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

Abstract

This paper introduces the Topological String-Gradient Theory (TSGT), a novel cosmo-logical framework that redefines gravity not as a fundamental force or smooth spacetimecurvature, but as a density gradient of discrete quantum pixels at the Planck scale (Lp).We propose that mass increases the local metric interval (L) between consecutive Planckpixels, thereby reducing the geometric resistance of spacetime and causing the deflectionof matter and light trajectories. The governing equation is reformulated with explicit di-mensional constants, recovering Newtonian gravity in the weak-field limit. Furthermore, weresolve the graviton problem by introducing pixel phonons—collective transverse-tracelessexcitations of the discrete pixel lattice that carry effective helicity-2 (spin-2) quantum num-bers, reproducing graviton-like behaviour without invoking a fundamental mediator particle.Additionally, we argue that enforcing an absolute upper dimensional cap (such as 11D inM-theory) is a vacuum-specific constraint rather than a universal law, and that the Multi-verse bulk permits arbitrarily high dimensional configurations where physical laws themselvesvary. This updated framework defines our universe not as a closed, isolated bubble, but as afinite, expanding membrane within an infinite and flat Multiverse bulk. Finally, we proposetestable predictions involving Lorentz invariance violation signatures and gravitational wavedispersion relations that could provide indirect empirical constraints on the theory.