In this final part of the miniseries on cosmology equations, the inflationary epoch of cosmic expansion is summarized in 'engineering' style. In Part 5, the expansion curve from the Friedmann equation has been given. The Friedmann equation does not hold for the first few moments after the Big Bang, because the expansion rate changed exponentially for a very, very brief period.
On a loglog scale, the radius of the observable universe against time has this form:
where r_{P} is the Planck length and t_{P} the Planck time (≈10^{43}s). For clarity (in a slightly faint figure), the horizontal scale is log(t/t_{P}) and the vertical scale log(r/r_{P}), where r is the radius of the observable universe at time t (with r in light travel time units, e.g. lightyears).
From t_{P} to about 10^{34}s, it seems like nothing much happened and then, in the incredibly short time interval of 10^{32}s, our observable space "exploded" from ≈10^{28 }meters to about one meter radius, effectively increasing by a factor ≈10^{28} in radius! Now that's inflation like we hope we never see again, monetary or otherwise!
The "nothing much happened" of the first ≈10^{34}s actually meant a lot! Since there was little expansion, all regions of the embryonic universe could equal out in temperature by means of normal radiation at the speed of light. After the inflationary "explosion", that would not be possible any time soon again, if ever.
According to inflation theory, the embryo universe then (at ≈10^{32}s) went through a phase transition from the 'false vacuum' that drove the exponential expansion, to a normal vacuum, that lost that ability (very loosely speaking!). The excess energy went into the creation of particles of matter and antimatter. The expansion rate started to slow down from an extreme value at that point.
From there on, the curve is just a loglog version of the Friedmann equation plot of Part 5. The significance of the times shown by the arrows on the right hand side are: 1000 years is when matter density started to dominate radiation density; 300 thousand years is when the universe became transparent (the CMB comes from that time); 10^{10} years is roughly the present.
If we plot the curve further into the distant future (easy on a log scale), it flares out like a trumpet, almost like during the inflationary epoch, but just over an immensely longer time scale.
The significance of 10^{14} years is that it is postulated to be the end of the "generative" era and thus the start of the "degenerative" era. Most of the matter of the universe will eventually be locked up in "dead" stars  white dwarfs, neutron stars and black holes... Sad!
I sincerely hope that this brief miniseries was useful. There's more, much more in the website's pdfs and, obviously, in the eBook Relativity 4 Engineers, with perfectly clear graphs!
PS: There's a Thanksgiving Special on underneath the last link!

Re: Cosmology Equations Part 6