Topological String-Gradient Theory: Metric Replication of Space-Time and Cosmological Evolution (Revised)

Abstract

This paper introduces the Topological String-Gradient Theory (TSGT), a novelcosmological framework that redefines gravity not as a fundamental force or smoothspacetime curvature, but as a density gradient of discrete quantum pixels at thePlanck scale (Lp). We propose that mass increases the local metric interval (L)between consecutive Planck pixels, thereby reducing the geometric resistance ofspacetime and causing the deflection of matter and light trajectories. The govern-ing equation is reformulated with explicit dimensional constants, recovering New-tonian gravity in the weak-field limit. Furthermore, we argue that enforcing anabsolute upper dimensional cap (such as 11D in M-theory) is a vacuum-specificconstraint rather than a universal law, and that the Multiverse bulk permits arbi-trarily high dimensional configurations where physical laws themselves vary. Thisupdated framework defines our universe not as a closed, isolated bubble, but as afinite, expanding membrane within an infinite and flat Multiverse bulk. Finally,we propose testable predictions involving Lorentz invariance violation signaturesand gravitational wave dispersion relations that could provide indirect empiricalconstraints on the theory.