# The theory of inflation

We have discussed the three main planks of evidence for the Big Bang model: the Hubble expansion graph (and consequent estimate of the age of the universe), the abundance of hydrogen and helium, and the cosmic background radiation. These leave little room for doubt that the basic model is correct. On the other hand, close examination of the model raises many questions – in particular the singularity, horizon and flatness problems (see posts below). Another problem is that it is not clear from the model how perturbations in the early universe led to the large scale structure of galaxies and galaxy clusters seen today.

A possible solution to these puzzles is the theory of inflation. First proposed by Alan Guth in 1981, inflation posits that in the very first fractions of an instant after the Bang, the young universe underwent an exponentially fast expansion (faster than the speed of light) – totally unike the Hubble expansion we see today. This does not violate principles of relativity, since relativity sets no constraints on the behaviour of spacetime itself.

An inflationary expansion of the very early universe offers a simple solution to the horizon problem: if the universe expanded arbitrarily fast, even the farthest flung points could once have been in thermal contact. In other words, the properties of distant points in the universe would not be determined by a competition between the finite speed of light and the finite age of the universe, as previously thought.

Inflation also offers a neat solution to the flatness problem: it was soon shown that, instead of deviations from flatness quickly leading to a runaway open or closed universe, deviations in an inflationary universe tend to be driven back towards flatness. The geometrical equivalent of this is to imagine a balloon being inflated to enormously large dimensions – of course the surface is driven towards flatness.

This is a simplified overview of the theory of inflation – the main point is that inflation offers a version of the Big Bang model in which the universe is driven towards the critical value of flatness/ mass density that exists today, far from accepting it as lucky coincidence.

What is most impressive about the theory is that, contrary to public perception, inflation was not originaly posited in order to address problems in Big Bang cosmology. In fact, the theory arose in an attempt to address certain puzzles in Grand Unified Theory (the branch of particle physics that seeks to unify the strong interaction with the electro-weak interaction). Guth’s proposal was at first treated with incredulity by the cosmological community – however, it was quickly realised that it offered an intriguing solution to the problems above.

As so often, the original model of inflation was found to contain a fatal mathematical flaw (the end of inflation was incompatible with the known universe). This flaw was soon overcome in a modified version of inflation by Linde and Steinhardt. Nowadays, many versions of inflationary models have been posited: which particular version is correct remains to be seen, but strong theoretical and experimental support for an inflationary universe has been forthcoming (more on this next day).

Filed under Cosmology (general), Cosmology 101

### 9 Responses to The theory of inflation

1. Hi we have very similar interests. As you know there are many verifiably concrete phenomena that are completely anomalous under current models. Therefore you will be most interested in the new cosmologic model that I am currently introducing. It is built entirely on one new premise: that matter and antimatter gravitationally repel. From that one premise the deductive method is applied and as a result a new model necessarily results. The best thing is that it is in complete agreement with all concrete and verifiable evidence. (It does have one nasty and ominous implication, but I don’t want to be a spoiler.)

Check it out and join the debate (either pro or con, your input is welcome) at: http://www.scientificconcerns.com/Forums/viewtopic.php?f=32&t=776

2. James

Cormac,

Very nicely done expositions. It’s particularly good to have some of the history and people woven into the story – in particular the lesser known, even unjustly unsung, characters pointed out.

I have to take issue with the comment that “relativity sets no constraints on the behaviour of spacetime itself” since I seem to recall that that’s actually the job of relativity… I think there are some field equations somewhere that supposedly lay down the law on what classical spacetime can get up to in public…

However, I do have a more serious concern. It seems clear to me that within my new cosmological model (which, of course, is in complete agreement with all concrete and verifiable evidence) that certain hedonistic thrill-seeking holiday-makers are playing havoc with the the spacetime continuum.

It is well known that freely moving bodies follow geodesic paths – and such paths describe the venerable geometry of Einstein’s universe. Well, not content wih this, it seems that some young upstarts have taken to skiing in perverse pseudo-geodesic patterns around innocent alpine villages. This has caused all kinds of temporal disturbances – easily seen by the fact they seem to outsiders to be back in the 1920′s.

This activity should stop – and those responsible should be help accountable.

3. Hasanuddin

hedonistic? geodisc? alpine? temporal disturbances?

You are joking with this, right?

4. cormac

James: not sure whether all of above is a joke. If not, you need to refresh your SR and GR. neither sets any limit on the expansion of spacetime…it has nothing to do with the speed of light!

5. James

Cormac: by “all of the above” I hope you restricted your atention to “James”?

I never mentioned the speed of light. The field equations are there to describe the way the whole manifold works – in fact as a classical problem you might be able to solve for the whole thing.

The speed of light business is built in since the manifold is assumed at the outset to be Lorentzian (locally Minkowskian – thus an example of pseudo-Riemannian – just to through terminology around).

So the speed of light is a geomtrical thing and really not what you measure on speedometers. Essentially the relatve spewd of two distant objects is meaningles. With SR you can in principle set up global coordiate systems and invent some mechanism for synchronising clocks within it. Then, hey, gomeasure!

In GR, no chance!

Really everyting LOCAl, and local the the gravitational field at the same point. (Think about Newton’s bucket, for example…)

P.S. I still think skiing is evil, and detrimental to the spacetime ecosystem.

6. James

Let’s try that last bit agin (I blame the browser..)

So the speed of light is a geometrical thing and really not what you measure on speedometers. Essentially the relative speed of two distant objects is meaningles. With SR you can in principle set up global coordinate systems and invent some mechanism for synchronising clocks within it. Then, hey, go measure!

In GR, no chance!

Really everything is LOCAL, and relative to the the gravitational field at the same point. (Think about Newton’s bucket, for example…)

7. phayes

Very good website, Cormac. However…

“the young universe underwent an exponentially fast expansion (faster than the speed of light) – totally unike the Hubble expansion we see today. This does not violate principles of relativity, since relativity sets no constraints on the behaviour of spacetime itself.”

Since the scale factor [a(t)] rate of change [da/dt ≡ ȧ] simply isn’t a speed, I have to agree that it is wrong (and confusing to students etc.) to compare it to the speed of light. If r(t) is the spatial separation between a pair of isotropic observers in a non-inflationary expanding FRW model then ṙ = (ȧ/a)r [Hubble] and ṙ is numerically > the speed of light whenever r is large enough anyway.

Cheers,
Paul.

8. phayes

Although this website is a very good (overview of cosmology) overall, there is no place in science for failure to respond to valid criticism or failure to amend error.

I would like to be able to recommend this website as a reliable resource for my own students.