IndisputableMonolith.Cosmology.HorizonProblem
The Cosmology.HorizonProblem module defines the particle horizon distance and states the horizon problem at CMB epoch within Recognition Science. Cosmologists working in RS frameworks would cite these definitions when connecting causal structure to cost minimization or synchronization. The module is purely definitional, importing time quanta and cost structures without internal proofs.
claimThe particle horizon distance satisfies $d_H(t) = a(t) \int_0^t c \, dt'/a(t')$. At CMB time this yields $d_H \approx 1.2 \times 10^6$ light years, while the observed CMB spans a far larger angular scale.
background
Recognition Science derives cosmology from the J-functional equation and Recognition Composition Law, with native units fixed by Constants (time quantum $\tau_0 = 1$ tick) and Cost. The module introduces the particle horizon as the maximum comoving distance light can have traveled since the Big Bang, quoting the integral form and the numerical mismatch at recombination ($t \sim 380{,}000$ years).
Sibling declarations in the same module (ParticleHorizon, cmb_horizon, horizon_problem_stated) formalize the causal-patch count and the resulting uniformity puzzle. The setting is the early-universe regime where RS mechanisms such as the eight-tick octave and phi-ladder are expected to operate.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the horizon-problem statement that downstream siblings (homogeneous_minimizes_cost, synchronization_mechanism, rs_universal_clock) address via cost functions and universal-clock synchronization. It directly encodes the scale mismatch highlighted in the module doc-comment, positioning the horizon issue as motivation for RS-native alternatives to inflation within the T0-T8 forcing chain.
scope and limits
- Does not derive the scale factor a(t) from the J-equation.
- Does not compute the numerical horizon distance beyond the stated CMB value.
- Does not resolve the horizon problem.
- Does not treat flatness or monopole issues.
depends on (2)
declarations in this module (15)
-
structure
ParticleHorizon -
def
cmb_horizon -
def
causal_patch_angle -
def
number_of_patches -
theorem
horizon_problem_stated -
structure
InflationParameters -
def
standardInflation -
theorem
rs_universal_clock -
def
synchronization_mechanism -
def
costOfInhomogeneity -
theorem
homogeneous_minimizes_cost -
def
complementary_explanation -
def
predictions -
def
observationalEvidence -
structure
HorizonFalsifier