Brain Farts and Conjectures

Disclaimer: This section contains a list of open problems that I am interested in. They are worked out to various degrees, from brain farts over vague intuitions to sharp workable conjectures. Note that nothing within this page claims any sort of cleverness let alone even correctness  (though I will try to update the list as soon as something is proven/once I find out that it has already been done).
So it is simply a list of problems that i find interesting and ideas on how to tackle them as well as random bullshit that comes to my mind. For the ideas on this list I either lack the time or the skills to work them out (or they are simply not even in a state where they can be worked out). I much rather see them solved by someone else then have them collect dust in the back of my brain. So if you have an idea how to flesh out any of them, I would be happy to collaborate on that. If you just wanna do it yourself I would appreciate an adequate acknowledgement (in case the thoughts presented here actually contain any novelty).
If you have a source that proves/disproves anything mentioned here please send a pointer my way so I can reduce the bullshit to a minimum.

The Questions [Q] / Ideas [I] / Conjectures [C] are labeled for easier reference in communication.

Causal Fermion Systems

Causal fermion systems is a new attempt to build a framework to unify the Standard Model of particle physics with General Relativity. The framework was mainly developed by Felix Finster.

In the conjecture section I will use the notation and structures introduced in the following papers:
Introduction for Physicists
Introduction to the mathematical framework and structures.

For an extensive treatment of (almost) everything known about the model so far check out Felix’s book on the topic.

Note that my knowledge about the framework is to this point only vague and hence anything I write here about the claims made from the framework might actually just represent my misunderstanding of the claims or the framework itself. Note that so far I was unable to find anybody who was able to give me a well funded critical opinion on the framework (other then the people directly involved, but due to obvious bias I don’t count that). So I’m happy for any thoughts and opinions as I am still trying to figure out myself whether I think it contains some novel physical reality or whether it is “just” a complicated mathematical machinery reproducing what we already know about the world.

Random Thoughts and interesting Papers

Cosmology without Cosmological Constant: On my trip to Melbourne I stopped at the IFA in Hawaii. Istvan Szapudi explained that with their recent paper where they found that when plugging the typical density of the Universe into the FRW equations instead of the average density, they can eliminate the cosmological constant while still being able to perfectly trace the evolution of \LambdaCDM. Even more they manage to resolve tensions that recently emerged between CMB measurements of the Hubble constant and local measurements.

Q1: The relevant question: Can their hands on approach be made rigorous? (Can one show that a solution to the full Einstein field equations exists that traces their approximation.)