This work presents the GQI/PHI Universe Theory, a comprehensive framework that unifies quantum information and cosmology through the concept of modular integrated information (ΦmodΦmod). Grounded in finite type I von Neumann algebras and Tomita–Takesaki modular theory, we derive a universal coupling function F(x)=(1+x)ln(1+x)−xF(x)=(1+x)ln(1+x)−x from three independent principles (CPTP monotonicity, Bregman duality, and modular thermodynamics). The theory is extended to quantum field theory in curved spacetime, yielding a finite modular difference operator that generates scale-dependent corrections to the primordial power spectrum, with amplitudes fixed by conformal anomalies. These corrections produce distinctive signatures in cosmological observables: a 1/k21/k2 modulation of the matter power spectrum (testable by DESI/Euclid), enhanced tensor modes, small non-Gaussianities, and potential CMB birefringence. The same formalism naturally explains dark energy as the residual value of ΦmodΦmod today (Φ0≈1.63Φ0≈1.63, w≈−1w≈−1), connects to an inflationary model with ns=0.963ns=0.963 and r=0.0044r=0.0044 (compatible with Planck), and offers geometric-informational interpretations of dark matter (as modular gradients), black holes (as modular processors), and the arrow of time. This document compiles the full derivations, mathematical foundations, cross-checked uniqueness proofs, numerical predictions, and a discussion of open issues, establishing a falsifiable framework that bridges quantum information theory and large-scale cosmology.
Gaspar Salvador García (Thu,) studied this question.