IndisputableMonolith.Cosmology.EarlyUniverse
Module formalizing the early-universe initial condition in Recognition Science: the cosmos begins in the unique zero-defect ledger state, identified with the Big Bang without a geometric singularity. It packages the zero-defect claim, a derived dark-energy density parameter in (0,1), a cosmological-constant resolution, and a no-singularity statement. Cosmologists tracing RS initial conditions and dark-energy structure would cite it. Arguments rest on the Law of Existence and the Initial Condition foundation modules.
claimThe universe begins in the unique zero-defect configuration: the Big Bang initial condition is the minimum-cost ledger state (not a singularity). The module also records a dark-energy density parameter $\Omega_\Lambda$ with $0 < \Omega_\Lambda < 1$, a resolution of the cosmological-constant problem in that setting, and a no-singularity claim for the initial state.
background
Recognition Science identifies existence with vanishing defect: $x$ exists if and only if $\mathrm{defect}(x)=0$ (Law of Existence). Cost is measured by the $J$-functional from the forcing chain; the unique minimum-cost configuration is the zero-defect ledger state.
The Initial Condition foundation (F-005) addresses the Past Hypothesis: why the universe began in a low-entropy state. This cosmology module specializes that story to the early universe, reading the Big Bang as that unique zero-defect start rather than a curvature singularity.
Constants supply the RS time quantum $\tau_0=1$ tick. Sibling declarations name the zero-defect initial state, $\Omega_\Lambda$ with positivity and upper bound, a cosmological-constant resolution, and absence of singularity.
proof idea
Module-level packaging, not a single theorem. It imports Cost, Constants, Law of Existence, and Initial Condition, then exposes sibling results: the initial state is zero-defect; $\Omega_\Lambda$ is defined and shown positive and strictly less than one; those feed a cosmological-constant resolution; and a no-singularity claim closes the geometric reading of the start. Downstream dark-energy evolution imports the module as a block. Individual proofs live on the siblings; the module's role is to assemble the early-universe narrative from those foundations.
why it matters in Recognition Science
Places the Big Bang inside the RS ledger: unique zero-defect start, minimum cost, no singularity. That supplies the early-universe side of the low-entropy Past Hypothesis (F-005) and ties existence to defect zero via the Law of Existence.
DarkEnergyEvolutionStructure (D-006: is dark energy constant or evolving?) imports this module, so the $\Omega_\Lambda\in(0,1)$ package and cosmological-constant resolution become inputs to the structural dark-energy equation-of-state framework. In the broader chain, zero-defect uniqueness and $J$-cost minima sit upstream of phi-ladder and forcing landmarks; here they are applied to cosmology rather than re-derived.
scope and limits
- Does not derive FLRW metrics, inflation, or Boltzmann nucleosynthesis from first principles.
- Does not compute a numerical value of $\Omega_\Lambda$ beyond the open interval $(0,1)$.
- Does not replace general-relativistic singularity theorems outside the RS defect ledger.
- Does not prove late-time dark-energy evolution; that lives in the downstream D-006 module.
- Does not re-prove $J$-uniqueness or the Law of Existence; those are imported.