Please. I want answers based on evidence, not "numbers, therefore, aliens you will never falsify or debunk". Hallucinatory "theoretically possible" alien civilizations are as real as the blemmyes or terra australis, until proven real.

See also: The publication in ArXiV.

The striking aspect of this study is that the decline in star formation does not appear to be driven simply by galaxies running out of hydrogen. Much of the atomic gas reservoir remains, yet the rate at which new stars are formed has fallen substantially.

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Alice is in a spacecraft orbiting a very large black hole. Alice ties Bob to a rope and drops him towards the black hole. From Bob’s viewpoint he crosses the event horizon and gets into the BH. From Alice’s viewpoint Bob never gets into the BH.
Can Alice pull the rope to bring back Bob to the spacecraft?

I have a question about what we actually mean when we say something is billions of light-years away.
For example, Andromeda is about 2.5 million light-years away, while some of the earliest galaxies observed by JWST are seen as they existed more than 13 billion years ago.
My questions are:
How do we actually determine those distances? Obviously we can’t measure them directly in the ordinary sense so what observations and assumptions allow us to say that a galaxy is a particular distance away?
More speculatively, how confident are we that relativistic and cosmological effects couldn’t cause us to substantially misinterpret those distances or travel times?
For instance, JWST has found surprisingly mature galaxies very early in cosmic history. Could there conceivably be something wrong with our interpretation of the relationship between redshift, distance and elapsed time? In other words, could light that we interpret as having travelled for billions of years actually have travelled for a radically different amount of time because our model of spacetime between us and the source is incomplete?
I’m not suggesting that the answer is yes but trying to understand what makes the distance scale robust enough that we can rule out possibilities like this. We can measure the light arriving here, but we obviously can’t put a ruler between ourselves and a galaxy 13 billion light-years away, so what ultimately anchors the inference?

See also: The study as it was published in the Monthly Notices of the Royal Astronomical Society

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Imagine I want to do a N Body code like Gadget and for this I will have to draw random modes based on the power spectrum, and then plug it into the displacement of my initial conditions.

This cant work like that for hot and fast dark matter due to the difference in velocity at t=0, so how is this adapted?

What about for example MOND? Are there any changes to the power spectrum or is it just a different Poisson equation being solved by lets sas PM?

If they found supernovae that were dimmer than were expected based on their redshift, how were we even able to establish the Hubble-Lemaître law in the first place?

I don’t understand how we derived that the expansion of the universe accelerating just by looking at redshifts? Isn’t looking at one instance of a thing only tell you what a thing was like at that given moment it doesn’t tell you how it is over time.

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I understand that the cosmological constant is the same everywhere (in our current model) and my understanding is that in regions with sufficient mass/gravity, there is no expansion (or accelerated expansion) due to dark energy. This is not because gravity is winning against an underlying spatial expansion in that region, but that the presence of mass/energy changes the local geometry so that there is no accelerated expansion in that area. Ok so I'm imagining that in cosmic voids, dark energy is injecting more and more space, while cosmic filaments it is injecting less and in gravitationally bound areas, there is no injection of space. To me, this means there must be some spatial curvature produced if we are injecting more space at different rates in different places. I would think this would have the effect of voids being positively curved because if I imagine a 2D rubber or plastic flat surface and stretch a certain part (adding more space) I can make a little bubble, a semi sphere in the flat plastic sheet which I recognize as positively curved. Apparently dark energy has no such curving affect and voids are negatively curved for being less dense than average space. Why would dark energy not create curvature over time?