## Wednesday, November 02, 2016 ... /////

### A documentary on string-inspired cosmologies

Are bouncing, cyclic, ekpyrotic, string gas and other cosmologies justified by any real evidence?

If you have 46 spare minutes, here's another video on string cosmology and things of this sort:

It has the same female host as a documentary on inflation and both of them were brought to us by Peter F.

Gabriele Veneziano – the founder of the first "stringy" formula in the history, the Veneziano amplitude (unless you attribute the breakthrough to Leonhard Euler because it's the Euler Beta function) – sketches some history and basics of string theory as well as his favorite (and much more controversial) topic in the following decades, "before the big bang" cosmological models.

I obviously consider all these models and claims about the very early Universe according to string theory to be much less established than string theory's statement about nearly flat or AdS spacetimes (especially those with some unbroken supersymmetry – note that dramatic early cosmology unavoidably breaks SUSY heavily). A few examples of the doubts will be mentioned momentarily.

On the other hand, I was much closer to the folks who were producing some of this research. It's particularly the case of Ali Nayeri who is a fun (Persian) guy in the show above. When they were creating their paper with Cumrun Vafa and Robert Brandenberger at Harvard, I was watching every step and it was amusing. You may probably find several TRF blog posts on that topic.

This documentary reminds me that they believe many of the same things as Veneziano which I simply don't believe. One of the central dogmas is that a geometric singularity is always an inconsistency so any consistent description of the very beginning must actually replace it with some geometrically large space.

You may hear many specific versions of this philosophy in the show. One of them involves T-duality. Physics on a circle of radius $R$ is the same as physics on a circle of radius $1/R$ in some string units. So far so good. But both Nayeri and Veneziano basically say that it "follows" that the very early evolution after the beginning with a growing $R\lt 1$ should be T-dualized so that you get a decreasing T-dual $R'=1/R$. They believe that it's unavoidable that some very early cosmology contains some shrinking Universe, a decreasing $R$.

I just don't buy it. The T-duality transformation also changes the value of the coupling constant $g_s$. When you carefully follow all these moduli and ask whether T-duality may always map any toroidal compactification to "large tori", you will find out (see Dualities vs Singularities) that the answer is "Yes" for several compactified dimensions. But when you compactify all or almost all dimensions – so that 1+1 or 0+1 large dimensions are left – there are extreme portions of the moduli space where the compactified manifold is "tiny" regardless of the T- or U-dualities that you perform. Only 1/2 of the space for 1+1 large dimensions; or a "future light cone" for 0+1 large dimensions may be dualized to a compactification whose all radii are large.

So I just don't think that that a smooth spacetime at the beginning of the cosmological evolution is made necessary by dualities. More generally, I also don't believe that it's needed for consistency. String theory is capable of defining consistent physics even on some backgrounds that look classically singular (orbifolds, conifolds) or that are entirely non-geometric. So the possibility that things may be made smooth at the very beginning is just a possibility and I think that a rather unlikely one.

I am even more skeptical about the attempts to make the cosmology $t\to -t$ time-reversal-symmetric and use T-duality for that. The evolution of the Universe involves an increasing entropy – and it is very quickly increasing at the beginning, indeed. So any would-be perfect symmetry is heavily broken by the cosmology. Also, they sometimes believe that the thermal circle obeys some T-duality so in the string units, the inverse temperature $\beta$ is equivalent to $1/\beta$. I just don't think that you may consider a higher-than-Hagedorn temperature in a kosher (or halal, for Ali and Cumrun) way at all. The partition sum is simply divergent for super-Hagedorn temperatures. When you approach the Hagedorn temperature from below, the assumptions of perturbative string theory have to be dropped soon or later.

This myth is also linked to a correction to Joe Polchinski's String Theory textbook that I am most proud about. You may find my name Motl on that page some 128 times, next to some small mistakes in the otherwise almost flawless textbook. But if you search for Hagedorn, you get the following hit:

p. 322 (4/18/99)*: Annoying mistake: in the line above eq. 9.8.18, the Hagedorn temperature should be _half_ of the self-dual value. So in eqs. 9.8.19 and 9.8.20, "$T_H^2$" becomes "$4 T_H^2$" everywhere. (Thanks to L. Motl)
You know, this is not just an extra factor of two or four that is incorrect, much like factors of $i$ and $\pi$ and others in many other equations. Here, the hypothesized absence of the factor of $4$ was actually used to make a rather qualitative and would-be pretty claim inviting you to deduce some far-reaching consequences. The self-dual value under T-duality is exactly the circumference of the thermal circle of the thermal path integral at the Hagedorn temperature, Joe wrote before the correction. So if you heat strings up and get to the Hagedorn temperature, you may just cross to the other side – hotter than Hagedorn temperatures – by performing a T-duality.

Except that this statement is wrong. The two temperatures differ by a factor of two. If you heat the strings up to the Hagedorn temperature and apply T-duality, the temperature jumps to 4 times the Hagedorn temperature. The interval from 1 to 4 Hagedorn temperatures cannot have any convergent partition sum, whether you apply a T-duality or not. There is really no careful reason why these temperatures should be the same. And I actually feel that Ali Nayeri and perhaps even Gabriele Veneziano and others still assume the wrong equality between these two temperatures because this assumption sounds "pretty". Except that it's false.

String gas cosmology in particular – pioneered three decades ago by Vafa and Brandenberger and revived a decade ago with Ali Nayeri's help – adds some other attractive "simplifying" stories. It is said to explain why exactly 3+1 dimensions are large. Well, stringy world sheets are 2-dimensional so exactly in 4 dimensions, two generic world sheets intersect at 0-dimensional points, and this intersection is the right condition needed to allow all these dimensions to grow by annihilating some wound strings.

Except that in string theory, one also has branes with assorted dimensions, not just 1-dimensional strings. For the branes, the counting is clearly different and the naively preferred spacetime dimension should be different, too. Nayeri and pals have insisted on having some explanation that in these brane gas cosmologies, the string's dimension remains critical and they've been explaining the arguments to me a few times but I have never gotten it or something – I still don't believe it can be true.

It's conceivable that some full explanation why we live in large 3+1 dimensions – either based on the string gas or something else – exists. On the other hand, it's also possible that the only explanation is environmental or "anthropic". I don't really have a trouble with Nature if it allows the environmental selection to pick the dimensionality 3+1 from 11 or so a priori possible choices.

There are other ideas in the documentary. The host correctly says that no one really buys Lee Smolin's ideas about "the universe born from a black hole". But she indicates that the status of this paper by four famous string theorists is the same. Well, it's a tough analogy. While the big claim of the four-author paper is surely not generally accepted, it's a paper trying to do very clever and quantitative things with combining the AdS/CFT descriptions of an ensemble of such spaces etc., with some nontrivial partition sums that string theorists working on "related but less ambitious" papers know very well. Smolin's claims are just childish stuff for popular books which is not backed by any tangible mathematics whatsoever. When an equation appears in this Smolin's paper, it's some equation found in 1900 that is added just to increase the number of equations. Or it may be a trivial equation that "obviously can always be written" and cannot qualitatively impact the pre-determined philosophical picture. Vafa and collaborators actually do need some mathematical properties of the objects they calculate with and these properties had the potential to kill their big idea altogether. So the "field" of the two papers is very different – Smolin's is just demagogic popular philosophy while Vafa's and pals' is a speculative paper trying to use modern calculational methods to study much more ambitious questions than the boring technical papers in the AdS/CFT industry.

As a guy discusses for a long time on the show, the string gas cosmological models are also claimed to be competitors to inflation. To persuade anybody, they should reproduce the successes of inflation, and avoid the production of new problems. I am not sure whether I believe either. The first thing one should predict is the approximately scale-invariant spectrum. Inflation does so for a clear reason – the expansion is exponential and therefore self-similar in the right way for a long enough time. My understanding is that the expansion in the string gas cosmology is unavoidably very far from an exponential one. I feel that "exponential" and "scale-invariant" are basically synonymous. Violating one means like violating the other.

So they tell us that everyone takes their ability to reproduce inflation's successes for granted and we should only be interested in the differences. The main difference discussed on the show is that the string gas cosmology only produces primordial gravitational waves at short wavelengths – Nayeri et al. predict or claim to predict a "blue tilt". Well, I don't take the claim "string gas cosmology is at least as good as inflation" for granted. I just haven't seen explanations of this claim that would satisfy me and, more seriously, I feel it's straightforward to produce explanations showing that string gas cosmology does not work as well as inflation. Because the theories are meant to be truly inequivalent, the string gas' explanation of the inflationary successes has to be very different. And because I was thrilled to learn how and why inflation works, I think that I need to feel a second similar thrill to admit that a different explanation of the same facts exists.

A female cosmologist gave an oversimplified (in my opinion) picture of how the (non)-observation of the tensor modes etc. would prove or disprove the various alternatives to inflation. OK, if you take their words seriously, they say that the tensor modes "discovered" by BICEP2 are good for string gas cosmology, see this 2014 blog post. Now, when the BICEP2 "discovery" looks questionable, this positive evidence has gone away and may have turned into a slightly negative evidence. But as always, the absence of new groundbreaking evidence always basically preserves the status quo.

In the 33rd minute, they define a much broader community of "these" cosmologists. Various loop quantum cosmologists are included and the "big bounce" is their shared belief. Well, as I have already mentioned, call me a big bounce skeptic. I am simply not a bouncing Czech. I don't believe that there's any evidence that the big bounce is implied either by the empirical or theoretical knowledge; and I don't really see any metaphysical advantage of a model with a big bounce. The female cosmologist justifies the bounce by a discrete spacetime. Well, the spacetime isn't discrete in this sense. These two questions – bounce and discreteness – aren't quite equivalent but they're overlapping. My skepticism about both has related reasons and they seem more technically established to me than any positive evidence these bounce people have presented.

Whether the space in the theory describing the very beginning is "large" or "small" is unknown and the preference for one answer or another is a pure prejudice. It's like arguing whether monotheism or polytheism is better. You may pick the monotheist Judeo-Christian picture but you should realize that it's really a religion. Your having an idea about a single or triple God doesn't really disprove the overpopulation of Zeus and his relatives.

Thankfully, Veneziano says the same thing around 35:00. You can't prove or disprove either of these claims. Some pre-big-bang cosmology is a possibility. But if it doesn't really explain any data or relationships and it doesn't increase the consistency in any mathematically verifiable way, it may be sensible to cut the whole pre-big-bang stage by Occam's razor. It may be said to be some unphysical fantasy added on top of the well-known cosmology whose consistency with the known physics is just a matter of legends and prejudices.

I am careful with razors and Occam's razors as well but I do prefer the minimal picture. The inflation seems to be the oldest era that actually explains something we need in physics (even though, obviously, I can imagine a very nice story about a previous era when the compactified dimensions got the shape they needed etc.). So it's economical to assume that there's some true beginning shortly before the inflation and the fundamental physical theory makes this beginning consistent. It may ultimately be equivalent to some Hartle-Hawking initial state that basically allows you to calculate the initial conditions for a Universe of radius $R=0$. One may invent more structured theories with some new eras but others may sensibly ask "Who ordered that?". The "established minimal" theory of the Universe does imply that there was a big bang singularity at the beginning, indeed.

So again, I disagree with the guy in the purple shirt who says that there can't be an "edge of the world in time". There very well may be one. I believe it's the same for an infalling observer inside the black hole. The singularity represents the end of his time. If there's a way to talk about "the life after the black hole singularity" at all, the continuation of the life must proceed by some non-local and basically non-geometric mechanisms. The big bang is just an image of that singularity. If one can exist, the other may probably exist, too.

The woman mentions Alex Vilenkin's claims that the Universe can't have a true beginning, see e.g. this 2012 blog post. I agree with her that the current arguments seem to imply that you can't avoid a true beginning, even in eternal inflation etc. So the addition of other bouncing phases in some cyclic or ekpyrotic cosmology is just making things complicated and non-minimal but ultimately cannot change the picture qualitatively.

Ali Nayeri says that he prefers no clearcut beginning. Great. Even if I thought it's possible, and I don't, it would be scientifically unavoidable to consider – for the practical predictive purposes – the theories about "what we can really predict". Because we couldn't have made observations in some causally disconnected regions of this "very ancient Universe", we need to approximate the knowledge about the "ancestor Universes" by some effective data, anyway. Call me an engineer if you wish but I think that such a theory that "integrates out" all this inaccessible pre-history in some complete way is exactly as scientifically complete as your "cosmological model without a clearcut beginning". So I believe that even if a picture without a clearcut beginning existed, it wouldn't be the only scientifically complete way to describe our Universe.

In the last minute, the host frames the program as a way to debunk the Šmoit-style claim that string theory can't be tested. Well, string theory surely has physical consequences but as I mentioned, I am not sure whether the implications for the very early or pre-big-bang cosmologies may be counted as good examples of these implications because a majority of the "hot ideas" are mostly about aesthetic preferences.