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## Some cosmological introductions …

I don’t know who Rob Sheldon is, but he doesn’t know much about cosmology. He recently was quoted in this post at uncommondescent.com regarding the geometry of the universe. If I lecture cosmology this year, I’ll set this passage as an assignment: find all the mistakes. It gets more wrong than right. I have an article for “Australian Physics” on common questions about cosmology that I’ll post here once it’s out (a fortnight, maybe). In the meantime, I’ll try to clear up a few things.

The discussion of the mathematics of curvature (flat, positive, negative) is about right. It’s when he discusses the universe that things go wrong.

It takes a lot of effort to find any curvature at all, and certainly it is difficult to get good agreement between different types of measurement.

Nope. That’s why it’s called the “concordance model of cosmology” – because the different measurements converge on the same set of cosmological parameters. For example, this plot.

… a “closed” universe that collapses back down to itself …

A common error. In a matter and radiation-only universe, closed implies collapsing. A cosmological constant and/or dark energy changes this: closed vs. open no longer divides collapse vs. expand forever. Here is the plot you’ll need, from John Peacock’s marvellous Cosmological Physics.

… one would like it to have positive curvature to avoid infinities …

Flat and negatively curved universes can be finite. A flat 3-torus, for example, is finite, unbounded and has a flat geometry. Einstein’s general relativity constrains the geometry of the universe but not its topology.

Negative curvature suggests an “open” universe that will expand forever, ending “not with a bang, but a whimper”, and gives a feeling of the infinite emptiness of existence. I’m not really sure what a “flat” universe portends, perhaps a feeling of driving the speed limit across Kansas.

If he doesn’t know the fate of a flat (matter-only) universe, then how much cosmology has he studied? It’s called the Einstein-de Sitter model, and it expands forever. Cosmology 101.

The Nobel prize was awarded 2 years ago for a claim that some observed supernovae are further away than the flat universe predicts, and therefore the expansion rate is accelerating.

Nope. The geometry of the universe and its rate of expansion are not the same thing. The supernovae are further away than a matter-only, decelerating universe predicts, and thus we believe that the expansion of the universe is accelerating. The supernovae data alone don’t decisively constrain the geometry of the universe. It’s really the CMB that does that. Look at this plot again. In equations, the geometry of the universe (+,flat,-) depends on whether

$\Omega \equiv \sum \Omega_i = \sum \rho_i / \rho_c$

is (greater,equal,less) than one, where $\Omega_i = \rho_i / \rho_c$ is the density of the energy component labelled $i$, normalised to the critical density. I’m treating the cosmological constant as a form of energy. Whether the expansion of the universe is accelerating depends on the acceleration equation, and the sign of

$-\sum (1 + 3w_i)\Omega_i$

- if positive (negative), accelerating (decelerating) – where $w_i$ is the equation of state of the component $i$.

But it shows that experimentally it is really difficult to find absolute distances between galaxies and quasars, so that most of our models are only weakly supported by data.

The supernovae data involves the distance between the supernovae and us. Distances between galaxies and quasars aren’t relevant.

That is, gravity is always attractive, so it will make a positive curvature universe, collapsing down to a point, unless something else were counterbalancing it. The Big Bang is outward kinetic energy, and that gives a negative curvature.

Misleading, at least. In a universe with only matter, gravity is attractive. But this does not mean that every matter-only universe has positive curvature. There are the flat and negative curvature ones. Sheldon is obviously thinking of the big bang as an explosion in space, with the expansion outwards being slowed by the attractive force of space. This is not the best way to think of the big bang. In any case, if the universe falls short of counteracting the “kinetic energy”, the universe expands forever. It does not collapse back to a point.

Only about 10% of the mass needed to balance the kinetic energy is visible, is in stars. We can add in red dwarfs, dust and molecular clouds, and we get up to about 30%. But roughly 70% of the necessary mass to “flatten” the universe is invisible, is unaccounted for.

Nope. Only about 0.5% of the critical density of the universe is in stars. About 5% is in baryonic matter – the matter we are familiar with. Red dwarfs, dust and molecular clouds make up a small fraction of the baryons. Most are in the form of hot ionised hydrogen in the outskirts  of galaxies and the intergalactic medium. If we add in dark matter, we get up to about 30%. Dark matter is not baryonic, so not red dwarfs etc. The remaining 70% is dark energy. It is required by observations but not directly observable.

In the present epoch, as in right now, the universe is experimentally as flat as can be measured—the “fine-tuned Big Bang” problem.

Nope. The flatness problem refers to the very early universe. As we go back in time, the universe gets progressively flatter. So even if the universe today wasn’t particularly flat, the very early universe (e.g. nucleosynthesis at 10 minutes) would need to be extraordinarily flat. So it seems like the initial conditions of the universe need to be fine-tuned.

About 70% of the matter that is needed to make it flat is unobserved—the “Dark Matter” problem.

Dark matter is 30%. Dark energy is 70%. We don’t have an unhealthy fixation with flatness. An open, matter-only universe was a possibility for a while, but was ruled out by observations.

There is some controversial data that the universe is becoming negatively curved in the next epoch.

The universe is beginning to accelerate, but remains flat. It is not the onset of negative curvature. The universe cannot change its curvature.

BTW, the hope that the search for the Higgs boson would reveal novel physics needed by the “inflaton”-field were dashed, making inflation a fast-receding threshold of confirmation.

We’ve known since the 1980’s that the Higgs field didn’t power inflation. Few people expected the LHC to tell us anything useful about inflation. The evidence for inflation is in cosmological predictions and data, not particle physics.

If you stick to observational astronomy books, they will all talk about a flat universe.

They will, but not at the expense of the other curvatures.

Cosmologists tend to be faddish thrill-seekers, and will tell you anything. The past 30 years of publishing has been particularly brutal, with nearly every cosmological model having a shelf-life in single digits. The “flat” cosmology is almost apophatically defined—as one cosmology after another is denied.

Coming from someone who would catastrophically fail Cosmology 101, this paragraph is meaningless. We’ve had the same cosmological model – the FLRW model – since 1922. All that has changed is our knowledge of the parameters of that model, and it has changed in light of observations. We have zeroed in on the right part of parameter space. Not smoothly or inevitably, but in the messy groping forwards of any science. The “brutality” has been via observations ruling out regions of parameter space. In science we call this increasing our knowledge. Sheldon should try it sometime. Here is a textbook to start him off.

### 6 Responses

1. Can I get an extra point in your class if I point out another error?
So by and large, I would ignore “inflation” as a solution for anything, since it merely “solves” one problem by introducing a dozen more.

I think inflation could still be wrong, but so far the evidence looks pretty good. Its the domninat paradigm for the early universe and he wants to just ignore it?
What i think there irony here is that most people are impressed by just how many different problems inflation solves in one go. It was actually invented to solve just one problem: the mono pole problem, nothing more . it was then noticed that it also solves the flatness and horizon problem and provides an origin for structure and gives us hot soup of particles. Not sure that replacing one problem with a dozen more, more like the other way round.

2. You note that it is well known that the Higgs field is not responsible for cosmic inflation – which I also understood to be true. However Matt Strassler in his blog suggests that this conclusion is not certain. Comments?

• Not certain, sure. He says: “At the present time, there is no established connection, direct or indirect, between (a) the Higgs field and its particle, on the one hand, and (b) cosmic inflation and the Big Bang on the other hand. Period. Any such connection is highly speculative — not crazy to think about, but without current support from data.”

But that doesn’t mean that physicist hopes were dashed at the LHC. It’s not even a cheap shot. It’s seeing a problem that isn’t there.

3. Thanks. I agree that his suggestion that discoveries at CERN somehow made inflation less likely is silly. I was just querying your assertion that we know Higgs is not responsible for inflation. I appreciate your blog including this particular discussion, and find it very illuminating and well expressed. Please keep blogging!

4. Have you seen the very recent article by George Ellis and Jean-Philippe Uzan in Astronomy and Geophysics February 2014 entitled “Inflation and the Higgs Particle”? Interesting speculation!

5. […] However, Luke recently offered some technical criticism of a post by Dr. Sheldon at Uncommon Descent Some Cosmological Introductions. […]