Dark energy is a hypothetical property of the Universe proposed in order to explain the accelerating expansion of the Universe we observe. In the late 1990’s, astronomers calculated the rate of expansion of the Universe by observing supernovas (exploding stars) across large distances in the Universe. When they plotted how fast the supernovas were expanding away from us as a function of their distance, they found that although the Universe has been expanding for its entire history, it has been expanding faster recently, meaning that something must be making the expansion speed up.

The currently accepted model of this is that empty space itself must have some amount of “dark energy” contained within it driving the expansion. If you picture a box filled with nothing but empty space, this energy will push outwards on the walls of the box and make it want to expand. Expanding the box will mean that there is more empty space inside the box, so there will be more pressure pushing outwards, so the box expands faster. This process can be seen in the expansion history of the Universe and will eventually lead to runaway expansion as the energy from empty space overwhelms the Universe.

Dark energy has never actually been observed in a lab (hence the “dark”) but we see very good agreement with this model in things like the cosmic microwave background and the arrangement of galaxies in the Universe. It also fits well into Einstein’s theory of relativity, which is our current theory for how space, time, and gravity work. So overall, dark energy is responsible for increasing the expansion rate of the Universe and will become increasingly dominant as time goes on.

Spacetime itself is expanding (‘stretching’) and as a result, galaxies are moving away from each other. However, this “Hubble expansion” also causes the mass density of the Universe to decrease with time because the same constant mass is being spread out over a larger volume (so at least part of your first explanation is also correct).

One implication of this decreasing mass density is that we don’t completely understand how dark matter halos (the objects within which galaxies live) grow their mass and radius over time. Dark matter halos are defined as “spherical overdensities” in the matter density field, and their radius is defined so that the density within the sphere is some number (usually 200) times the mean density of the universe. But if the mean density of the universe is decreasing with time, then you would need a larger radius to enclose the same overdensity at later times. So did a halo’s radius/mass grow because it genuinely accreted more mass, or because the mean mass density of the universe decreased? This is called dark matter halo pseudoevolution and is an active area of research — related to your question about the internal gravitational binding energy of objects overcoming the cosmic expansion.

Finally, and perhaps counter-intuitively: The expansion is accelerating and is thought to be due to dark energy, whose energy density stays constant with time. This implies that there is more dark energy now than in the past (otherwise the dark energy density would decrease, since the volume keeps increasing due to the expansion).

These are all great questions that definitely confuse a lot of people when they learn about cosmology, and they are all related to the fact that the Universe is a 3 dimensional bubble in a higher dimensional space. This is a weird concept, so a useful analogy is to think of the your place in the Universe as like an ant on a balloon. To the ant, the surface of the balloon looks like it is just flat ground. It would think that the world it is inhabiting is just a flat two-dimensional space since it can move in the X direction and the Y direction, but it is not aware of the Z direction going in/out from the balloon’s center. So even though this balloon exists in 3D space, the ant’s world is 2D. 

If we inflate the balloon, then every part of the balloon stretches out uniformly, meaning that any two points on the surface of the balloon will get further away from each other. I put a picture demonstrating this below:

The ant staying in one place will think that the ground it’s staying on is stationary and that everything else is moving away from it, but really the ant is being carried outwards just the same as everything else. If you have a balloon lying around, I recommend drawing dots on the surface and blowing it up to see this in action.

For our Universe, pretty much the same thing is happening, with us being the the ants on the surface of the balloon. However, instead of the surface of the balloon being 2D, the Universe is  3D and the balloon/Universe is being blown up in higher dimensional space (the currently leading theory says 11D). So let’s use this analogy to look at the answers to your questions.

How is everything moving away from us? This is the same as for the balloon. As the Universe gets “blown up,” the space between any two points in empty space will expand, so even though we are on expanding space, we will think that we are stationary and everyone else is expanding away from us, which is indeed what we observe.

Where is the center? The center of the balloon isn’t on the surface of the balloon, it’s somewhere off in the “higher dimensional” 3D space. The same goes for the Universe, where the center of our expansion is in some 11D location that we can’t comprehend or observe.

How could an infinite Universe fit in a small space? When we talk about the Universe fitting into a small space, we have to thin about it in the higher dimensional space rather than from our perspective. Think about folding a piece of paper in half a bunch of times. You’re taking a large 2D object and compressing it down into a smaller 3D space. If the sheet of paper was infinitely thin, you would be able to just keep folding it in half forever, compressing the 2D object infinitely. So any object that has fewer dimensions than the space it inhabits can be compressed to take up effectively no space. Our Universe started at a single small point in this 11D space and has been expanding in a 3D way since then.

Does the Universe have edges? This is more of a question of semantics than anything else. Current theories say that the Universe is flat and infinitely large (like the piece of paper I was just talking about), so it has no edges (this is also kind of like the surface of the balloon also doesn’t have edges, although we have never observed the Universe to be curved like the balloon’s surface). However, we can’t see the entire Universe because the Universe is only 13.8 billion years old and light can only travel so fast. So the furthest things we can see are things that gave off light at the beginning of the Universe and that have been sending their light our way for that entire time, and we can’t see anything further away than 13.8 billion light years (the distance light travels in a year). So in this sense, the area of the Universe we can actually see (the “observable Universe”) does have edges and those edges are 13.8 billion light years away from us.

I think the period of the Universe’s expansion you’re talking about is inflation, which was an incredibly short period of incredibly fast expansion almost immediately after the Big Bang. It’s kind of hard to talk about what happened to time during that period though for a few reasons. First, it only lasted for an almost unfathomably short amount of time (~0.01 nonillionths of a second) so it’s not like things could really move or change much over the course of it. Furthermore, the early Universe didn’t even really have that much stuff in it that could really experience time in the way we think about it. There were no molecules or atoms or even protons or quarks. It was essentially just a soup of energy and quantum probability. But I think the core of your question is how the rate of time flow would be affected if space was being stretched so dramatically, and the answer to that is that we don’t really know or have the capacity to know. We experience time at a rate of 1 second per second and that is what controls the rate of chemical reactions in our brains, so there isn’t really any way to talk about time flowing at different speeds because we (and the rest of the Universe) would experience it the same way regardless.

This is indeed what we believe to be true in the Universe. Astronomers currently have a lot of evidence that points to the Universe being infinite in size, but we can only see 13.8 billion light years in any direction, a relatively small bubble of the overall Universe. This means that if a galaxy started too far away from us (say, 50 billion light years), its light wouldn’t have enough time in the 13.8 billion year life of the Universe to get to us by now, so we wouldn’t be able to see it. As the Universe gets older, it becomes possible to see more and more galaxies since their light has had more time to traverse the Universe, but this is complicated by the fact that the expansion of the Universe is carrying them ever further away from us all the time. So there are galaxies that will always be effectively impossible to see because they are so far away that even by the time we see them, they will be so far away they will be essentially invisible.

Annihilation would have happened very early in the Universe (around 1 second after the Big Bang), releasing a huge number of photons as you said. However, the problem is that the Universe didn’t turn transparent until more than 300,000 years after the Big Bang, so these photons would just bounce around, spreading out the energy into a diffuse glow. Eventually, when the Universe did turn transparent (when atoms finished “condensing” out of the cloud) then the photons would be free, but any distinct flash would be long since smeared out by then. Instead, we see what astronomers call “the surface of last scattering” (the Cosmic Microwave Background) which is when the photons finally broke free of the clouds of matter in the early Universe.

There is no particular reason why the Universe should be flat. In fact, this seeming coincidence is a major problem that any modern theories of cosmology have to account for. The prevailing hypothesis for how the Universe got flat (and other otherwise unexplained phenomena) is called Cosmological Inflation, which basically states that almost immediately after the Universe began, it expanded so fast that it smoothed out any curvature that might have existed, making it look perfectly flat. This is essentially the same as blowing up a balloon to be so big that the ant wouldn’t be able to see that it is curved.

One of the key properties of the Universe is that it is uniform on large scales. Everywhere in the Universe had essentially the same starting conditions after the Big Bang, so everywhere should have developed exactly the same as everywhere else once you average out local disturbances like galaxy clusters. This can be seen in maps of the Universe that we have made so far, where there may be small features like galaxies and clusters that deviate from average, but on the whole, each part of the picture looks the same. So since the Universe looks the same on average no matter where you are, it shouldn’t matter which direction JWST is pointing when it looks to the beginning of the Universe. The first stars and galaxies should be approximately the same no matter where you look. The flatness of the Universe doesn’t really come into this directly, that really just dictates how geometry works over large scales and gives us insight into the extremely early history of the Universe.

There currently isn’t any real experimental evidence for extra dimensions. Theoretical physicists are mostly just going by the fact that extra dimensions makes the math work out better when trying to explain certain things, like inflation, the Big Bang, and how gravity works. String theory, one of the leading unifying theories of particle physics, relies on a large number of extra dimensions, but currently has not been experimentally verified. We may also see evidence of extra dimensions if we can observe the effects of our Universe running into another universe in higher dimensional space, which would theoretically cause wobbles in spacetime called gravitational waves. These have yet to be observed though.

Many astronomers have considered the possibility that dark matter is not something new and exotic but is instead just a bunch of normal stuff that is too dim to see, but it just doesn’t fit the data we have. The idea of MACHOs (MAssive Compact Halo Objects) making up the missing mass in dark matter halos floated around in the 80s and 90s for a while, but if there were indeed that many planets, small stars, or black holes floating around, we would expect them to pass in front of normal stars relatively often, leading to an eclipse or a gravitational lensing event that we would be able to detect with telescopes. We have seen events like this happen, but not at a high enough rate that it would explain all of the missing mass in the Universe, so there must be something else going on. Furthermore, the models that we have of the Big Bang (which are extremely well calibrated to real data nowadays) predict exactly how much “normal matter” should exist in the Universe, and there is still a large amount of missing stuff left over that we can’t account for, so dark matter seems like it must be something exotic.

Dark matter is indeed very important to galactic and cosmological astronomers since its mass dominates the mass of normal matter and is responsible for forming most large structures in the Universe. The search for what dark matter actually is, though, is more in the realm of theoretical and particle physics. Astronomers observe galaxies, galaxy clusters, and the early Universe to constrain the properties of dark matter and inform future theories though. Theoretical physicists have created theories for multiple different kinds of particles that would explain observations, and now the correct one must be determined. 

MACHOs (MAssive Compact Halo Objects) were an early contender for what dark matter could be (along with WIMPs) and were particularly non controversial because they were just said to be normal things things that were too dark to see (like dead stars, black holes, rogue planets, etc.). They have been ruled out over the past few decades though because 1) even if they’re totally dark, we should be able to see when they pass in front of things, which we don’t, and 2) dark matter has been observed to be essentially non collisional (i.e. it just passes straight through itself) which things like black holes or planets wouldn’t do. So while it is a sensible suggestion to say that dark matter is just normal matter that is dark, it doesn’t fit the picture, so more exotic answers are needed. 

There are a few candidates that are currently popular in the search for dark matter. One of the oldest and most well known are WIMPs (Weakly Interacting Massive Particles). Breaking down that definition, WIMPs are particles that have mass (and thus gravity), but they only interact with other normal particles with the weak force, which is very hard to detect and almost never comes into play. Because of this, they are very hard to detect and many experiments in the past few decades have failed to see any indication of them. 

Another popular particle right now is called the axion. Unlike the WIMP, it is theorized to interact with the electromagnetic force, meaning it can turn into photons in the right conditions. It is theorized to have a mass about 1 million to 100 million times less than the electron, but if there were enough of them, they could still account for the missing mass we observe. An experiment called ADMX (Axion Dark Matter Experiment) is currently scanning for different masses of axions and should hopefully produce interesting results in the next few years.

Another option are sterile neutrinos. You may know about regular neutrinos, which are small inconsequential byproducts of some nuclear reactions. Neutrinos hardly ever interact with anything since they only use the weak force, but they do have some tiny unknown amount of mass; however, the properties of neutrinos are well known and do not match the properties of dark matter. Sterile neutrinos, however, are theoretical “mirror” neutrinos that wouldn’t even interact with the weak force and thus are even harder to detect, but they may have enough mass to make up dark matter if they exist. Theory predicts that they should interact with neutrinos also, but current neutrino detectors haven’t seen any evidence of them. 

So basically, dark matter is still a complete mystery, and whoever can figure out what it’s actually made of will surely win the Nobel prize and revolutionize several different fields of physics and astrophysics.

General relativity and the curving of spacetime are always hard to wrap your head around, so physicists and astronomers like to use metaphors when teaching the concepts. The analogy of the bending of space behaving like the stretching of a sheet of fabric that the Earth is sitting on works well for understanding the system in 2D, but unfortunately the Universe is 3D so things have to get more complicated.

Instead of spacetime being a flat sheet, imagine it being a block of foam, and instead of gravity pulling things outward, imagine it pulling everything inwards (like it does in real life). Putting the Earth inside this block of foam will draw a bunch of foam inwards to the Earth, stretching out all of the foam around it and distorting spacetime. This is the effect that the Earth has on everything around it, so it’s not a “top” and “bottom” thing, it’s the same all around. 

Here is an illustration to help you visualize it:

When we are talking about movements within the solar system, we must think heliocentrically (centered on the sun) rather than geocentrically (centered on the Earth). The information we receive from the sun is based off of its position ~8 minutes ago, but that is its position relative to the stationary frame of reference of the solar system, not the rotating frame of reference of the surface of the Earth. Even though the sun appears to move through our sky, it is still staying in substantially the same place, so its perceived position doesn’t actually change much over the 8 minutes that the information takes to reach us.

The speed of gravity is another interesting concept that is still not 100% resolved in physics, but we have observed it to travel at almost exactly the speed of light. Special relativity says that no information in the Universe can travel faster than light or else it would violate causality, and this includes gravity. A major test of this occurred in 2017 when UC Santa Cruz astronomers observed two neutron stars merging in a distant galaxy. Despite the gigantic distances involved (140 million light years), the light and gravitational effects from this arrived at the same time, indicating that the gravity was travelling speed of light. The fundamental physics surrounding the propagation of gravity are still not totally solved so it is possible that gravity may travel imperceptibly slower than light, but that is not currently known.

So if the sun were to move or change in the solar system, we would not know until both its light and its gravity reached us ~8 minutes later, and these changes would match up with each other.