IndisputableMonolith.Relativity.Cosmology.FRWMetric
FRWMetric module supplies the Friedmann-Robertson-Walker line element, scale factor, Christoffel symbols, and Ricci components for homogeneous isotropic cosmologies. Workers on Buchert averaging or optical rescaling in Recognition Science import these objects when constructing averaged equations or Sachs optics. The module contains only definitions and no theorems.
claimThe module introduces the scale factor $a(t)$, the FRW metric $ds^2 = -dt^2 + a(t)^2 [dr^2/(1-kr^2) + r^2 dΩ^2]$, the Christoffel symbols $Γ^λ_{μν}$, and the Ricci tensor components $R_{00}$, $R_{ij}$ on the FRW background.
background
This module aggregates geometry and calculus primitives inside the Relativity.Cosmology namespace. It defines the standard FRW line element together with its connection and curvature tensors for use in homogeneous isotropic models. The upstream Geometry module supplies the general metric and covariant derivative machinery; the Calculus module supplies the differential operators applied to the scale factor.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
These definitions are imported by the Buchert module to formalize algebraic cancellation of the kinematical backreaction $Q_D$ and by the OpticalExtension module to rescale the Ricci focusing term by $Υ(a)$. They also support the GW.ActionExpansion and GW.TensorDecomposition modules. The objects close the step from the Recognition Science forcing chain (T0-T8) to observable cosmology.
scope and limits
- Does not specify the stress-energy tensor or matter content.
- Does not solve the Friedmann equations.
- Does not treat perturbations or inhomogeneities.
- Does not derive the metric from the Recognition Science functional equation.