# B What was the curvature of the early universe?

1. Oct 14, 2016

### newjerseyrunner

I was reading about the first few Planck seconds and noticed no mention of general relativity other than the horizon problem. I some googling and only came up with some 1979 research that took the assumption that gravity was less powerful in the past, which I find suspect and Was developed before inflation was figured out. So what is the modern idea of the geometry of space near the beginning of time? Is there any direct evidence of anything or would it be purely mathematical conjecture which we know can't reconcile GR and QM at those scales. As inflation pushed faster than light, would the uncurving of the universe as the energy spread out responsible for the primordial gravity waves that I've heard about but don't really understand?

Related GR question, if you have tightly curved space because of ultra high densities then greatly expanded the space, how long would it take for it to flatten? Does space instantly transform to the energy density changes or does it take time. (I don't mean propogate which I know happens at c.). If the curvature is X because of x energy and instantly there is x-y energy, is the curvature X-Y or will it be somewhere in between because curve changes gradually?

2. Oct 14, 2016

### Zypheros_Knight

The inflation was and is accelerating, I don't know if it was faster than the speed of light! (the universe's speed limit would be the speed of light at most).

3. Oct 14, 2016

### newjerseyrunner

This is not right. Dark energy is not the same thing as inflation (probably.). Spacetime can expand much much faster than light, only information is restricted to that speed.

4. Oct 14, 2016

### Staff: Mentor

Where? Please give a specific reference.

5. Oct 14, 2016

### Staff: Mentor

Rightly so. This is certainly not part of the current mainstream model in cosmology.

First of all, "the geometry of space" is coordinate dependent. The usual meaning of this term when used without qualification is "the geometry of spacelike slices of constant FRW coordinate time", so I'll assume that's what you mean. But it's good to be aware that this "geometry of space" is coordinate-dependent.

The short answer to your question is that, in inflationary cosmology, we don't know and it doesn't matter, because inflation makes the geometry of space flatter and flatter the longer it goes on, regardless of how it started out.

If you're talking about QM as in the portion of the very early universe's history when quantum gravity effects were significant, then "the geometry of space" isn't well-defined to begin with in this regime, so it's meaningless to ask what it was.

No. The primordial gravity waves are due to quantum fluctuations in the spacetime (not space) geometry, which are believed to be significant at the "edge" of the quantum gravity regime, so to speak--where a well-defined spacetime geometry is just coming into being out of whatever quantum gravity stuff came before. But all this is, AFAIK, rather speculative; we don't have a good theory of quantum gravity, so we don't have a good theory of how it transitioned into a well-defined classical spacetime geometry either.

It depends on how flat you want it to be.

I'm not sure what you mean by "transform to the energy density". Have you looked at the Friedmann equations? Do you understand how they relate the energy density (and pressure) and the expansion rate and its rate of change?

This isn't possible; the stress-energy tensor has zero covariant divergence, so energy density can't instantaneously change like this.

6. Oct 15, 2016

### Zypheros_Knight

I read a little and now I think you were right about the speed of expansion of space-time much* more than the speed of light.....The idea that something can go faster than the speed of light was hard to let go....yet again physics is nothing without maths so I request that you formulate a mathematical expression for this.

Edit*: Dark energy and Inflation are different things!...inflation is the expansion of space-time while dark energy is just energy! We wont know more about the dark energy, I hope that this research will solve that problem.

7. Oct 15, 2016

### bapowell

The universe does not expand a particular speed, and so saying that the universe expanded faster than light during inflation is nonsensical. Look up Hubble's law and you'll see how the rate of expansion is related to recession velocity. You'll find that at a certain distance objects recede at super luminal recession speeds in both inflationary and non-inflationary spacetimes.

Inflation was also caused by energy, and dark energy also leads to accelerated (inflationary) expansion, so the distinction is not so clear: they're both general terms. Generally "inflation" refers to primordial accelerated expansion driven by the vacuum energy of some scalar field. Dark energy is posited as causing the current accelerated expansion of the universe. It too could be the vacuum energy of a scalar field. The main difference is the energy densities of the two expansion periods.

8. Oct 15, 2016

### newjerseyrunner

"The universe expanded faster than light" is a misnomer. There are still parts of the universe that are moving apart faster than that from our perspective.

Expansion can be expressed as the time it takes to double the diameter of the universe. So the distance between two objects increases by a factor of two of time. If after one second two objects are one foot apart, the next they are two, then four, then eight, then sixteen.

Because of the uniformity of the microwave background radiation, cosmologists believe that the universe doubled many times over in a very brief period of time.

Now the speed of light is a limit only from the point of view of the observer. You can never observe anything moving faster than light relative to you. Two photons traveling in opposite directions can and are traveling away from each other st twice c from our reference frame. Now that reference frame is relative to the space itself. If you expand the space itself, that reference frame becomes distorted. No motion through space exceeded light speed, it was the space itself that changed.

Inflation and Dark energy both push the universe apart. They may be manifestations of the same thing, but they may not be. We have no mathematical description of either. The equations we learned in high school for gravity and electromagnetisms look very similar, they ended up very different when we looked closer.

9. Oct 15, 2016

### bapowell

This is a confusing thing to say, that we don't have a mathematical description of inflation or dark energy. We do. In fact, we also have physical descriptions of them of varying degrees of adequacy (inflation is arguably better motivated and understood, but I'm biased).

10. Oct 15, 2016

### newjerseyrunner

My mistake. I thought there were still numerous theories for the trigger, the mechanism, and end of inflation? Is it reasonable to say that it's still very unclear so to whether they are manifestations of the same thing or unrelated? I'm certain no experiments have ever reached those energies to test the math.

Dark energy might be very difficult to ever get a grasp on, I don't see a way to ever do experiments at the scales needed. I'm hoping that it sort of just falls out of a theory sort of like how a graviton-like particle popped out of string theory.

11. Oct 15, 2016

### bapowell

We use the CMB to test inflation. Several aspects, including the near scale invariance, adiabaticity, and gaussianity of the primordial perturbations, the presence of super-horizon correlations in the polarization spectrum, and the uniformity of the CMB temperature, support the inflationary hypothesis. Indeed, there are many proposed inflation models (based on, among other things, different potential energy functions of the putative field that drove the expansion), but measurements of the CMB and large scale structure can be used to constrain the parameters of these models. So, we certainly can test the math.

Don't forget, in science there will always be multiple ways of describing natural phenomena. We can only hope to rule out those that fail, and corroborate those that succeed, in describing the phenomena.

But you are correct that we lack a sure-fire candidate for the inflaton or dark energy, and so an exact physical description remains to be found. But we've got many well-motivated physical ingredients to work with (scalar fields, vacuum energy) that should be relevant to successful descriptions.

12. Oct 15, 2016

### Zypheros_Knight

https://arxiv.org/pdf/1001.4061v1.pdf <------ an article on a method to detect dark energy.