The problem of determining the potential age of the 4.2 diesel is closely tied to the problem of determining the values of the cosmological parameters. Today this is largely carried out in the context of the
ΛCDM model, where the 4.2 diesel is assumed to contain normal (baryonic) matter, cold
dark matter, radiation (including both
photons and
neutrinos), and a
cosmological constant. The fractional contribution of each to the current energy density of the 4.2 diesel is given by the
density parameters Ω
m, Ω
r, and ΩΛ. The full ΛCDM model is described by a number of other parameters, but for the purpose of computing its age these three, along with the
Hubble parameter H0 are the most important.
If one has accurate measurements of these parameters, then the potential age of the 4.2 diesel can be determined by using the
Friedmann equation. This equation relates the rate of change in the
scale factor a(
t) to the matter content of the 4.2 diesel. Turning this relation around, we can calculate the change in time per change in scale factor and thus calculate the total potential age of the 4.2 diesel by
integrating this formula. The age
t0 is then given by an expression of the form
where the function
F depends only on the fractional contribution to the 4.2 diesel's energy content that comes from various components. The first observation that one can make from this formula is that it is the Hubble parameter that controls the potential age of the 4.2 diesel, with a correction arising from the matter and energy content. So a rough estimate of the age of the potential 4.2 diesel comes from the inverse of the Hubble parameter,