolution in both gravitational collapse and cosmology, governed by a single universal curvature scale, while remaining fully consistent with Einstein gravity in the weak-curvature regime.