# A Brief on the Expansion of the Universe

**The “ordinary Big Bang and expansion” (no inflation, no dark energy)**

Einstein’s General Relativity allows a solution (FLRW metric) where an empty Universe expands. Imagine that you have particles (say, hydrogen atoms) in a cubic grid with exactly 1 light year between nearest particles. (We assume that their mass is so tiny that this Universe essentially behaves as if it is empty). And after each second distance between each particle increases by 1 meter. Not because they move, but because space “grows”. That’s that solution.

Even though empty Universe is expanding without slowing down (distance between test particles grows by exactly one meter per second, all the time), note that if you look back into the past of this Universe there were times when test particles were much closer together – say, only a billion km apart – and they moved away at exactly one meter per second too. It’s clear that there was a moment where they had to be zero meters apart. That’s the “Big Bang” moment. The moment itself is problematic (singularity!), but any moment after that is not. For example, one microsecond after this moment test particles were 1 micrometer apart. It’s a bit curious that in this scenario expansion seems to be very rapid at first (“density” of test particles falls very quickly), and millions of years later, it looks very gradual, but expansion rate is in fact constant.

**Big Bang with accelerating expansion**

Now, if you use General Relativity equations with cosmological constant Λ > 0, the picture changes. Grid of test particles grows not by exactly one meter per second all the time. Now it grows faster with time. If Λ is very small, at first speedup is not noticeable, but later it will be: test particles will not only move away from each other, they will seemingly do it faster with time.

That’s one possibility what dark energy is – maybe it’s just Λ. However, GR with Λ = 0 but with some other field permeating all space and having appropriate property (negative pressure) will have exactly the same behavior.

**B****ig Bang with matter**

How presence of matter changes this? FLRW metric with homogeneous distribution of matter will expand too, but expansion will slow down. (Heuristically, “matter will attract itself and try to shrink the Universe”). If there are lots of matter, expansion rate can even go to zero and expansion starts to go backwards. Between “too little matter, eternal expansion with nonzero rate” and “too much matter, expansion stops and reverses” there is a borderline case where expansion never stops, but its rate falls ever lower, tending to zero with time, but never reaching it (that’s “critical density Universe”). This all was about “normal” matter, with positive pressure. With “negative pressure matter” the effect is opposite – this was already described in the previous paragraph – that’s “dark energy”.

**B****ig Bang with inflation**

And finally, what if dark energy field is variable (e.g. it has several possible stable values) and one of these values is large (or there may be several such fields)? Alternatively, what if Λ can not only be larger than zero, but can be VERY MUCH larger than zero? Nothing unusual will happen, the Universe will behave as described above: grid of test particles grows faster with time. But very, very much faster. That’s inflation. (If you have a separate “large value dark energy field” for it, that’s “inflaton field”).

If you have inflationary Universe, even with matter, it expands astoundingly quickly, essentially becoming empty within a very small fraction of one second. And if then suddenly Λ (or dark energy) goes down to a very small value, you get an empty symmetrical flat expanding Universe. If “Λ going down” releases energy (in a form of appearance of new particles everywhere), you get a NON-empty symmetrical flat expanding Universe. As of 2016, this model fits observational data rather well.

Congrats nikkkom! I think you should be able to still make edits if you need to.

"Einstein’s General Relativity allows a solution (FLRW metric) where an empty Universe expands. Imagine that you have particles (say, hydrogen atoms) in a cubic grid with exactly 1 light year between nearest particles. (We assume that their mass is so tiny that this Universe essentially behaves as if it is empty). And after each second distance between each particle increases by 1 meter. Not because they move, but because space “grows”. That’s that solution."This is very much subject to interpretation. Note the following:1) The cosmologically interesting FLRW solutions are NOT empty in that the stress energy tensor is nowhere vanishing.2) In the limit of actually empty, you have the Milne solution which is just flat SR spacetime in funny coordinates in which the 'hubble flow' bodies are inertial with invariant relative velocity accounting for all of the red shift. These relative velocities are all sub-luminal, but the expansion rate (which is a coordinate quantity, NOT an invariant) is super-luminal. Yet, in standard cosmological coordinates, this truly empty solution is the one with maximal expansion rate (of solutions with zero cosmological constant).3) In the cosmologically meaningful solutions, if you set up Fermi-Normal coordinates, which are the closest analog if Minkowski coordinates in SR, you find that the Doppler of receding bodies is primarily due to relative velocity, and that this relative velocity is sub-luminal. 4) The growth of distance between bodies over time is wholly a coordinate dependent quantity. Distance growth over time requires a choice of foliation, and a choice of time coordinate, neither of which are invariant.5) As is well known, there is actually no such thing as an unambiguous relative velocity over substantial distance in SR. Thus a claim that recession rate does not represent relative motion is meaningless (because relative motion is ambiguous). However, it is true that parallel transport of a 4-velocity from one event in any spactime to any other event in the spacetime, produces a path dependent relative velocity < c.

Nice explanation of expansion, Nikkkom!

Excellent intro to cosmology using so few words!

You wrote: “

It’s a bit curious that in this scenario expansion seems to be very rapid at first (“density” of test particles falls very quickly), and millions of years later, it looks very gradual, but expansion speed is in fact constant.”This is well stated, but I just have a concern about the term “

expansion speed” in that sentence, which has caused some confusion in the past. I think what you intended is normally referred to as the “recession rate” (between two particles) because the speed of expansion depends on the size of the area that one considers. If it will not lengthen the article too much, it may also be useful if you could bring in the expansion rate or Hubble value (H) somewhere.Good short but all cases has been examined … very nice article…

Yes, I think replacing “expansion speed” with “expansion rate” everywhere in the text is okay.

Congrats nikkkom! I think you should be able to still make edits if you need to.

A questão é, manter o sistema em equilíbrio exige que a mudança cosmológica seja constante. Não voltando a ideia de Albert Einstein mas observando o efeito de partículas ordenadas demonstrados no LHC. O palco de Isaac Newton explicava que o espaço não era alterado, porém com as observações feitas no LHC podemos claramente ver que o palco afeta a ação e a ação afeta o palco. A velocidade em que é alterado e muito rápida quase que imperceptível!

I object to this in the closing paragraph – “Λ going down” releases energy (in a form of appearance of new particles everywhere), you get a NON-empty symmetrical flat expanding Universe. As of 2016, this model fits observational data rather well.”

What observational evidence supports this assertion?

Observational data supports the theory that inflation did happen.

And observational data supports the theory that Universe is not empty.