Relativity and Cosmology Blog

Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. My website "Relativity-4-Engineers" has more in-depth stuff.

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Regards, Jorrie

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Cosmology Equations Part 6

Posted November 20, 2006 6:00 AM by Jorrie
Pathfinder Tags: cosmic inflation cosmology

In this final part of the mini-series 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 log-log scale, the radius of the observable universe against time has this form:

where rP is the Planck length and tP the Planck time (≈10-43s). For clarity (in a slightly faint figure), the horizontal scale is log(t/tP) and the vertical scale log(r/rP), where r is the radius of the observable universe at time t (with r in light travel time units, e.g. light-years).

From tP to about 10-34s, it seems like nothing much happened and then, in the incredibly short time interval of 10-32s, our observable space "exploded" from ≈10-28 meters to about one meter radius, effectively increasing by a factor ≈1028 in radius! Now that's inflation like we hope we never see again, monetary or otherwise!

The "nothing much happened" of the first ≈10-34s 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 ≈10-32s) 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 anti-matter. The expansion rate started to slow down from an extreme value at that point.

From there on, the curve is just a log-log 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); 1010 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 1014 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 mini-series was useful. There's more, much more in the web-site'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!


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Anonymous Poster

Re: Cosmology Equations Part 6

11/21/2006 2:49 PM

I have just read the first few pages of you explanation of Einstein theory of relativity.

What a waste of time, absolute rubish, mathamatical nonsence.

Einstein is wrong in all his theory!!!

Bunkum and balderdash.


Join Date: Jul 2006
Posts: 840
In reply to #1

Re: Cosmology Equations Part 6

11/21/2006 8:13 PM

Easy to say, Dear Guest, but mathematics is a 'testable' art. I rather liked the conclusion, The ancient vedic scriptures which give the age of this micro-universe as 101 years and one day of Lord Brahma (His first attempt at creating a mere 4 dimensional universe under the instruction of a subordinate expansion of Maha Visnu) Check out:- ....concurr with this conclusion, 3.1415904 x 10 exp 14. years. 101years x 360days x 24 hours x 60 minutes x 60 seconds, (plus 24 hours x 60 x 60) Bear in mind Lord Brahma's year is 360 days, the degrees subtended in a full circle. and his second is a 'lakh' or a hundred thousand of our years. The 'Brahma Samhita' or Song of Causeality starts with mathematical equations.

'Pi' to the exponential of 14, how charming and delightful a notion. Bravo! I say.

In my view science without mathematics is non-science. also non-sence. I noted with interest that these old vedic fables estimated the age of our planet to a 'day' or twelve hours of Brahma. i.e. 4.32 billion years. It makes one wonder, were these ancient sages just making lucky guesses? They seem to have worked out the 'Saros' the ancient Chaldean Cycle of Solar and Lunar Eclypses. (18 years 11 days & 8 hours) Cosmology has yet to explain the very 'lucky' coincidences that all the highly eccentric periods of our satellite just happen by sheer chance to be in near perfect 'rational' or 'cardinal' synchronicity. and just the perfect size/distance.

Sir Isaac Newton was astounded that the 1999 Total Elcypse over Portsmouth occured on the same day that the 6th perturbation (variation of the angle of the eclyptic) should also reach a perfect cardinal fraction. He set his 6th perturbation to the actual hour of the total eclypse so we all suspect a slight 'tweak' to his observations.tut tut! Of interest is the fraction itself, it just happens to reflect the perturbation in the most 'poetic' fashion. Also we may have observed, that on the winter solstice of December 21st 1999. the Sun rose perfectly dead bulls-eye centre with the exact centre of our Milky Way Galaxy. What a wonderful set of perfect co-incidences. Pure luck perhaps, but truely remarkable. I have just remarked on it. Happy Thanksgiving, I am thankful to be here to gaze in wonderment.

"Neither man nor woman can be worth anything until they have discovered that they are fools. The sooner the discovery is made the better, as there is more time and power for taking advantage of it." William Lamb
Engineering Fields - Aerospace Engineering - Retired South Africa - Member - The Rainbow-nation Engineering Fields - Engineering Physics - Relativity & Cosmology Popular Science - Cosmology - The Big Picture!

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In reply to #1

Re: Cosmology Equations Part 6

11/22/2006 1:27 AM

Dear Guest, your "Einstein is wrong in all his theory!!! Bunkum and balderdash."

is a great contribution to engineering/scientific debate - really!

You are entitled to your opinions, but if you maintain this standard of discussion, I'm afraid you will be blocked...

"Perplexity is the beginning of knowledge." -- Kahlil Gibran
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