Expansion in general relativity

[oldman]

The general relativistic expansion of the universe over 14-odd billion years has been explained again and again in popularisations, in standard texts and has been the subject of much discussion on this forum. Such expansion is "slow", meaning that to us it is quite imperceptible. We find it analagous to the "ordinary expansion" of a heated rod, where the (proper) separation of component atoms increases slowly with time. Folk often liken the universe's expansion to the blowing up of a balloon with pennies stuck to it. All this familiarity may make such expansion seem well understood.

But consider instead a more extreme situation where general relativistic expansion is "fast", as in the inflationary episode. Here the proper separation of elements of mass/energy increases extremely rapidly. Their "proper separation velocities" are very large. And indeed (because this is an exponential process) so are their "proper separation accelerations". But in general relativity one does not talk of forces, and Newton's second law relating force to acceleration doesn't apply on a "global" scale.

Instead, under these circumstances, we are told that all change --- that must include separation, velocity and acceleration --- is driven by "the inflaton potential" and how steeply this potential varies with "the inflaton field".

This invention seems to me very like "the gravitational potential" and how steeply this potential varies with "the gravitational field"; more familiar factors that control the "ordinary" expansion of the universe.

Do cosmologists just accept the inflaton and gravitational fields as given mysteries of nature? Or do they have a deeper level of understanding of these things?

 

[Jorrie]

The general relativistic expansion … is "slow", meaning that to us it is quite imperceptible. We find it analagous to the "ordinary expansion" of a heated rod, where the (proper) separation of component atoms increases slowly with time.

I don’t understand your ‘slow expansion’. On cosmic scales, the expansion is super-fast and not imperceptible. On a local scale, there is no expansion – things are generally gravitationally bound.

But consider instead a more extreme situation where general relativistic expansion is "fast", as in the inflationary episode. Here the proper separation of elements of mass/energy increases extremely rapidly. Their "proper separation velocities" are very large. And indeed (because this is an exponential process) so are their "proper separation accelerations". But in general relativity one does not talk of forces, and Newton's second law relating force to acceleration doesn't apply on a "global" scale.

Instead, under these circumstances, we are told that all change --- that must include separation, velocity and acceleration --- is driven by "the inflaton potential" and how steeply this potential varies with "the inflaton field".

This invention seems to me very like "the gravitational potential" and how steeply this potential varies with "the gravitational field"; more familiar factors that control the "ordinary" expansion of the universe.

The inflaton field should be very unlike a gravitational field, because it is thought to create anti-gravity. How it works, I think nobody knows… I recall that it has been said that “inflation is a scenario, not quite a theory or hypothesis”.

 

[oldman]

I don’t understand your ‘slow expansion’. On cosmic scales, the expansion is super-fast and not imperceptible. On a local scale, there is no expansion – things are generally gravitationally bound.

The expansion of the Hubble flow, with H = 70 Km/sec per Mpc, corresponds to a strain (change in length per unit length) of about 2 x10 ^ -18 per second. If that ain't slow, what is?

The inflaton field should be very unlike a gravitational field, because it is thought to create anti-gravity.

I was very tentatively implying that may be they aren't that different, except in sign -- i.e. that the anti-gravity of inflation is gravity reversed.

How it works, I think nobody knows…

I agree. All we know is that (at a Newtonian level) masses attract but don't repel, and that (at a GR level) mass/energy distorts spacetime so that geodesics converge. But we don't know exactly how mass/energy accomplishes either feat. Hence gravity remains a given mystery.

 

[SpaceTiger]

Do cosmologists just accept the inflaton and gravitational fields as given mysteries of nature? Or do they have a deeper level of understanding of these things?

Well, you should ask the GR crowd for a deeper understanding of the concept of a "gravitational field" in modern physics, but gravitation is generally framed in terms of a metric. This gives the geometry of spacetime, which is shaped by the matter and energy contained within. This matter and energy then moves in response to the local geometry.

Loosely, I suppose you can think of the geometry of spacetime as the "gravitational field", but in GR it is quite distinct from the "inflaton field" (or any other quantum field). The inflaton field is a (theoretical) scalar field that is just another energy component to the universe, like light or matter. As with any energy component of the universe, it can shape the metric and change the rate of expansion of the universe. Unlike radiation or matter, however, the inflaton field can have a negative pressure and can therefore cause the expansion of the universe to accelerate. A period of accelerated expansion provides a relatively simple means of solving the horizon, flatness, and monopole problems in cosmology.

 

[Jorrie]

The expansion of the Hubble flow, with H = 70 Km/sec per Mpc, corresponds to a strain (change in length per unit length) of about 2 x10 ^ -18 per second. If that ain't slow, what is?

Interesting! Now the question is, do we say that gravitationally bound structures do not expand with the Hubble flow, or is that expansion just imperceptible?

If we think of the Sun's orbit around the Galactic center, at a radius of about 30 x 10^3 ly, it will be an expansion of the order 10^-4 ly/century (if my sums are right on a Saturday night!). Now that's definitely not measurable by us humans!

 

[marcus]

Do cosmologists just accept the inflaton and gravitational fields as given mysteries of nature? Or do they have a deeper level of understanding of these things?

SpaceT is right that you should ask fundamental physics researchers about that.
Basically the cosmologist job is to use established theory like GR (plus if they have to various speculative scenarios) to explain the observations.

No one should ever assume that GR is a finished theory. Evidence is it must emerge from something deeper. It has singularities, it has not yet been quantized, one needs a coherent picture of matter interacting with geometry. maybe matter IS an aspect of geometry.

Several QG researchers have found that inflation comes naturally out of Loop Quantum Cosmology WITHOUT AN INFLATON.
Martin Bojowald has a paper about this.

Ganashyam Date has a paper called something like "Genericness of Inflation in Loop Quantum Cosmology".

Roy Maartens of Portsmouth (a top phenomenologist uncommitted to loop or string or any particular approach) checked it out.

Arxiv has papers about the untuned automaticness of inflation in LQC written by Bojowald, Pamampreet Singh, Maartens, Date and others. You will find their articles if you search Arxiv.org by author name.

that still should not be good enough. the quantum fundamentals of gravity is work in progress.
but cosmologists should not just accept.
indeed cosmological data is being used to CHECK QG MODELS.
cosmologist and quantum gravitist ultimately have a reciprocal effort to arrive at more basic understanding of spacetime and matter---their fundamental degrees of freedom and how they interact.

 

[DaveC426913]

Interesting! Now the question is, do we say that gravitationally bound structures do not expand with the Hubble flow, or is that expansion just imperceptible?

If we think of the Sun's orbit around the Galactic center, at a radius of about 30 x 10^3 ly, it will be an expansion of the order 10^-4 ly/century (if my sums are right on a Saturday night!). Now that's definitely not measurable by us humans!

I think the general idea is that gravity overwhelms the expansion. A galaxy in an expanding universe will not get any larger - which is what the 'pennies on the balloon' is demonstrating.

 

[Jorrie]

You’re right, but it does not mean that something that is overwhelmed because it is small does not exist! Maybe we do say it is just too small to be noticed?

 

[MeJennifer]

You’re right, but it does not mean that something that is overwhelmed because it is small does not exist! Maybe we do say it is just too small to be noticed?

Wait, I thought the expansion was simply some scalar that applied for all space-time and apparently only the space part, but is it now suggested that gravity overwhelms it for places with large masses?

 

[oldman]

SpaceT is right that you should ask fundamental physics researchers about that.

Yes, I've followed his advice in the Relativity forum and the "GR folk" have satisfied my curiosity: they seem to agree that gravity is indeed a mystery... one of many, I guess.

The guidance you have given to other aspects of gravity is appreciated. I'll pursue these avenues.

 

[Jorrie]

Wait, I thought the expansion was simply some scalar that applied for all space-time and apparently only the space part, but is it now suggested that gravity overwhelms it for places with large masses?

Mmm..., yep, that’s in effect what we say. It’s the difference between large-scale metrics and small-scale metrics (which are both solutions the EFEs, e.g., the FRW metric and the Schwarzschild metric). The cosmological expansion of space is only noticed on large scales, yet it may very well be just a summation of a very large number of infinitesimal expansions!

Maybe both the mentioned solutions are simply 'good enough' approximations of reality? I would really appreciate a guru’s response to this 'maybe'.

 

[hellfire]

Several QG researchers have found that inflation comes naturally out of Loop Quantum Cosmology WITHOUT AN INFLATON.
Martin Bojowald has a paper about this.

I know that you know what you are writing about, but this sounds a bit misguiding. IMHO what Bojowald has shown is that under the assumption LQC is valid it is possible for an inflationary phase to emerge in a sub-Planckian scale. I would make a difference between "inflationary phase" and "inflation". The first one is just a phase of exponential expansion of space. The second one is a theory that implies also an initial mechanism for the process of structure formation. Such a thing is not included in Bojowald's result. But, by the way, the beauty in Bojowald's results is that, contrary to inflation, it does not violate any of the classical energy conditions of general relativity and there is no need for an unobserved scalar field.

 

[marcus]

hellfire,
thanks for the careful review and improvement of what i said.
sometime i will post a few of the Loop Cosmology papers on the natural inflation phase that occurs generically in LQC, in hopes that you will comment in more detail. It's interesting, and could use some more discussion

(not just limited to Bojowald's papers on it, but including them)

I would like to learn your views on it. but since it would be offtopic in this thread, I'll wait for another opportunity.