Emergent Temporal Flow from Signature Change and its Cosmological Implications

This work proposes a fundamental transition in the early universe where the metric signature changes from Euclidean to Lorentzian, triggered when vacuum energy exceeds a critical threshold. By introducing a continuous energy flux ($\rho_{flow}$) from the Euclidean sector, we present a unified framework to address major cosmological anomalies.

Key highlights of this upload:

• Hubble Tension: Resolution of the discrepancy between $H_0 \approx 67.4$ and $73.1$ km/s/Mpc through a dynamical temporal channel.

• $S_8$ Tension: Suppression of matter growth via quadratic viscosity $\epsilon = \kappa^2$, where $\kappa = 3/8\pi$.

• NANOGrav Validation: Consistency with the stochastic gravitational wave background (SGWB) with a spectral index $\gamma \approx 3.15$.

The upload includes the full manuscript (PDF), Python source codes for figure generation, and Monte Carlo simulation data for statistical validation.