Temporal Texture Gravity — Paper B: The Texture Tower and the Activation Boundary

What if the rapid expansion of the early universe and the dark energy accelerating it today are actually two sides of the very same coin?

This paper presents the cosmological sector of Temporal Texture Gravity, introducing a unified mechanism that connects the beginning of the universe to its present day. Instead of inventing separate, unrelated fields for early inflation and late-time dark energy, the model introduces a "Texture Tower"—a multi-scale hierarchy of temporal fields—governed by a single, moving "activation boundary".

This activation boundary acts as a dynamic threshold that sweeps through scales as the universe expands:

• Early Universe (Inflation): During the early cosmic epoch, the boundary sweeps downward, progressively freezing heavier temporal modes one after another. This coordinated freeze-out drives the rapid, controlled expansion of inflation.

• Late Universe (Dark Energy): As cosmic expansion slows over billions of years, the boundary reverses direction and sweeps upward. It thaws previously frozen modes starting with the heaviest, naturally generating the late-time dark energy acceleration we observe today.

By deriving how perturbations pass through these activation events, the paper establishes clear, falsifiable observational signatures:

• Strict Dark Energy Limit: The framework proves a strict, parameter-free bound for dark energy ($w \ge -1$), ruling out "phantom" dark energy in the healthy sector. Any confirmed, high-significance measurement of phantom dark energy would directly falsify the model.

• Asymmetric Cosmic Footprints: When temporal modes activate, they leave distinct, step-like imprints and ringing patterns in cosmic microwave background fluctuations (scalar modes), while gravitational waves (tensor modes) pass through unaffected.

By replacing separate cosmological assumptions with a single boundary equation, this paper offers a streamlined, highly testable framework for cosmic evolution.