Singularity as an Epistemic Artifact: Finite Cyclic Cosmology without Actual Infinities

In the paper's words

Cosmological singularities — states in which density, curvature and temperature diverge — mark the breakdown of predictive physics at the Big Bang and inside black holes, and they block any quantitative continuation of collapse or of the early universe. Whether these infinities are features of reality or artifacts of the mathematical representation remains open. This paper tests the conjecture that actual infinities in gravitational physics are artifacts of adopting a linear, unbounded number line, and that in a cyclic framework a "singularity" is a transition between epochs rather than a physical infinity.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. In a closed dust universe with density parameter $\Omega_0$, recollapse occurs at the finite scale factor $a_{\max}/a_0 = \Omega_0/(\Omega_0-1)$; for $\Omega_0 = 1.2$ this gives $a_{\max} = 6\,a_0$ and a density at recollapse of $\rho_0/216$.

   from Abstract

2. Using SKA1 dipole forecasts, the ratio of the kinematic dipole to the large-scale-structure dipole is $R = 0.0046/0.0031 \approx 1.48$ with forecast uncertainty $\pm 0.76$.

   from Abstract

3. A quantitative observational anchor: the ratio of the SKA1 forecast kinematic dipole amplitude to the large-scale-structure dipole amplitude, $R = 0.0046/0.0031 \approx 1.48 \pm 0.76$, derived with full arithmetic and propagated uncertainty (Section 4.7).

   from 1. Introduction

4. Then $\Omega_0 - 1 = 0.2$ and $$a_{\max}/a_0 = \frac{1.2}{0.2} = 6.$$ With dust scaling $\rho \propto a^{-3}$, the density at recollapse is $$\rho(a_{\max}) = \rho_0 \left(\frac{a_0}{a_{\max}}\right)^{3} = \rho_0 \left(\frac{1}{6}\right)^{3} = \frac{\rho_0}{216} \approx 4.63 \times 10^{-3}\,\rho_0.$$ The recollapse point is therefore reached at a finite scale factor with a finite, indeed small, density; the divergence in this model sits at the endpoints $a \to 0$, which Section 4.3 re-parametrizes.

   from 4.2 Finite recollapse in a closed dust universe

5. Hence $$\rho(a_{\max}) = \frac{\rho_0}{8.012 \times 10^{9}} \approx 1.25 \times 10^{-10}\,\rho_0.$$ As $\Omega_0 \to 1^{+}$, $a_{\max} \to \infty$ while the density at recollapse tends to zero: the "infinity" approached in the linear scale-factor chart is reached through a family of entirely finite states.

   from 4.2 Finite recollapse in a closed dust universe

6. The number $N \approx 8.50 \times 10^{60}$ is the finite budget within which any cyclic construction must fit the observable universe's history.

   from 4.5 Discrete clock spanning the Hubble radius

How it is done

1. Alternative quantizations support the same direction. [4] proposes a quantization of homogeneous cosmological models combining the Dirac constrained-system method, Fock space construction, second quantization and a Diagonalization Ansatz (Bogoliubov transformation plus Heisenberg equation), arguing that canonical, loop and path-integral quantizations apply quantum mechanics too straightforwardly and that the Wheeler–DeWitt functional differential equation "does not allow to solve the generic problem in principle" [4].

   from 2. Background and Related Work

2. The paper's claims are of two kinds.

   from 3.1 Scope and honesty of the construction

3. The audit question is whether the theorem's conclusion is a statement about the manifold or about the chart in which $\lambda$ is linear.

   from 3.4 Audit of singularity-theorem hypotheses

4. Geodesic incompleteness means that the affine parameter $\lambda$ of some geodesic has a finite bound, say $\lambda \lt \lambda_{\max}$, with no extension beyond it.

   from 4.4 Audit of the singularity-theorem hypotheses

What would falsify it

1. Cosmologists and gravitational physicists face a concrete, unsolved problem: the classical theories they use predict that certain physical quantities become infinite.

   from 1. Introduction

2. The practical cost is severe: no equation of state, no initial condition and no prediction can be formulated at or beyond an infinite quantity, so the origin of the universe and the final state of collapse currently lie outside quantitative physics altogether.

   from 1. Introduction

3. Model builders would gain a design principle — choose parametrizations in which every observable is bounded — and observationalists would gain discriminators between "transition" and "termination" readings of the same data.

   from 1. Introduction

Where the claim stops

1. Where a number is a projection rather than a derivation, it is labeled as such with its assumptions.

   from 3.1 Scope and honesty of the construction

2. It would be falsified by a demonstration that some invariant, chart-independent quantity — e.g. a curvature scalar or a geodesic length computed in a manifestly finite representation — diverges in a way that no re-parametrization can remove, or equivalently that the wraparound construction of Section 4.5 cannot be made dynamical without reintroducing an unbounded parameter in the equations of motion.

   from 6. Discussion

3. The recollapse and clock models are not solutions with realistic matter; the recollapse density $\rho_0/216$ is a consequence of the dust assumption and changes with the equation of state.

   from 6. Discussion

Where to read

1. Abstract240 words · 1 min
2. 1. Introduction501 words · 2 min
3. 2. Background and Related Work907 words · 4 min
4. 3. Methods399 words · 2 min
5. 4. Analysis1,288 words · 6 min
6. 5. Results219 words · 1 min
7. 6. Discussion568 words · 2 min
8. 7. Practical Implications and Engineering Pathways556 words · 2 min
9. 8. Conclusion201 words · 1 min
10. Provenance and AI Involvement225 words · 1 min