## Friday, November 02, 2018

### Cosmopapers by Banks and Fischler; and Arkani-Hamed et al.

Some interesting conceptual papers about cosmology have been posted to the hep-th archive for us to see them today. The shorter and vaguer one was posted by my PhD adviser (well, up to 9/11/2001) Tom Banks and Willy Fischler, whom I also know well:
Why The Cosmological Constant is a Boundary Condition
On their 12 pages, they somewhat heuristically – we've gotten used to it – argue that the cosmological constant isn't a field, it isn't a term in local equations. Instead, it's a term in the boundary conditions that is imposed upon the local dynamics by some soft gravitons carried by the holographic screen, the boundary of your causal diamond.

Some approximately one-sentence-long references to the UV/IR duality, Matrix theory, and AdS/CFT are being made to support their case. Unfortunately, in all of them, I would need to ask them: Could you please be a little bit more specific about the Step 2 ("here a miracle occurs")?

I am sympathetic to the possibility that the cosmological constant shouldn't be understood as a term in the local equations at all – it could be some non-local holographic effect. I've presented similar proposals for dark energy and dark matter, like the holographic MOND. But I don't see progress in the new paper – and that possible progress is the reason why I read new papers if I read them.

There are some obvious problems. If you allow the cosmological constant to be a non-local effect, why aren't all other terms in our local equations that we use also derived from such non-local causes? How do you derive the approximate locality and Lorentz invariance at all? There are lots of such basic questions. They really want to start physics from scratch – the axiomatic Holographic Space Time is obviously meant to be the ideology underlying all such ideas, I forgot to say.

If you start your physics from scratch, using completely new foundations, and you can't show the approximate equivalence to the validated laws of physics that we actually use, you really have to reproduce all the achievements of the recent millenniums and centuries, e.g. Newton's achievements, to show that your new theory is also on a right or viable track. I don't see any of these things. What I see is a funny acknowledgement by Tom:
The work of T.Banks is NOT supported by the Department of Energy, the National Science Foundation, the Simons or Templeton Foundations or FQXi.
Brave and amusing. Tom is still supported by Rutgers, isn't he? So this apparent bragging about Tom's financial independence is a bit exaggerated. Somewhat more seriously, the following paragraph really captures what I find so utterly irrational about these papers:
The second part of our paper will be devoted to the evidence from AdS/CFT that the c.c. is a parameter related to I.R. boundary conditions, which, via the well known UV/IR duality, is the UV definition of the boundary CFT. We have been somewhat surprised that these well-known and completely agreed upon facts about AdS/CFT have not changed the community’s view of the bulk c.c. problem in field theory.
What is the exact "change of the view of the community" about the bulk c.c. problem that should have taken place and what is the exact evidence that this change should have taken place?

Tom and Willy, could you please be more specific while explaining Step 2, "here a miracle occurs"? What I see in Section 2 is the observation that in some semi-serious paper, Ted Jacobson derived Einstein's equations without c.c. That's great. Albert Einstein also wrote the original equations without the c.c. These historical events surely don't imply that c.c. must be omitted, do they? Einstein and Jacobson forgot something that must be written down in a general theory of a certain kind.

In string theory, the value of the c.c. in a vacuum is a parameter of the effective field theory that is calculable for every specific stable vacuum within string theory – just like the strength of an electromagnetic interaction is. What is the difference? Why should the c.c. be a holographic boundary condition and the fine-structure constant shouldn't? Or should it?

Now, in Section 3, some comments are made about the AdS/CFT correspondence. Indeed, all the dynamics of the AdS/CFT pair is encoded in the UV behavior of the CFT. Because it's a CFT, its UV behavior is really the same as its IR behavior – but again, that's because of the conformal symmetry, not the much fancier UV/IR maps. But what does it say about the right bulk interpretation of parameters such as the c.c.? Nothing. The boundary theory doesn't directly and immediately imply the locality of the bulk theory or anything related to it.

Instead, what's interesting is that if we do a lot of work, we may extract a dual bulk description that is basically local – and in a higher-dimensional spacetime because the holographic coordinate is included. Now, yes, the c.c. could require a different, non-local-in-the-bulk description. But I don't see any evidence for this exceptional status of the c.c. term. Instead, Tom and Willy choose not to enlighten the local character of the effective field theory in the bulk at all. So they're just throwing the baby out with the bath water. They're "showing" (not really) that the events in the bulk may be completely non-local, directly controlled from the boundary of a causal diamond. But that's not exactly what we want to show if we want the new theory to be satisfactory. We mostly want to show lots of locality.

Also, what annoys me is that the reference to the "well-known UV/IR duality" seems to lack any precision so its actual purpose is to ask the reader: "Dear reader, please get high with us and totally ignore differences between the UV and IR, while the UV/IR duality is why you should." I am sorry but this is not how the UV/IR duality may be interpreted. The UV/IR duality is a rather specific link between short and long distances. There are still lots of statements about short and long distances that can't be easily interpreted as statements from the opposite extreme of the length scales.

The CFT is generally said to be "a reason to think that some parameters in the bulk are boundary conditions". That's a rather general but subtle thesis. Finite regions of the bulk basically allow the spacetime to be changed to the "proximity of any vacuum", although Tom and Willy have disputed even this assertion. But in AdS/CFT, the CFTs are numerous and they are different according to the asymptotic behavior of the bulk fields at infinity. For every superselection sector, measured locally somewhere near the AdS boundary, you may find a different CFT. It means that the CFT freezes something. But we should study what exactly is frozen. I think it's right to say that the values of the "massless fields" are frozen. If there's no quintessence-like scalar field that adjusts the cosmological constant, it cannot be "frozen" by the choice of the boundary CFT. It has really been frozen from the beginning because only discrete values of the c.c. (just like the fine-structure constant) are allowed in consistent and stable stringy vacua. To say that the c.c. may be adjusted means to say that there is a whole moduli space of unequivalent CFTs – the c.c. may be adjusted. But isn't it clearly untrue for the CFTs we know?

Quite generally, looking at the complexity and general spirit of the equations is enough to be almost certain that they haven't found a way to link these totally novel ways to think about the bulk physics to the established ones. So what's left is that there may be completely different ways to look at the bulk physics. I agree with that bold suggestion – but I knew it decades before seeing the paper.

Nima et al.: making cosmology as controllable as the flat space

In a vastly more technical, 108-page-long paper
The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities,
Arkani-Hamed, Baumann, Lee, and Pimentel do some steps that are, in some sense, opposite to those by Tom and Willy. They actually want to demystify physics in the cosmological context ;-) while the addition of the extra fog almost seems to be the goal of Tom's and Willy's papers.

Now, Nima et al. really want to change a pessimistic part of the "folklore" that is believed by many experts, and it's the following:
La la la. (I included that lemma to make it clearer that it's folklore.)

Scattering in the flat space may be described by precision amplitudes because there are infinite asymptotic regions in the spacetime that allow us to prepare the initial and measure the final states. They fix the state of the fields to make the scattering really controllable.

In the anti de Sitter (AdS) space, something similar is possible, the scattering states may be prepared near the boundary of the AdS space, and that's where the CFT fields live. Their off-shell correlators tell us something very precise about the bulk scattering in the AdS space.

Now, the de Sitter (dS) space and generic cosmologies don't have any asymptotic regions, so the initial and final states can't be precisely prepared, and nothing like exact amplitudes apparently exists in those cosmological contexts at all.
It's the last, bold paragraph that is "pessimistic" in a sense because it suggests that whenever cosmology (especially de Sitter-like) cosmology is involved, we may be forced to give up all attempts to describe physics by unique and completely precise sets of complex probability amplitudes. We don't have enough space, time, and peace to prepare the initial and final states in violent cosmology conditions. That might be why the amplitudes can't be measured accurately (one human also can't re-live many episodes of the cosmic life). And the operational philosophy of physics might guarantee that if something is impossible to measure, it may also be meaningless to calculate it.

OK. Many of these views are philosophical in character – and they vaguely philosophically agree with what we learned from relativity and quantum mechanics. If there's no operational procedure to measure something, it may be physically meaningless and the truly profound theory of Nature may also prevent us from calculating such things or even talking about them.

Great. There is no real proof that these statements about the non-existence of observables in cosmology are correct. But they're defeatist and Nima et al. are basically weakening them. How? Well, they just pick some important cosmologies that are actually de-Sitter-like as well – namely the cosmic inflation – and do lots of initial steps to show that the observables may actually be just as quantitative and meaningful as they are in the "controllable" cases of the flat and anti de Sitter (AdS) space.

How do they do it?

What they do is a variation of the exercises that Nima and pals have been doing a lot in recent 10-15 years, depending on where you exactly start. The twistor minirevolution led Nima and others to carefully re-analyze the conditions obeyed by the scattering amplitudes – and how much these conditions are sufficient to uniquely reconstruct the whole S-matrix of scattering amplitudes, among other things. So the conditions were things like unitarity, Lorentz invariance, and the existence of some particular singularities in the scattering amplitudes – that have some clear interpretation.

These conditions have partly explained some simple formulae in the twistor-like variables, they allowed a recursive construction of ever more complicated amplitudes, and other things.

Nima et al. simply said: Can't we do the same thing with the de Sitter space during inflation? And with this call, they just went to work and wrote 108 pages of complex formulae to support the affirmative answer. Instead of the naive flat-space or AdS methods to anchor or peg the particles that scatter at infinity, these guys attached the fields and particles to the apparently conformally-symmetric behavior of the fields in the de Sitter space.

You know, the $$AdS_d$$ space has the isometry $$SO(d-1,2)$$. Similarly – imagine we're doing just a Wick rotation – the $$dS_d$$ space has the $$SO(d,1)$$ isometry. Those may be interpreted as analogous conformal symmetries. After all, this analogy between dS and AdS spaces was also hoped to be relevant by Andy Strominger's dS/CFT correspondence – although I think that the latter was just wrong because he promoted irrational links between the analytical continuation of AdS and some S-brane-like objects.

When Nima et al. claim that something is analytically continued, it just is.

So their result is a parameterization of all the scattering in the inflating dS space in terms of some four-point functions of scalar fields, and actually the soft limit is said to be enough to define everything. Some spin-raising operators may be added to deal with all the higher-spin fields. And some contact terms may be added to make it work. But when it's done, all the scattering may be derived. And they also assert that these amplitudes may be related to the flat-space ones by an analytic continuation of the momenta.

So the inflating dS space may have been completely moved from the "pessimistic" cosmological branch governed by dragons, witches, fog, and God to the "optimistic and enlightened" group that already included the flat-space and AdS amplitudes. If true, this is what clearly counts as progress – as Feynman has said, and my religious readers will surely forgive the blasphemy, every time science finds something new, it reduces the habitat for God. Nima et al. may have just kicked God and His cousin, fog, from the inflating dS spacetime regions.

You know, I would suspect that such things may be done but these guys – that have Nima inside so often – just go and do it. They analyze how the special form of the inflating dS space may regain the full control over the asymptotic behavior of the inflationary epoch as an arena for scattering. They may figure out how many $$n$$-functions are really enough to produce all the amplitudes – if some general principles that may almost be considered unavoidable "symptoms of consistency" are added. They find some specific detailed novelties – e.g. that higher-spin fields are really "derived" in this context (because inflation can make you spin). And they can figure out which claims about the analytic continuation and the presence of singularities are correct and which are not.

Incidentally, the reconstruction of the amplitudes is made possible, to a large extent, by the Lorentz symmetry or whatever replaces it in AdS and dS space. Just today, the Sudbury Neutrino Observatory published its "most complete ever" verification of the Lorentz symmetry in the neutrino sector. They included 40 completely new limits on 15 operators. All Dirac-type Lorentz-breaking neutrino-sector operators were addressed for the first time. Leslie Winkle's predictions are less defensible than ever before.

You know, the paper by Tom and Willy, and that by Nima et al., are sort of about "very similar things". They are about boundary conditions on fields in a gravitating curved spacetime and the effect of these boundary conditions on the calculations of the scattering in some small region of the curved bulk spacetime. But they say very different things. Tom and Willy say that "the invisible hand of the asymptotic region or holographic boundary can do random ad hoc magic to invalidate the previous assumptions about physics, such as the bulk locality that also applied to c.c." while Nima et al. say "we want the hand reaching from the asymptotic region to be under the full control of the people and it is obliged to respect the principles that we actually believe to be true, such as the conformal symmetry".

So the topics are the same but at some moment, the assumptions, direction of research, and strategies became almost exactly opposite. Although I am not consuming drugs ;-), I share Tom's and Willy's desire to have some truly original, intrinsically holographic, and new foundations for the bulk gravitational physics but in the absence of a theory that actually incorporates the knowledge that science has, I find it obvious that the efforts similar to those by Nima et al. are more likely to lead to progress, even if the direction may be in some sense opposite to "what the heart wants".