Does cosmology answer why the universe exist?

No a particular wave function applies when a system in a particular informational viewpoint interacts with another. It does not require a presence of an "observer", any more than in relativity (lengths and time are affected by relative motion, even when no "observer" is present.)
Yes, I tried to visualize that. Seems to me that all relativity requires the presence of at least two observers (objects of any kind in motion).

I can understand that two objects approaching each other create an relative compression in spacetime and vice versa.

But does that condition exist all the way between the two objects or is there a gradual increase of compression as two objects approach each other?
An example is the gradual increase in pitch in a motorcycle's engine as it approaches and after passing, a gradual decrease in pitch as they recede from each other.

Does distance have any effect on the compression or expansion of wavelengths (spacetime)?
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Just ran across this interesting presentation.

It occurred to me that this might even support the proposition of a toroidal universe.
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Just ran across this interesting presentation.
It occurred to me that this might even support the proposition of a toroidal universe.

Just a more recent update on the proposition of a toroidal universe.

IMO. this concept would answer many outstanding questions. A causal dynamic singularity, spacetime expansion (inflation) and contraction, conservation of energy, wave function, universal constants, physical constants, mathematical constants, flow of time, all the apparent universal properties and dynamics would be answered by this simple "bounded" looped system, which does not preclude the concept of a multiverse.
Smaller-Scale Toruses
Torus-shaped energy fields don’t just exist at the universal scale; they exist at every scale of reality…
This video shows that our Local Group of galaxies is located near the centre of a 1.7 billion light-year-wide toroidal energy flow between the Dipole Repeller and the Shapley Attractor.
The Next Article continues the theme of toroidal geometry down to the galactic scale.
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Does cosmology answer why the universe exist?
Or only "how"?

What is the meaning of life in the eyes of a cosmologist?
Cosmologists tend to look into the “how,” not the “why.”

“why” may not even be a meaningful question., it suggests some sort of purpose.

Consider mountains humans thought they had been there as long as the earth had been around which could have been forever.

Modern science has since discovered plate tectonics, not only do we know how these work, move but also time scales, mountains and the earth are not eternal.

Is a “why question” here now meaningful?

Same with something closer to home and probably more profound.

Why are we here? Humans? The biggest question for 1000s of years till Darwin. Once “how” is discovered, “why” fades away.
From what the Webb telescope is seeing, the whole of current cosmology theory may need to be altered.
Possibly, not thrown out though. There was a BB, there was a quark gluon plasma, nucleosynthesis, expansion cooling decoupling and CMBR. Galaxy formation LamdaCDM? Yes could be a tweak.
It cannot throw away Creation by God.
The question was about cosmology. Cosmologists build theories and use models to make sense of the data.
When an observation does not fit within the theory then theory needs to be looked at. What you are claiming is nothing to do with the science.
Possibly, not thrown out though. There was a BB, there was a quark gluon plasma, nucleosynthesis, expansion cooling decoupling and CMBR. Galaxy formation LamdaCDM? Yes could be a tweak.
In fact CC posted an article on this very topic a few days ago:

Here's an extract from Ethan Siegel's comments:-

"But what is it, exactly, that’s amiss?

A lot of people immediately resort to the spectacular or fantastical as far as explanations go. They assert that all of standard cosmology might be wrong, and perhaps we should throw out the Big Bang as the explanation for the origin of our Universe as well. They hypothesize new laws of physics (like a new, early form of dark energy that existed early on) or new physical phenomena (like the Universe being born with supermassive black holes) or new exotic forms of matter (like a novel, long-lived particle that decays into normal matter at relatively late cosmic times).

But that shouldn’t be your first resort, as a scientist. That should be your last resort: after you’ve exhausted all of the mundane explanations. And there are a number of things that are quite mundane to consider. We should first make sure that these effects aren’t playing a major role in causing these galaxies to appear with the properties they appear to have, and we should also make sure that our expectations for how the Universe ought to behave are in line with the way the Universe actually behaves.
For one, the early surveys that are pointing to these conflicts are coming from very small, and possibly atypical, regions of the sky. There are surveys coming that will cover some ~50 times the area that are showing these early galaxies, and we might well see a “regression to the mean” of this apparent effect.

For another, it’s possible that light from an active supermassive black hole at the centers of these galaxies is “polluting” our view, and making us think that these galaxies are more massive and rich in stars than they actually are. A full spectroscopic analysis of these galaxies, not yet available, will be needed to determine if this is the case.

For yet another, it’s possible that these galaxies aren’t actually brighter and more massive than we expect — at least, not by the amount we’ve initially concluded — because JWST is overperforming. It could simply be the case, at least in part, that JWST’s better-than-expected eyes make these galaxies appear brighter than they will turn out to be when properly calibrated.

And finally, it’s possible that we’ve gotten some detail like gas cooling, halo identification, the nonlinear growth of structure, or the effects of stellar feedback or magnetic fields incorrect.

In other words, it’s possible that either the preliminary data is unreliable or that our assumptions for how the early stages of cosmic structure formation proceed are flawed. While there are some early observations that could wind up pointing to a tension between what JWST is seeing and what our current understanding of the laws and composition of the Universe are, any such assertions that “the Big Bang/ΛCDM/standard cosmology is in trouble” are definitely premature at this point. Without better data — i.e., a deep, large-area, robustly calibrated, spectroscopic survey — we don’t even know if these galaxies truly possess anomalous properties. An in-progress JWST survey, COSMOS-Web, should settle the issue."

And even if they do, there are an enormous number of astrophysical possibilities that invoke no fundamentally new physics that could potentially account for why these galaxies would exist with these large masses and brightnesses. The only thing that would truly shock us at this point, and to be clear, this is not what the data indicates at present, is if there’s more mass inside these early galaxies than the normal matter known to be in the Universe could potentially account for. It’s entirely possible, even if these early galaxies are as bright and massive as the most optimistic estimates are, that boring old gravitation, electromagnetism, and stellar/gas physics can explain what we see.
Probably not. See post 110.
Some data out from Chandra, I have posted a thread on it
Another challenge to LambdaCDM. I do not know enough about the theory to know if tweaking some of the parameters will fix the the conflict, or if they have to rethink it.
Probably not. See post 110.
I think the OP question was answered. "Why" is not a great question in science. It is a better question in philosophy. There are "what the hell is going on!?" Questions in science, especially cosmology right now with the MOND V DM debate and the Hubble tension. That is another thread!