Historical content. This page belongs to the former “solved problems” section. The Tratado de Fundamentos (v35, Jun 2026) does not present these problems as solved: it develops them in full, classifies several results as conditional and keeps seven open fronts. The values of S and the thresholds quoted here may correspond to the earlier formulation. The current classification of each result is in the status of the results.

Big Bang Singularity

What happens at t = 0? Why do the laws of physics “collapse” at the initial singularity?

This page is a translation of the Spanish original. Where they differ, the Spanish text prevails.

The Problem

In standard cosmology, extrapolating backward, we arrive at a point where the density and temperature become infinite. This is the singularity problem: Einstein's equations predict their own invalidity.

The Classical Singularity

ρ → ∞, T → ∞, R → 0

When a(t) → 0, everything diverges

$$\rho = \frac{3H^2}{8\pi G} \xrightarrow{a \to 0} \infty$$
  • Infinite density: All matter at a point
  • Infinite temperature: Energy per volume → ∞
  • Infinite curvature: R_μνρσ diverges
  • Invalid laws: GR is not predictive beyond that point

Theoretical Problems

General Relativity

  • Predicts the singularity
  • Penrose-Hawking theorems
  • Reasonable energy conditions
  • Inevitably fails at t = 0

Quantum Physics

  • l_Pl ~ 10⁻³⁵ m is a limit
  • QFT fails at smaller scales
  • We need quantum gravity
  • There is no complete theory

The MCMC Solution

The MCMC avoids the singularity through the Primordial State and the primordial imperfection δ₀:

Primordial State (S = 0)

Instead of a singularity, the MCMC postulates an initial state of maximum finite tension:

$$S = 0: \quad Mp \approx Ep, \quad P_{ME} = \delta_0 \neq 0$$

In this state:

  • No entropy: S = 0 (there is no distinction)
  • No time: dt = 0 (time is born at S = 1.001)
  • No space: The metric is not defined
  • Finite tension: Mp, Ep are finite (not infinite)

The Primordial Imperfection δ₀

The Primordial State is not perfectly symmetric. There is an intrinsic imperfection δ₀ that is the source of all dynamism:

$$P_{ME}(S = 0^+) = \frac{Mp - Ep}{Mp + Ep} = \delta_0 \neq 0$$

This imperfection is the engine of cosmic evolution. Without δ₀, the Primordial State would be static forever. δ₀ generates:

  • CPT violation at S₀.₀₉₉ (baryon asymmetry)
  • Birth of time at S₁.₀₀₁
  • ECV and MCV as released/retained tensions

The “Big Bang” as a Transition

What we call the “Big Bang” is the sequence of entropic transitions driven by δ₀:

$$S: 0 \xrightarrow{\delta_0} S_{0.099} \xrightarrow{CTP} S_{1.001} \xrightarrow{tiempo} \cdots$$

This transition is not an “explosion” from a point, but the gradual emergence of the universe from the Primordial State.

Why Is There No Singularity?

Classical GR

  • a(t) → 0 implies ρ → ∞
  • Assumes continuous space
  • There is no lower limit
  • Extrapolation to t = 0

MCMC

  • a does not exist for S = 0
  • Space emerges with S > 0
  • Density always finite
  • There is no “before” the Primordial State
Singularity → Imperfection δ₀
Finite tension with intrinsic dynamism

The universe did not “begin” at an infinite point, but “emerged” from a pre-geometric state driven by the primordial imperfection δ₀

Maximum Finite Density

Upper Bound Imposed by δ₀

The MCMC imposes a maximum density of the Planck order, but finite, precisely because δ₀ ≠ 0:

$$\rho_{max} = \rho_{Pl} \cdot (1 - \delta_0^2) < \rho_{Pl}$$

Where ρPl ~ 10⁹³ g/cm³ is the Planck density. The imperfection δ₀ has a double role:

  • Prevents the singularity: ρ never reaches infinity
  • Generates dynamism: It is the “spark” that starts the evolution

δ₀: Source of All Dynamism

One Imperfection, Multiple Consequences

The primordial imperfection δ₀ not only avoids the singularity, but is the sole source of all cosmic phenomena:

  • S₀.₀₉₉: CPT violation → baryon asymmetry
  • S₁.₀₀₁: Birth of time and mass gap
  • ECV (ρ_id): Tension released into space
  • MCV (ρ_lat): Tension retained in structures

δ₀ is the ontological “original sin” that makes the existence of the universe possible.

Comparison with Other Proposals

Proposal How It Avoids the Singularity Limitations
LQG (Loop) Discretization of space Not a complete theory
Bounce cosmologies Prior contraction Requires NEC violation
Eternal inflation Shifts the singularity Does not really eliminate it
MCMC Timeless Primordial State Requires a new ontology
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