Since #56, a lot of trial and error has happened and the 'final' design happened to be quite an ordinary balloon, with the expansion energy (vacuum and momentum) supplied by a pump or pressure reservoir that simply inflates/deflates the balloon to simulate the Friedman equations. All other efforts were hampered by either exotic fluids or very difficult concepts to fathom. The present 'best buy' is at least 'engineering-friendly' in that we can even contemplate building it!

1 Specification

It is proposed that spec. 1.2.3 to 1.2.5 be replaced by:

1.2.3 Vacuum (Change note: this post)

Vacuum energy (cosmological constant) shall be included in any inflating/deflating mechanism of the balloon.

1.2.4 Total Energy

It may be assumed that the energy of expansion is included in the algorithm that inflates/deflates the balloon.

1.2.5 Momentum

It may be assumed that the momenta of the skin and all energy on it are included in the algorithm that inflates/deflates the balloon.

2 Design

For the Design part, it is proposed that the 'special fluid' design be scrapped and the 'ordinary balloon' of reply #228 be inserted. Here is a summary:

Assume a balloon material that retains its elasticity over a reasonable range of balloon radii (at least enough range to illustrate the principles). A sensor system measures the balloon radius (R) directly and also determines the rate of change (ΔR/dt). A pump/reservoir/valve system supplies or withdraws gas to/from the balloon at a rate that will keep ΔR/dt = R H, where H is a function of R and the energy density makeup of the cosmos to be simulated. H, the time variable Hubble parameter, is obtained from:

H² = H₀² [(1-Ω₀)/a² + Ω_m/a³ + Ω_r/a⁴ + Ω_Λ]

where H₀ is the (present) Hubble constant, Ω₀ = Ω_m + Ω_r + Ω_Λ is the present total energy density parameter, a=R/R₀ the expansion factor, Ω_m the present matter energy density parameter, Ω_r the present radiation energy density parameter and Ω_Λ the present vacuum energy density parameter.

The operating equation is then:

(ΔR/dt)² = R²H² = R²H₀² [(1-Ω₀)/a² + Ω_m/a³ + Ω_r/a⁴ + Ω_Λ]

'Guest' has proposed a neat little high level algorithm for this system in reply #242. In its final form, it should be part of the design section.

3 Tests

Since the balloon is ensured to follow the Friedman equations (at least theoretically), paper 'tests' would not be very meaningful. It is proposed that the 3 cases (de Sitter, Einstein-de Sitter and Lambda-cold-dark-matter (LCDM)) be simulated and the results shown here for comparison to other simulations.

Of more interest may be specific 'applications' of the simulation, e.g., the 'cosmic teardrop', 'tethered galaxy' and redshift:distance experiments.

-J