A Novel Framework for Quantum Residuals from Pre-Bigbang Phase Transitions and their Connection to Riemann Zeta Zeros

This research proposal introduces a novel theoretical framework that establishes a profound connection between quantum residual modes arising from hypothetical pre-Bigbang phase transitions and the statistical properties of the Riemann zeta function's non-trivial zeros, specifically their pair correlation function. The paper analyzes the roll-down dynamics of an imaginary-mass scalar field within the Us phase (conceptualizing pre-Bigbang universes, or 'cosmic seeds') and its transition into the Ug phase (representing post-Bigbang universes, including our own, generated from the Us phase). Through this analysis, we derive the spectral density, ρres(ω), of the surviving high-frequency modes, which represent the "quantum residuals" of this transition. A central conjecture of this work is the deep spectral correspondence between ρres(ω) and the fluctuation term ϵ(α) observed in the Montgomery pair correlation function of zeta zeros. This proposes that the "memory" of fundamental symmetry-breaking events in the early cosmos might be encoded in the seemingly abstract distribution of prime numbers. We present observational forecasts for these residual signatures across various cosmological phenomena and precision experiments, including: Anomalies in the Cosmic Microwave Background (CMB) temperature multipole spectrum at high (e.g., > 2000). Excess noise spectral density in precision interferometer experiments (e.g., relevant for gravitational wave detectors like LIGO/LISA). Additional damping in the low-frequency gravitational wave background (f<10−9 Hz). This study aims to bridge fundamental number theory and observable cosmology, offering new avenues for experimental tests of theories concerning quantum gravity and the very early universe. The proposed project plan outlines an 18-month research schedule, key deliverables including simulation data, and strategies for risk mitigation.