Cosmological Puzzles that Dissolve

Several famous problems of standard cosmology—Olbers' paradox, the horizon and flatness problems, the cosmological-constant catastrophe, and the age problem—are artefacts of an expanding, finite-age universe; in a static, attenuating medium they do not arise. Olbers is resolved by optical attenuation, and the constant problem dissolves because a uniform jammed background does not gravitate. These are distinguishing statements.

Four problems motivate large parts of standard cosmology: Olbers' paradox asks why the night sky is dark if the universe is infinite and static; the horizon problem asks how causally disconnected regions share one temperature; the flatness problem asks why the density sits so close to critical; and the cosmological-constant problem asks why the vacuum energy is not vast.

The puzzles, and why they are interpretation-bound

Four problems motivate large parts of standard cosmology. Olbers asked why the night sky is dark if the universe is infinite and static. The horizon problem asks how regions of the microwave sky that were never in causal contact share the same temperature to one part in 10⁵. The flatness problem asks why the present density sits so close to critical that the early universe was tuned to one part in 10⁶⁰. The cosmological-constant problem asks why the quantum vacuum energy, estimated near 10¹¹³Jm⁻³, exceeds the observed dark-energy density near 10⁻⁹Jm⁻³ by a factor of about 10¹²⁰. Each presupposes an expanding universe with a finite age and an inflationary or fine-tuned beginning. We take them in turn.

Olbers' paradox, resolved by attenuation

In a static, uniform universe of source number density n and luminosity L, the brightness contributed by a shell of radius r and thickness dr is the per-source flux L/(4π r²) times the shell's source count 4π r² ndr, so without absorption the integral ∫₀^(∞) nLdr diverges—the classical paradox. The lattice-optics cosmology of Chapter 7 attenuates each source by e^-κₒₚₜ r, with κₒₚₜ=H₀/c, giving

which is finite. The attenuation length 1/κₒₚₜ=c/H₀ is the same Hubble length that sets the low-redshift distance law (Chapter 7); the very quantity that produces the redshift also resolves Olbers. The night sky is dark because distant light is absorbed by the medium, not because the universe is young—a distinguishing resolution that needs no expansion.

Horizon and flatness: problems that do not arise

The horizon problem is a problem only because expansion places distant patches outside each other's past light cones. In the static picture the microwave background is present lattice emission (Chapter 9): its uniformity is the uniformity of a medium in present thermal equilibrium, set by ordinary local thermalisation rather than by causal contact in a hot beginning, so no horizon mismatch arises. The flatness problem is likewise a statement about the time evolution of the density parameter Ω(t) in an expanding model; a static medium has no such running Ω to tune toward unity, so the fine-tuning the problem describes is absent. Neither problem is solved—each simply never appears, which is the stronger distinguishing claim.

The cosmological-constant catastrophe dissolves

The deepest of the four is the vacuum-energy problem. Here the framework makes its sharpest distinguishing statement, and it follows directly from Chapter 3. Gravity in this volume is the momentum of absorbed inflow: only a sink—a region that annihilates quanta—produces a net inward flow and therefore gravitates. A uniform, unperturbed jammed background annihilates nothing and drives no net inflow, so however large its zero-point energy density, it exerts no gravitational force and curves nothing. The 10¹²⁰ mismatch between the estimated vacuum energy 10¹¹³Jm⁻³ and the gravitating dark-energy density 10⁻⁹Jm⁻³ is a mismatch only if vacuum energy is assumed to gravitate; in this framework it does not, and there is no cosmological constant to predict in the first place. The accelerating-expansion data that Λ was introduced to fit are already accounted for, without dark energy, by the static distance law of Chapter 7 (χ²/dof=0.50 against the supernova Hubble diagram).

The age problem, reinterpreted

Finally, the inverse Hubble time H₀⁻¹≈1.4×10¹⁰yr is, in the expanding picture, an age—the time since the beginning—and stars or structures older than it create tension. In the static picture H₀⁻¹ is not an age but the characteristic attenuation timescale 1/(κₒₚₜc): the e-folding distance of light divided by c. Nothing in the framework forbids objects older than H₀⁻¹, because H₀⁻¹ does not date an origin. The volume makes no positive claim about the age of the universe (it asserts no cosmic history); it removes the tension, which was an artefact of reading an attenuation rate as a birth date.

Simulation: the dark sky

The one quantitative item, Olbers' integral, is checked directly. Simulation A sums the brightness of a uniform source distribution out to large radius, with and without the e^-κₒₚₜ r attenuation, confirming divergence in the first case and convergence to nL/κₒₚₜ in the second:

# A: integrated sky brightness, uniform sources, kappa_opt = H0/c
no attenuation:   B(R) grows without bound as R increases   (Olbers paradox)
with attenuation: B -> nL/kappa_opt  (finite)               -> dark night sky

The brightness saturates at the finite value nL/κₒₚₜ once attenuation is included. This chapter introduces no new physics: it shows that four standard puzzles are consequences of the expanding interpretation, and that the static, attenuating medium of Chapters 7 and 9 either resolves them quantitatively (Olbers) or never raises them (horizon, flatness, Λ, age)—a coherent set of distinguishing simplifications.