Saturday, March 05, 2022

Did the early universe inflate?

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

One of the most amazing discoveries of the past century has been that the universe expands. This is one of the insights physicists derived from Einstein’s theory of General Relativity. Yes, that guy again! But after this discovery, physicists made the theory more complicated. They added the hypothesis that not only does the universe expand, but that early on, right after the big bang, it expanded exponentially, blowing up space by 30 orders of magnitude in a fraction of a second.

This rapid exponential expansion in the early universe is called “inflation” and it does not follow from Einstein’s theory. Why did physicists add this complication? How does it work? And do we have any evidence that it’s actually correct? That’s what we’ll talk about today. Did the early universe inflate?

In the popular science media, inflation is sometimes presented as if it was established fact. It isn’t. Its status is similar to that of particle dark matter. They are both unconfirmed hypotheses. But while most physicists agree that particle dark matter has yet to be empirically confirmed, opinions about inflation are extremely polarized.

On the one hand you have people like Alan Guth, one of the inventors of inflation theory, arguing that the theory has made many correct predictions and that evidence speaks for it. On the other hand, you have people like Paul Steinhardt, interestingly enough also one of the inventors of inflation, who argue that inflation doesn’t make any predictions and isn’t even science. In an essay some years ago, Steinhardt together with Anna Ijjas and Avi Loeb wrote “inflationary cosmology, as we currently understand it, cannot be evaluated using the scientific method.”

Which side is right? They’re both right and they’re both wrong. Stay with me for some minutes and I hope it’ll start making sense.

The major disagreement between the two sides is philosophical, and we have to get this out of the way before we can talk about the science.

Guth, and most of his colleagues really, argue that physicists have used models of inflation to make predictions which were later confirmed, such as some properties of the large scale structure and the cosmic microwave background, notably the scalar spectral index which is somewhat smaller than one, and that space is on average flat, to good precision. This agrees with observation and they think this is evidence in favor of inflation. Steinhardt’s side holds against this that inflation models really predicted anything so that *those predictions which turned out to fit to observations can’t speak in favor of inflation.

On that count, Steinhardt’s people are clearly correct. Just because someone made a correct prediction doesn’t mean they have a good scientific theory. They may just have been lucky. And if you make sufficiently many different predictions, the chance that one of them later fits to observations is very high. Predictions are really overrated. Whether a scientific theory is good or not has nothing to do with the time at which one does a calculation with it. What matters instead is how much data you can correctly explain with it, so Guth’s argument doesn’t hold water.

What Steinhardt’s people are arguing in an nutshell is that inflation is such a flexible hypothesis that it can be made to fit any data. To see why they say this, let us have a look at how inflation works. You conjecture that in the early universe there was no matter but a new type of field called the inflaton field. The inflaton field has a potential energy and it has an initial condition. This potential energy and the initial condition – here comes the problem – are described by a bunch of parameters and functions.

The potential energy gives rise to the exponential expansion of the universe. But as the universe expands, the field sheds its potential energy. And when it’s done with that, the field decays into the normal particles of the standard model. And dark matter, if you think it exists. Which it may not. In any case, the inflaton field disappears so we can’t see it today. And once the inflaton field is gone, you take what’s left and from this you calculate what we should observe.

So the way inflation works is that you put in some parameters, initial values, and functions and out come numbers for what we should measure. There are literally hundreds of models for inflation and each makes somewhat different predictions.

Steinhardt and his people now argue, that regardless of what we observe, you can always fumble together an inflationary model that would fit to the observations. Therefore, the idea has no predictive power.

Guth and his side have two answers to this which actually contradict each other. First, you often hear them claim that inflation has made unambiguous predictions, as I said earlier, that the spectral index is somewhat smaller than one and that the curvature density of space is small today, indeed so small that at present it’s consistent with zero.

Problem is, this is patently untrue. If you look at the old literature, before we had the data, it’s easy enough to find inflationary models that predicted a spectral index larger than one. And inflation doesn’t predict the curvature at all. Inflation merely decreases the initial value that you picked for the curvature. But for any value that we observe today, there is *some initial value.

The second answer you will hear from the defenders of inflation is that, yes, we have a lot of inflationary models and they predict anything, so, contradicting the first argument. But we just determine the correct parameters and the potential from observations and that’s the same we do with the standard model of particle physics. For example, in a recent podcast to which I leave you a link below, Alan Guth made the following claim.
“It is certainly true that there are many different versions of inflation which you describe well, that depends on what you assume about the potential energy function for the inflaton field. That could be models there are models with many inflaton fields, more complicated potentials and interactions between them. So there’s a large variety there. But that’s exactly the same situation as one has in quantum field theory and how it relates to the standard model of particle physics.”
Another example, in response to the SciAm article by Steinhardt and coauthors, a group of cosmologists wrote a letter. This letter was signed by a lot of big shots in the field, Alan Guth and Andrei Linde and David Kaiser, but also Steven Weinberg and Frank Wilczek and Ed Witten. They wrote
“the testability of a theory in no way requires that all its predictions be independent of the choice of parameters. If such parameter independence were required, then we would also have to question the status of the Standard Model, with its empirically determined particle content and 19 or more empirically determined parameters.”
It is correct of course that for a theory to be testable not all its predictions have to be independent of the parameters. But it does require that you predict more data points than you have parameters. A scientific theory requires that you get more out than you put in, otherwise you don’t explain anything, you’re overfitting data.

And when it comes to fitting data, the situation for inflation is not remotely comparable to the standard model of particle physics. In particle physics, those 19 parameters explain literally terabytes of data. This means it’s a model with extraordinarily high explanatory power. But for inflation, the data you’re trying to predict comes down to a few numbers. In this case, the input of the models is actually more complicated than the output. This means they’re crappy models without explanatory power.

That you use the same procedure as for the standard model is completely irrelevant. That in my understanding is what Steinhardt’s side claims. And they are clearly correct on this count, too. Inflation predicts anything, and no this is not standard scientific methodology. Standard scientific methodology would require you to stick with models that have explanatory power.

Steinhardt by the way argued exactly the opposite 20 years ago. The reason he changed his mind seems to have been that many cosmologists have argued that inflation leads to a multiverse and Steinhardt doesn’t like the multiverse. So now he has made up his own alternative to inflation which is a type of cyclic cosmology. This didn’t really do his argument any favor.

Not that Guth’s side did any better. Another “argument” which the defenders of inflation raised in their letter was this:
“According to the high-energy physics database INSPIRE, there are now more than 14,000 papers in the scientific literature, written by over 9,000 distinct scientists, that use the word “inflation” or “inflationary” in their titles or abstracts. By claiming that inflationary cosmology lies outside the scientific method, [Ijjas, Steinhardt, and Loeb] are dismissing the research of not only all the authors of this letter but also that of a substantial contingent of the scientific community.”
This argument sadly shows that social reinforcement is a real problem in physics. Some of the biggest names in the community signed up to what is basically an argument from popularity, clearly a logical fallacy. It’s because of arguments like this that people don’t trust scientists.

In any case, that’s it with the philosophy, now let’s talk about the science. I just told you why Steinhardt’s people are right, so now let me tell you why they’re wrong.

They’re wrong because that there are many physicists who have fumbled together complicated models for inflation is correct but beside the point. Of course it means there’s a colossal waste of time and money going on. But for what the science is concerned really you should ask whether there is *any* simple model of inflation from which you get out more than you put in. And the answer to this is yes. You just have to look at the right models and the right data.

The most impressive data which simple inflationary models explain is a peculiar correlation in the cosmic microwave background, that between the temperature and the E modes, called the ET correlation. Doesn’t really matter if you don’t exactly know what this is, the point is it’s something which has been observed, and it a non-trivial correlation in the data which you can calculate from bunch of simple inflationary models. These models are good explanations for observations.

An example of such a simple model that fits with all current data is Starobinski inflation. In this figure you see that it’s right in the middle of the experimentally allowed region. But some other simple models are good too.

That there are also many other models which don’t work doesn’t really matter. Unless I guess you’re one of the 9000 or so people who have published papers on that.

So to summarize. Guth is right in saying that inflation is good science. But he is wrong with the reason for why that’s the case. Steinhardt is right with pointing out that Guth’s argument doesn’t hold up. But his conclusion is wrong because there are other reasons for why inflation is good science.

However, that doesn’t mean inflation is right. Physicists have proposed many other theories for the early universe, for example cyclic cosmology, and those can also explain observations. And maybe in the end one of those other theories will be the better explanation. We’ll talk about some of those alternatives another time, so don’t forget to subscribe.

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