Black Hole State Dependence as a Single ParameterHe does accept that the operators have to be state-dependent (well, he's been a co-author of Papadodimas) but tries to minimize the state-dependence – by saying that the dependence is just through one number, a time shift. He says that while it's hard to construct the black hole interior field operators and people used to say that it was impossible (within AdS/CFT), constructions exist that depend on the pure state. But the underlying problem is that the time runs backwards inside – and therefore one may fix the problem by quantifying how much time has elapsed (in the opposite directions) since the moment when the inside-clock and outside-clock matched.

I remember that Raju and Papadodimas actually used the time shift as an

*example*of the notion of the dependence of the constructions on the pure states. It could have been more than just an example – such a time-dependence could be the whole thing.

There is some point I can't resist to make: ergodic theory. If you have a system in thermal equilibrium, it evolves sort of chaotically and classically, you visit the vicinity of all regions that are sufficiently close to any point of the phase space. Ergodic theory says that the average over the slice of the phase space is the same as the time average. By some unnatural map, you may trade the dependence on the phase space – whose quantum generalization is naturally the dependence on the pure microstate – for the time-dependence. This equivalence is basically a matter of the ergodic theory even though the required map is seemingly unnatural.

Whether or not Rik's paper is "correct" really depends on how much you can do with this map – whether the parameterization through the full pure state or through the time shift is the more natural one, I think. There can't be any "total hurdle" that could perfectly invalidate his paper because the pure states may be arbitrarily precisely encoded in a time shift by the ergodic trick.

The second paper I want to mention is

Quintessence Axion Dark Energy and a Solution to the Hubble TensionThey claim to have a nice answer to the double question "what is dark energy and dark matter made of" as well as the question "why the hell do we get these huge tensions in the estimates of the Hubble constant now". Again, I would say that these huge tensions mean that we should interpret the precision cosmology from the late 1990s as an "illusion due to good luck" and that cosmology is really understood with a much worse precision than we have been saying for two decades!

In recent years, we were tempted to say that the age of the Universe was 13.83 billion years, for example, and the error margin could be something like 0.01 billion years and shrinking (optimism) – but that's almost certainly wrong and the actual error margin is probably comparable to one billion years again. Well, the disagreements about the Hubble constant seem to be around 10% now.

These three Chinese-Japanese authors including Motl-Motosport Suzuki extend the MSSM, the minimal supersymmetric standard model, by an axion superfield. The energy density of an axion may be rather small, parameterically speaking, so I find it nice for them to identify the contribution from an axion with the dark energy (cosmological constant). Their model happily admits a discrete symmetry \(\ZZ_{10}\) which suppresses the proton decay. With this discrete symmetry and some R-symmetry, they may naturally get a gravitino dark matter of mass \(1\GeV\) or so, reheating temperature around a few million \({\rm GeV}\), non-thermal leptogenesis, and remove the tension between the measurements of the Hubble constant by realizing that the axion is a quintessence field that adds some new time dependence to the cosmological constant.

Well, I am surely not persuaded yet that this is "the model" that should replace the simpler Lambda-CDM models but it is obviously possible that this model or some similar model will become the established preferred "standard model of cosmology" in the future. We will probably need some new, currently unknown, observational evidence to get sufficiently certain about this advance, I think. Some kind of a more direct detection of the gravitino and/or the axion would be stunning, of course.

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