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I hope this exact question is not a duplicate. I have looked into some high rated answers/questions, but found no satisfying/understandable answer. This is my current line of throught:

  1. In the inflation model, a strong expansion of the universe is assumed during the period, after which we start counting time today. This inflation has a yet unknown cause and ends spontaneously.

  2. Then a slower expansion happens which decelerates due to the energy content of the universe.

  3. Eventually (due to the cosmological constant), the universe again accelerates to expand.

I do not understand (2). With inflation gone and dark energy not yet strong enough, what fuels this expansion?

EDIT:

It seems to boil down to two ingredients:

a) an initial expansion rate that is given by the termination properties of inflation via an athropic principle approach.

b) an "inertia" of the spacetime expansion, which is necessary to allow the inital value to carry forward into future several billion years.

I want to re-phrase my question: What causes spacetime to have "inertia", i.e. why does its expansion not react instantly on its ingredients?

EDIT 2:

Koschi made me aware of the Friedmann eqs. which describe what I was looking for. The simple picture drawn by popular news outlets that I knew, does not capture some aspects of these eqs.

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    $\begingroup$ I do not really understand the part "why does its expansion not react instantly on its ingredients?"... would to you mean by that? We use Friedman's equations, to find out how energy content (i.e. "ingredients") and spacetime influence each other. There is no "delay" of spacetime reacting to the energy content. But: The initial condition, which is obviously very important, is not given, but has to be put in, but once this has been done, the equations describe the expansion very well. $\endgroup$
    – Koschi
    Commented May 18, 2021 at 12:36
  • $\begingroup$ @Koschi thank you for mentioning Friedmann eqs. This is what I was looking for. They put forth eqs. of motion for space time, where the "forces" acting on the scale factor are given by the contents of the universe. My faulty understanding is from my layman knowledge of: "energy pushes inward, dark energy pushes outward", which is obviously a severly lacking picture drawn by eager university PR. This defines no inertia and on its own would have led to a contracting universe after the inflation. If you could at least slightly elaborate on this in your answer, I can accept it. $\endgroup$
    – tobalt
    Commented May 18, 2021 at 12:46
  • $\begingroup$ You are right, energy does not "push inward" by default... if the universe expands after inflation, it will continue to do so, even if the ordinary matter and radiation is dominating the energy density. $\endgroup$
    – Koschi
    Commented May 18, 2021 at 12:54

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I think your question concerns what is called the problem of a "graceful exit" at the end of inflation, which is to say, how the conditions before the end of an inflationary episode can lead to the observed conditions after inflation---that is, a highly uniform universe with a very regular expansion. As far as I know it has proved to be very difficult to argue convincingly that inflation leads to a graceful exit; the best we can do (I think---this is just based on general reading) is to place very special conditions on the hypothesized inflationary process.

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  • $\begingroup$ The term "graceful exit" implies that the expansion could be explained by specifics of the inflation process. However, the universe expands for billions of years after the inflation ends. During all this time with dark energy "weaker" than the energy content, my current understanding (obviously wrong) would imply that the universe would contract $\endgroup$
    – tobalt
    Commented May 18, 2021 at 12:07
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    $\begingroup$ @tobalt The idea is that the end of inflation somehow yields the conditions observed, which includes that all the matter/radiation is initially on trajectories which (after averaging over small regions) correspond to the Hubble flow. It is like throwing something upwards in a gravitational potential well: if you give it enough initial velocity, then it will stay up for a long time. $\endgroup$ Commented May 18, 2021 at 12:35
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Spacetime doesn't have inertia. The matter in it does, and the expansion is just the expansion of that matter. See this answer.

If you can arrange for reheating to produce a homogeneous, isotropic, expanding matter distribution (the graceful-exit problem mentioned in Andrew Steane's answer), then the continued expansion over billions of years is just (the general-relativistic version of) Newton's first law. Nothing needs to drive it.

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  • $\begingroup$ But the second derivative of the scale factor is a finite quantity in the Friedmann eqs. So that means that the scale factor first derivative changes only gradually. I would call this property inertia. Or does the scale factor not describe the "size" of spacetime, but of its contents? $\endgroup$
    – tobalt
    Commented May 19, 2021 at 18:24
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    $\begingroup$ @tobalt The Friedmann equations describe the evolution of a homogeneous isotropic distribution of matter under its own self-gravitation. If there's no matter ($ρ=p=0$), then the solution is Minkowski or (anti) de Sitter space, and there's an infinite family of different FLRW coordinate charts that cover any patch of it, all satisfying the Friedmann equations. There has to be matter present to break the symmetry and give you an unambiguous scale factor. $\endgroup$
    – benrg
    Commented May 19, 2021 at 18:49
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It is expected that the inflaton decayed into the Standard Model particles, directly, or indirectly, ending inflation. Therefore, after inflation the expansion is assumed to "be fueled" (i.e. driven) by the energy in radiation, meaning actual photons, but also all other particles of the standard model, since they had such high energy that all of them were relativistic, meaning their kinetic energy was much higher than their mass (in natural units). At temperatures higher than the so-called electroweak scale, also it is assumed that the Higgs mechanism was not yet at play, rendering all the particles massless, and relativistic, anyway. After the universe cooled down further, most particles became non-relativistic, and photons have lost a lot of energy because of redshift, so there was a certain time that we expect the universe to be matter dominated... but still, in both eras, there was the right amount of energy to keep the expansion going.

Actually, how radiation and matter can fuel the expansion is a basic discussion in every cosmology textbook and lecture script, so I highly recommend looking into one of these!

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    $\begingroup$ I understand that everything within space was very energetic and moved around fast. But how does this matter for the geometry of space itself? If you say that this energy content drives expansion, then how is it that this same energy content is usually made responsible for driving the universe to a collapse? This is the dilemma for me. $\endgroup$
    – tobalt
    Commented May 18, 2021 at 11:52
  • $\begingroup$ I'm not sure about the use of the term "fueled" in this answer. The "answer" seems to be your second paragraph, which is not an answer but a statement that it is discussed elsewhere. $\endgroup$ Commented May 18, 2021 at 11:55
  • $\begingroup$ @AndrewSteane I do not really understand... the single question was, "WHAT fuels the expansion...?" the answer is, "radiation and matter". I think the technical details of how this works can easily be found in books. $\endgroup$
    – Koschi
    Commented May 18, 2021 at 11:59
  • $\begingroup$ @Koschi "The question is, how much energy you have, and how fast the universe initially expands". Without any other reason, I would assume this initial expansion to be zero. Obviously, this is historically wrong. And I want to understand why. Would you briefly describe, under which circumstances the energy content of the universe accelerates expansion ? This would be a strong addition to the statement that it does. $\endgroup$
    – tobalt
    Commented May 18, 2021 at 12:02
  • $\begingroup$ Sorry, I had to delete my comment, there was something wrong: @tobalt The geometry of space is shaped by its energy content... this is what Einstein's field equation say. A universe with matter can also lead to a collapse. The question is, how much matter/energy you have, and how fast the universe initially expands. $\endgroup$
    – Koschi
    Commented May 18, 2021 at 12:03
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The present cosmology model is called the "Big Bang" because its first manifestation as a model was a "Bang" of energy, an explosion of what is now the total energy of the universe, from a singularity that was allowed to be within general relativity. It used to be a nice < shape with time starting from the original singularity. It has evolved now to this complicated model

enter image description here

Continued observations of the cosmic microwave radiation, the need of quantum mechanics when distances become very small , that there exists still expansion of the universe, not just kinematic explosion limits, have developed the Big Bang current version above.

Quantum mechanics is used to spread the effects of the singularity over time 0, because a basic tenet of mainstream physics is that the underlying nature of everything should be quantum mechanical, so the singularity becomes fuzzy.

Then the uniformity of CMB necessitated the inflation period, where the expansion was rapid homogenizing the energy everywhere ,and then the particles appeared and slowly as the universe expanded according to the original Bang we come to the observable universe, which is observed to be still expanding, not just following an initial explosion.

You ask:

What caused the universe to expand in the epoch right after inflation?

What exploded was a lot of mass/ energy , and the explosion was fueled in the original Big Bang at time around 0. All explosion have an original energy imparted to the exploding masses, which then continue following the kinematics. In the case of the Big Bang the kinematics are those of general relativity.

With the need for inflation, the assumption is that the original explosion input energy has expanded in time up to the end of inflation, in the plot above. Then it was assumed the original Big Bang explosive impetus took over with a constant expansion.

Except , it has been observed that there is an accelerated expansion, as seen in the plot . This is modeled as dark energy, and how this happens is still a matter of on going theoretical and observational research.

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  • $\begingroup$ Need to change "continuing expansion" to "accelerated expansion" in last paragraph? $\endgroup$
    – isometry
    Commented May 19, 2021 at 7:20
  • $\begingroup$ @isometry thanks. done $\endgroup$
    – anna v
    Commented May 19, 2021 at 7:41

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