A Dual-Component Engine for Simulating Non-Singular Cosmological Bounces (v31.2)

[Rupayan52]

Hello everyone,

I’ve recently open-sourced v31.2 of the Bandyopadhyay Cyclic Manifold, a computational cosmology engine that might be of interest to researchers working with N-body simulations, SPH, or FLRW metrics.

Our previous versions relied on scripted cutoffs to avoid singularities (e.g., forcing a bounce when $\rho \geq \rho_{Planck}$). Version 31.2 completely discards these prescriptive flags in favor of emergent fluid dynamics.

Core Physics Architecture

The engine operates on a tripartite energy loop ($I_{total} = I_{dark} + I_{baryon} + I_{vacuum} \equiv 1.000000$) utilizing two distinct sectors:

• Dark Matter (PM Grid): Collisionless scaffolding driving the gravitational crunch via a fast Poisson solver ($\nabla^2 \Phi = 4\pi G \rho_{DM}$).
• Baryonic Fluid (SPH): Collisional matter that resists infinite compression via a vectorized Smoothed Particle Hydrodynamics kernel.

What's New in v31.2?

1. The Hydrodynamic Bounce: The cosmological bounce is now mathematically emergent. It triggers solely when the internal SPH fluid pressure ($P = k\rho^2$) violently overcomes the inward PM gravitational tensor.
2. True Hubble Flow: Spacetime expansion is coupled directly to the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. The comoving box mathematically stretches via the scale factor $a(t)$, carrying matter outward in a genuine Hubble Flow.
3. Adiabatic Relaxation Layer: To prevent "Initial Condition Shock" from particles spawning in quasi-random distributions, we implemented a velocity-damping phase for early epochs, allowing the fluid to naturally accrete into Dark Matter halos before the crunch accelerates.

The engine is written in Python, accelerated via JAX, and optimized for TPU execution.

Code & Interactive Colab: https://github.com/Rupayan52/String-Star-Manifold

I would highly value any critical feedback from the fluid dynamics or cosmology communities, particularly regarding our tuning of the SPH fluid stiffness ($k$) relative to the PM grid resolution.