A Unified Emergent Model for Cosmic Acceleration and Galactic Dynamics: The PXT UP Framework

Title: A Unified Emergent Model for Cosmic Acceleration and Galactic Dynamics: The PXT UP Framework Note: Revised version with refined academic language and clarified scope. No change to the core theoretical framework. Author: Pham Xuan Tung(Independent Researcher, Cao Bang, Vietnam) Abstract: We present the PXT UP Framework, a novel modified gravity theory within the f(R,T)f(R,T) class, designed to unify the explanation of cosmic acceleration and galactic dynamics without invoking Dark Energy or particulate Cold Dark Matter (CDM). Grounded in the "Nested Reality" postulate, this framework models the universe as an open thermodynamic system interacting with an external Background Environment. This interaction is encoded in the Einstein-Hilbert action via a trace-dependent scalar function, g(T)g(T). We propose a specific saturation ansatz for this interaction term: g(T)=−2Λeff/(1+(T/ρm,0)3/2)g(T)=−2Λeff/(1+(T/ρm,0)3/2), where TT is the trace of the energy-momentum tensor. This functional form naturally interpolates between three distinct physical regimes based on local matter density:(i) At low densities (galactic scales), it reproduces MOND-like phenomenology, explaining flat rotation curves;(ii) As density approaches zero (late-time vacuum), it asymptotes to an effective cosmological constant ΛeffΛeff, driving Cosmic Acceleration;(iii) At high densities (early universe and galaxy clusters), it exhibits a saturation mechanism that acts as a natural screening effect. Crucially, this screening mechanism suppresses the growth of structure at cluster scales relative to the standard model, offering a natural physical resolution to the ongoing S8S8tension (sigma-8 tension). We performed a rigorous Joint MCMC analysis using datasets from Planck 2018 (CMB), BAO, Pantheon+ (SNe Ia), and DES Y3 (Weak Lensing). The results demonstrate that the PXT UP model achieves a goodness-of-fit comparable to the standard ΛΛCDM model (Δχ2≈+4Δχ2≈+4 with the same number of free parameters), while successfully resolving the Fine-Tuning and Coincidence problems. The theory makes sharp, falsifiable predictions for future surveys, including a specific non-unity gravitational slip (Φ≠ΨΦ=Ψ) and a dynamic equation of state w(z)w(z). Keywords: Modified Gravity, f(R,T) Gravity, Dark Energy, Dark Matter, MOND, S8 Tension, Hubble Tension, Cosmic Acceleration, Nested Reality, Emergent Gravity, PXT UP.