## Monday, June 24, 2019

### Turok et al.: a quantum fluctuation complaint against inflation

...and like most of Turok's papers, it's fundamentally wrong...

Most of the arXiv.org papers that I cover are papers that I consider good – innovative, interesting, correct, solving something, presenting real possibilities. But I am not one of those people who think that people's judgement should be censored so that only "nice" appraisals are heard. In a healthy scientific process, one must unavoidably hear about wrong and bad papers. The elimination of wrong things is actually the primary procedure that the scientific method revolves around.

One very bad hep-th paper today is
Quantum Incompleteness of Inflation
by Di Tucci, Feldbrugge, Lehners, and Turok (Potsdam+Perimeter). Helpfully enough, the alphabetic sorting of the author names coincides with the sorting according to the increasing age or experience. Neil Turok is obviously the "boss". The last, oldest three authors have written numerous wrong papers criticizing the Hartle-Hawking paradigm for the initial wave function of the Universe. Now, Alice Di Tucci, the most junior member, was added to write a very similar criticism of cosmic inflation, too.

Neil Turok has written numerous papers claiming that inflation and other pillars of state-of-the-art physics is just wrong. He has claimed that inflation didn't solve any problem of the fine-tuning style. I believe that his criticisms unmask his deep misunderstanding of the difference between the past and the future, the fundamental rules of reasoning in science, and he generally fails to get what a good student must understand rather early on.

As I discussed e.g. in Alan Guth and Inflation, one may easily explain why cosmic inflation solves the flatness problem and other problems. By assuming such an innocent thing as a positive value of the vacuum energy density $$V(\phi)$$ as a function of a scalar field, the inflaton, it produces a de Sitter space which may be sliced in an FRW way. In those coordinates, it looks like an exponentially expanding space. The volume naturally goes up and the density of magnetic monopoles, perturbations of the metric and other fields etc. goes down. So one naturally produces a nearly perfect exponentially large space with exponentially small defects and perturbations. It still has a lot of energy density in the inflaton's kinetic energy and that may be used to create nicely homogeneous seeds of galaxies at the end of the inflation.

The flatness may be described by the parameter $$|\Omega-1|$$, a deviation from the flatness. In the normal cosmology, one may show that as the Universe was getting older, $$|\Omega-1|$$ was visibly increasing. Because $$|\Omega-1|$$ is observed to be really small even today, the regular cosmology implies that it had to be really tiny when the Universe was really young. Because this unnaturally small value of $$|\Omega-1|$$ had to be chosen in each region of the Universe which seems independent from all others, the required amount of fine-tuning seems insanely huge. Inflation modifies this conclusion by a term from the vacuum energy density that basically implies that $$|\Omega-1|$$ has been going down, so its small current value is explained assuming natural enough initial conditions. Within inflation, the large, nearly flat, nearly homogeneous, nearly monopole-free etc. Universe is a largely unavoidable result of some evolution that only differs from the regular inflation by some de-Sitter-related terms with the opposite sign than we're used to.

The explanation involving the exponential expansion is analogous to an explanation of the destroyed Hiroshima in Summer 1945. That event has boiled down to a nuclear chain reaction – another exponentially growing process. The existence of an object – the Little Boy – which is qualitatively similar to other objects (because uranium is analogous to hydrogen) but that also naturally ignites a chain reaction is an explanation of a huge explosion. In the same way, inflation is an explanation of the explosion that has made our Universe this large and nearly flat etc.

Turok just doesn't get that the equations of inflation make the "final state" which we observe much more plausible – not insanely unlikely – and he nonsensically talks about the highly special fine-tuning of the initial conditions which the inflation demands – which is clearly the opposite of the truth.

Lots of cosmologists have explained to him why he is just plain wrong but he keeps on pretending that he still believes in his bogus criticism. Now, "on top of his usual powerful arguments against inflation", as he spins them, he also adds a "quantum mechanical criticism". It seems very clear to me that Turok has first decided what the conclusion should be and then he ordered the three more junior collaborators to write some equations – almost 100 displayed equations, rather non-trivial ones – to make the paper look more scientific. But the equations don't actually imply the conclusions when you're analyzing things properly.

What is the basic logic supposed to be? They calculate something about the inflation using the Picard-Lefschetz theory, the same mathematical method that Turok has employed in his criticisms of the Hartle-Hawking program. In something they call the semiclassical approximation, although it differs from all the calculations that are considered the semiclassical approximation by sane cosmologists, they decide that the path integral gets contributions from two stationary points, not just one. Aside from the expanding Universe, there is also a history involving a bounce. Here a miracle occurs, they suddenly claim that it means an inconsistency, and inflation is doomed.

None of these big statements make any sense. If they analyzed the perturbations using the semiclassical methods properly, they would find out the usual conclusions about the spectrum of primordial gravitational waves that are predicted by cosmic inflation – and related things. Instead, they just use all these terms and their equations as tools to make their wrong statement – the inflation doesn't work – look more credible.

It makes no sense to go through all the equations and I am convinced that not a single reader of their paper aside from themselves will pay attention to every equation in their paper. What's more important is that the big methodological assumptions how all the mathematics should be used are incorrect. For example, on Page 11, we read
The propagator consists of the interference of two classical solutions.
But this sentence is a deep misunderstanding of the perturbative treatment of a QFT. A propagator is by definition the building block that is extracted from the quadratic approximation of the action as it fluctuates around a single classical configuration. If you derive Feynman diagrams – with propagators and vertices – you must first find a classical solution, i.e. an extremum of the action, then you expand the action around that point. The terms linear in the perturbations are absent because it is a solution. The bilinear ones give you a free field theory and you derive the propagators from them. And the higher-order ones produce the vertices.

To write a propagator as a sum over two different classical solutions is just a conceptual mistake.

OK, they discuss the existence of two saddle points as if it were a catastrophe. It's normal for basically any nontrivial function of a complex variable to have two or many saddle points. This mundane fact doesn't imply any breakdown of mathematics or physics which is what they irrationally claim. One must be careful how to treat the several points. In most cases, it's just one of them that is dominant and the others contribute some tiny corrections or great corrections to very special effects that would be otherwise impossible (e.g. 't Hooft's interaction coming from instantons) or something else.

The existence of additional stationary points is interesting physics to be studied, not a sign of the Armageddon!

The propagator obtained from two stationary points at the same time isn't the only conceptual blunder in the paper, of course. For example, on page 32, we read:
Our calculation demonstrates that quantum gravity effects cannot be ignored at the beginning of inflation – put differently, the beginning of inflation is highly sensitive to UV effects, not just in the sense of its potential being sensitive to curvature corrections etc., but also in terms of its quantum vacuum. Since all predictions of inflation depend sensitively on the quantum vacuum, this is not a small issue.
These sentences clearly show that they just don't get what is the "range of validity" of inflation or "what interval of issues inflation is supposed to address". The beginning of any theory about the very early events in the Universe is unavoidably sensitive to UV effects because the Universe started as a small and hot one which is where the UV effects matter. In principle, at the very beginning of the life of the Universe, the finest effects in quantum gravity or the Planck scale physics matter. This is not "bad news" in any way. It's basically a tautology – two nearly equivalent ways to describe the very scientific discipline. To spin this fact negatively is totally irrational.

An ABBA song about Turok's town and the victory status of his papers.

But cosmic inflation isn't a final theory of quantum gravity solving all the subtleties of the Planck scale physics. Instead, cosmic inflation is another epoch in the history of the Universe which took place at shorter characteristic distances (and higher energy scales; and when the Universe was younger) than the regular big bang theory; but the scale of inflation is still assumed to be lower than the Planck scale.

However, the beginning of inflation is close enough to the Planck scale which means that all relevant physical questions of that moment are obviously sensitive to the UV physics to a greater extent than the low-energy phenomena that e.g. condensed matter physicists observe today. But the success of inflation is that the end of the inflation is almost insensitive to the detailed initial conditions. The fundamental dumbness of the Turok-style criticism of inflation is that he always talks about the "beginning" where the alleged Turok problems are supposed to hide.

But that completely misses the point because what inflation – or a similar cosmological theory – explains or is supposed to explain isn't the beginning of inflation but the end of inflation or the current state of the Universe which is what we actually observe! Because the regular big bang theory epochs seem to be theoretically understood, at least approximately, the understanding of the "present state of the Universe" is almost equivalent to the understanding of the "end of inflation" – one may rather reliably translate between these two moments. You can't find any comment about the "end of inflation" in his papers!

If there are some Planckian pathological effects that seem wrong in inflation, it's at most a challenge, not an argument against inflation. Unless Turok or someone else performs a rigorous analysis of inflation within a consistent theory of quantum gravity, which probably means string theory, and they haven't done so, any analysis must be considered preliminary and any inconsistency in it may very well be an illusion. Even if the success of inflation were "only" confirmed at the classical level, it would be huge evidence in favor of inflation – and a reason to try harder.

The success of inflation is that as inflation proceeds, and adds some 50-60 or more e-foldings to the size of the Universe, the conditions in the Universe get more hospitable and more compatible with our observations at the present which is a good thing. That's how scientific theories are supposed to work: they add some mechanism or something that should explain our present observations. The scientific theories are rated according to how well they perform this task. The focus by Turok et al. on the beginning of inflation or its assumptions means that Turok et al. don't really understand the scientific method as a whole. Science can't dismiss a theory a priori (incidentally, they spell it as "a priory", oops). Science evaluates theories according to their ability to produce lots of desirable conclusions about the present observations from a limited set of assumptions (e.g. about the initial state).

The new Turok et al. paper has lots of pictures, with some contours in a complex plane. The prettiest picture is the colorful one on page 21 (22 of 37). You may see that the content of this colorful picture is very similar to the pictures in my 2003 paper with Andy Neitzke (which is approaching 250 followups). In fact, the contexts are really analogous – perturbations in a gravitational theory – and we were dealing with some highly analogous problems (I won't say that the problems are completely equivalent but the proximity is clear).

In my and Neitzke's calculation of the quasinormal modes – a new method, after a "continued fraction" algebraic method that cracked the problem a month earlier – we dealt with some Bessel's functions and two independent solutions of a related equation, an "outgoing wave" and an "incoming wave". In the complex plane, these two were mixing up with each other according to some monodromy rules. We needed some 3 weeks of intense thinking to clearly formulate what is happening with these two solutions and how the effects – and the monodromy – implies the statement about the frequency that was proportional to $$\log 3$$, as we knew in advance.

So we knew the right result, we knew that a "monodromy" was relevant from the beginning, but we were still confused about detailed properties of the statement we wanted to make that would imply what we needed. But we would have never published a paper before it made sense – e.g. a paper claiming that the $$\log 3$$ isn't there because we couldn't prove it for 3 weeks, or a paper claiming that the quasinormal modes calculations are intrinsically inconsistent or something like that. If things don't make complete sense after 2 weeks, well, you need at least 3 weeks! A blurry, confusing picture that someone preserves for some time proves absolutely nothing – except for an upper bound on the professional skills of the person. Here, Turok et al. are also dealing with the co-existence of two solutions describing some perturbations of a metric in general relativity. And they also just try to fill details to obtain a result they "know", namely that there is something wrong about inflation.

The main difference is that the result we assumed with Andy as a known one was correct because it was actually calculated by another solid method of mine (also approaching 250 citations). On the other hand, Turok is only trying to defend an arbitrary, wrong, unjustified or unjustifiable assertion against inflation. If he thinks that it's supported by something, it's mainly supported by his ego that outshines his physics abilities by several orders of magnitude.

It's unfortunate when research is organized in this way – when senior collaborators who have mostly produced wrong statements in their life get the power to "force" their junior collaborator to collaborate on the technical content of a paper whose conclusion is both incorrect and decided in advance. Such junior collaborators are turned into collaborationists.

This paper is just wrong. Aside from the misunderstanding of "what it means for a theory to explain something" and some rudimentary conceptual mistakes, what I find amazing is how the authors completely ignore what is actually known about these matters. People have used equivalent semiclassical calculations to calculate the primordial gravitational waves predicted by inflation and related effects. One could argue that the knowledge of these calculations belongs to the required toolkit of any modern theoretical cosmologist today. Turok et al. don't say what's wrong with those calculations. They just present their, different calculation whose final claims are completely different and clearly much less compatible with the observations. Nevertheless, they seem to suggest that this new, very different calculation should just replace the normal semiclassical claculations of inflation because Turok has a larger ego. Sorry, science doesn't work in this way.