The Big Bang as the First Collapse Front: A Singularity-Free Origin

Abstract. Standard cosmology begins with a singularity at $$t = 0$$. In the Gravity as Collapse (GAC) model, pre-Bang spacetime has collapse density $$\rho_C = 0$$ everywhere, yielding scalar curvature $$R = 0$$. No geometry, no time, no physics. The Big Bang is the first objective collapse event: $$\rho_C$$ jumps from $$0$$ to $${>} 0$$ at a null hypersurface $$\Sigma$$. Proper time begins: $$d\tau = k\, dC$$, $$k = \sqrt{\hbar G / c^5}$$. Spacetime emerges. No initial singularity. No cause required — the first collapse is the origin of causality. The result is falsifiable via CMB collapse asymmetry and LSS collapse fronts. This completes general relativity without quantizing gravity.

1. Introduction

The Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic universe:

\[ ds^2 = -dt^2 + a(t)^2 \left( \frac{dr^2}{1 - k r^2} + r^2 d\Omega^2 \right) \]

At $$t = 0$$, the scale factor $$a(t) \to 0$$, and the Hubble parameter $$H = \frac{da/dt}{a} \to \infty$$. The Ricci scalar diverges:

\[ R = 6 \left( H^2 + \frac{k}{a^2} + \frac{dH}{dt} \right) \to \infty \]

This is the cosmological singularity — the universe begins in infinite density.

The Penrose-Hawking theorems prove that, under reasonable energy conditions, gravitational collapse leads to geodesic incompleteness. Cosmic censorship hides black hole singularities, but the Big Bang is a naked singularity from the past.

We resolve the cosmological singularity using the Gravity as Collapse (GAC) model, where:

Gravity emerges from collapse density: $$R = -8 \pi G \rho_C$$
Time is procedural: $$d\tau = k\, dC$$, $$k = \sqrt{\hbar G / c^5}$$
No physics exists before collapse.

2. Collapse Density and the Pre-Bang State

Define collapse density as the rate of quantum-to-classical transitions:

\[ \rho_C(x) = \frac{dC}{d^4 x} \]

In realized spacetime, $$\rho_C {>} 0$$. Pre-Bang, quantum superposition dominates everywhere:

\[ \rho_C = 0 \quad \text{for all } x \]

Thus,

\[ R = -8 \pi G \rho_C = 0 \]

No curvature, no geometry, no time. The pre-Bang state is a timeless void — not a quantum foam, not a stringy phase, but the absence of collapse.

3. Theorem: No Cosmological Singularity

Theorem. In the Gravity as Collapse model, the universe admits no initial singularity.

Proof.
Let $$\mathcal{M}$$ be the spacetime manifold with metric $$g_{\mu\nu}$$. By the model:

The scalar curvature is $$R = -8 \pi G \rho_C$$.
Pre-Bang ($$t < 0$$), quantum superposition prevents collapse: $$\rho_C = 0$$.
Thus, $$R = 0$$ for $$t < 0$$.
All curvature invariants vanish when $$R = 0$$.

The Big Bang is the first collapse front at $$t = 0$$: $$\rho_C$$ jumps from $$0$$ to $${>} 0$$ at null hypersurface $$\Sigma$$. Spacetime begins. No divergence occurs. $\quad \blacksquare$

4. The First Collapse Front

The Big Bang is the null hypersurface $$\Sigma$$ where:

\[ \rho_C = \begin{cases} 0 & \text{for } t < 0 \\ > 0 & \text{for } t \ge 0 \end{cases} \]

This is the inflection manifold between the probabilistic future and the deterministic present.

Time begins:

\[ d\tau = k\, dC \]

The first collapse event creates the first proper time increment.

No initial conditions. No inflaton. No quantum gravity.

5. CMB and Large-Scale Structure

Collapse fronts propagate at light speed. The CMB is the relic of the first collapse front.

Predictions:

CMB temperature anisotropy from collapse fluctuations
Large-scale structure from collapse density perturbations
No B-mode polarization from primordial gravitational waves (collapse is not dynamical)

Falsifiable via Planck, Euclid, and CMB-S4.

6. Experimental Tests

Experiment	Prediction	Current Capability
CMB collapse asymmetry	Non-Gaussian collapse signature	Planck+ (2026)
LSS collapse fronts	Void collapse boundaries	Euclid (2027)
BMV/QGEM	No pre-collapse gravity	Ongoing (2026)

7. Assumptions and Falsifiability

This result is conditional on the GAC model. Key assumptions:

$$\rho_C = 0$$ for $$t < 0$$ (no collapse pre-Bang)
$$R = -8 \pi G \rho_C$$ (collapse = curvature)

These are falsifiable:

BMV/QGEM: $$\phi = 0$$ pre-collapse $$\to$$ GAC true
CMB: No collapse signature $$\to$$ GAC false

8. Discussion

This model resolves the cosmological singularity without quantizing gravity. The Planck scale is the interface between quantum potential and classical reality. Future work includes:

Deriving $$\rho_C(t)$$ from quantum field theory in FLRW spacetime.
Numerical simulation of collapse fronts using lattice methods.
Extension to inhomogeneous cosmologies.

9. Conclusion

The Big Bang is not a singularity. It is the first collapse front from a pre-spacetime state where $$\rho_C = 0$$. Spacetime begins where collapse begins. This framework provides a unified, testable resolution to the origin of the universe using the minimal possible assumptions.

References

D. Low, "Gravity as Collapse: The Emergence of Determinism from the Quantum Future," Zenodo (2025), doi.org/10.5281/zenodo.17359070
S. W. Hawking and R. Penrose, "The Singularities of Gravitational Collapse and Cosmology," Proc. R. Soc. Lond. A 314, 529 (1970)
A. H. Guth, "Inflationary universe: A possible solution to the horizon and flatness problems," Phys. Rev. D 23, 347 (1981)