Local Scalar Emergent Time Model (LSETM): A Covariant Framework for Local Matter Creation and Emergent Time

Version 10 — Updated Release This revision introduces a new falsifiable kinematic signature, the "Scalar-Induced BTFR Offset", derived from the adiabatic contraction of dark matter halos driven by local matter creation. Crucially, it incorporates ALMA [CII] observational data of the HZ4 system (Herrera-Camus et al.) to empirically substantiate the existence of dynamically mature rotating disks in the early Universe (z ≈ 5.5), thereby supporting the accelerated assembly mechanism. This document presents a unified approach to solve current cosmological tensions through the Local Scalar Emergent Time Model (LSETM), a covariant framework in which a sectorized scalar coupling induces effective matter creation that locally modifies the proper-time flow within the dark sector. The model provides a possible explanation for the hubble tension and several JWST-related anomalies—such as the early emergence of massive galaxies, the Little Red Dots population, and the high-redshift iron abundance—via accelerated assembly bias (gravitational catalysis) and nonlinear mass growth, while remaining compatible with atomic clock constraints. LSETM is consistent with local tests (ROCIT) and with Pantheon+ data, and leads to falsifiable predictions, including a characteristic “Triple Correlation” and a distinctive redshift-drift signal. A complementary phenomenological toy model further indicates the need for effective creation rates of order ∼ 11.9 Gyr⁻¹ in galaxies at redshifts z ≈ 9–16.5 to reproduce the observed anomalies. Note: This manuscript represents preliminary work. A complete and extended version of the LSETM framework, including detailed microphysical constraints and full parameter fits, is currently under development. Contact: [email protected]