Intrinsic Metric Time Dilation in Early and Late Cosmology: A Geometrodynamic Solution to the Horizon Problem and Dark Energy beyond the Inflationary Scenario

This work postulates a fundamental and far-reaching modification of the established standard model of cosmology (Lambda-CDM). The aim is to eliminate the theoretical necessity of a hypothetical scalar Inflaton field, which serves as the primary mechanism for solving initial value problems in modern cosmology, and to replace it with a purely geometric solution.Based on the profound ontological premise that time is not a fundamental background parameter but an emergent property of the spatial fabric (introduced here as the "Density-Time Hypothesis"), a direct, analytical coupling between the local energy density rho and the time component of the metric tensor g_00 is formulated.It is mathematically rigorously derived within this work that in the limit where volume approaches zero (i.e., in the Planck era), an asymptotic metric time dilation occurs (N >> 1). This dilation increases the effective causal horizon massively. This enables thermodynamic equilibrium across the entire currently observable region of the universe without postulating a superluminal expansion of space.Furthermore, it is shown that a dynamic time gradient exists, acting relative to the metric expansion of space. This gradient forces a freeze-out of primordial quantum fluctuations, thus providing a natural explanation for structure formation.The work also extends the model to the late universe: The observed apparent acceleration is identified as a geometric residue of time relaxation. A quantitative analysis constrains the exponent n of the Lapse function to the range 1