Why do cosmologists say that gravity should "slow down" the expansion of the universe?

Submitted by crazunggoy47 t3_11fkfeq in askscience

As I understand it (with my PhD in astronomy, but not in cosmology specifically), cosmic expansion means that space-time itself is expanding. I get the whole "inflating balloon" analogy. OK.

I read things about how if the universe has > critical density then it will collapse (again). Or even if it's subcritical, then it should at least be slowing down in its expansion (were it not for dark energy driving faster expansion, that is).

The explanation I typically see for an expected slowing of the expansion is that gravity is an attractive force — it should pull stuff back together. Most explanations I read tend to end there.

But why would you expect gravity to arrest the expansion of the universe in the first place? The expansion is not a conventional explosion away from a center. It's not the case that other galaxies are flying away with some kinetic energy that is being transformed in to gravitational potential energy. Rather, expansion is an isotropic inflation, where everything gets further away from everything else as space-time expands.

If a particular galaxy were to get pulled by gravity in a way that would cause the universe to "slow down" its expansion, then would direction would that be? There is no center of the universe. The gravitational forces acting on any galaxy should be (on average) isotropic (but for some clusters and large-scale structure, but I don't think that's relevant to this question).

TL;DR — The statement "gravity [should] slow the universe's expansion" appears fallacious to me, and yet I see it everywhere*. What I am misunderstanding?

* by everywhere I mean, e.g., Forbes, Scientific American, Harvard, many others. Ctrl-F for "gravity" in these articles.

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nivlark t1_jak3izy wrote

Locally, the expansion of the universe still obeys the first law of thermodynamics: considering a fixed proper volume of space, expansion acts to dilute the energy density within that volume, doing work in the process.

The energy to do this "comes from" the expansion, which means it slows down over time in the situation where there are attractive forces (i.e. gravity) associated with the energy density. Conversely the present-day universe has its energy density dominated by dark energy, which behaves as a repulsive force which ads energy to the expansion, accelerating it.

For a rigorous derivation of this behaviour your best bet is to get an introductory cosmology textbook and look into the Friedmann equations.

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DocJanItor t1_jam805g wrote

That answer seems kinda counterintuititive to me considering that the universe is larger than the equivalent size it should be for its age and the speed of light. Thus, the expansion of the universe has obviously gone faster than light and has broken a major physical limitation of the universe itself. Why would we expect that expansion follow other in universe laws?

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nivlark t1_jamd3iu wrote

Sufficiently distant objects have apparent recession velocities greater than the speed of light, but this doesn't break any physical laws. Special relativity says that velocity measured in an inertial frame will never exceed the speed of light, but cosmologically distant galaxies are not inertial from our perspective.

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ableman t1_jammpqd wrote

> Special relativity says that velocity measured in an inertial frame will never exceed the speed of light, but cosmologically distant galaxies are not inertial from our perspective.

We are in an inertial reference frame, so we are measuring from an inertial reference frame, it shouldn't matter what frame they're in, SR works just fine on accelerating objects, as long as the observer is inertial. If you meant to say we're not in an inertial reference frame, it's a very poor explanation, because that's just a No True Scotsman fallacy, but also just seems wrong? The whole point of inertial reference frames is that you can tell whether you're on one or not with a local experiment.

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nivlark t1_jaogkfl wrote

Our reference frame is only locally inertial, where "local" means "close enough that the global geometry of spacetime can be ignored". In special relativity spacetime is flat everywhere and there is no such distinction, but in GR the same is not generally true.

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zutnoq t1_janifi1 wrote

Indeed, the inertial-ness of a reference frame is only a local property (local here meaning infinitesimal displacements).

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Aseyhe t1_jamocwu wrote

Repeating a response I made to a similar question elsewhere in the thread:

Relative velocities of distant objects aren't well defined in curved spacetimes. It's often said that distant objects are receding faster than light, and there are standard ways of writing down their distance such that the distance grows faster than the speed of light. However, there is no relativistically meaningful sense in which these objects are moving faster than light in relation to us. Also, the distance isn't uniquely defined either.

In intuitive terms, the relative velocity is the angle between two vectors in spacetime. Imagine drawing two arrows on a sheet. If those arrows are in the same place, you can measure the angle between them. If they are in different places, but the sheet is flat, you can also define the angle between them uniquely. However, if they are in different places and the sheet is not flat, the angle between the arrows is not uniquely defined.

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DocJanItor t1_jan4djg wrote

Doesn't matter about their current velocities. The universe is 14B years old. It's bigger than 28B light years wide. Therefore the universe had to expand faster than the speed of light.

Further, light goes through the universe. The universe expands outside of itself into who knows what. We have no idea if the speed of light applies outside of the universe. Same for thermodynamics.

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Ape_Togetha_Strong t1_jan9j7f wrote

It sounds like you're imagining "expansion" to be some outward expansion from a point in space, rather than spacetime expanding everywhere. There's no reason to tie the age of the universe to its size (other than just how its size changes proportionally, relative to itself with time). It could have been any size prior to inflation. The fact that the observable universe is larger in lightyears than the age of the universe in years is not surprising or particularly meaningful.

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Possible-Quail-7376 t1_jb1bhnu wrote

allright but the universe as we know it might be one string, layer of whatever. looking at the big picture, anything goes really. assuming the universe is same shape as the rest of stuff (toroidal) doing same stuff as atoms, quantum particles and stuff like that on what knows dimensions..

well, i guess we live in positive side of universe since stuff seems to expand. One string in a field. perhaps that is the part what scientists would call the universe part.

to be continued...

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Hudimir t1_jango8k wrote

What you said about dark energy acting as a repulsive source, I am now confused how so.e scientist recently came to the conlusion that black could be sources of dark energy. Especially because afaik black holes are incredibly dense objects made form "normal" matter that collapsed due to their gravity. Here dark energy being a repulsive force doesnt make sense to me if all we can observe is the incredibly powerful gravitational waves of black holes.

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summitrow t1_jao6p2q wrote

Dark energy and black holes are separate. Black holes are objects that are black because their gravity well is so strong that light cannot escape them. Dark energy is a force that pervades all of spacetime. We measure how much dark energy there is by the red shift of galaxies outside of our local group, and other standard candles like class 1a supernova and Cepheid variable stars. Is there a dark energy particle? Is it a fundamental force like the strong force in an atom? We don't know. So far we can just measure its impact on the expansion of the universe.

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Hudimir t1_jao97us wrote

Correct me if i misunderstood. So in that article where they say black holes might be the source of dark energy they say so, because they measured/observed more dark energy impact around those black holes? Also fyi i am currently studying undergrad physics so the very basics(e.g. black holes are black because light cannot escape them) I think, I understand, so you can complicate more if you have the knowledge.

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VegaGraviton t1_jaok1al wrote

I had a brief reread of the articles discussing the theory. Bear in mind that my personal background is in Cosmic Inflation and so I'm not intimately familiar with this theory. From what I gleamed Einsteins Equations can predict an object that is essentially a concentrated bundle of Vacuum Energy, which is a commonly theorised candidate for Dark Energy. This object would look and act like a Black Hole to outside observers. Therefore, any Black Hole that we observe could in fact be a source of Dark Energy, and we wouldn't be able to tell with our current understanding of the model.

Essentially its a mathematical model that has been proposed, rather than any new observations.

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summitrow t1_japc8y4 wrote

Yes light cannot escape them, which is because of the incredibly strong gravity well of a black hole.

The very recent articles on black holes and dark energy are very speculative.

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everythingist t1_jak455w wrote

Long answer is long but here's a way to think about it that is physically accurate and not oversimplified as far as I know (I took general relativity 15 years ago so things get fuzzy and I could be forgetting a relevant detail or two)

A dark energy dominated (ie accelerating expansion) universe will have negatively curved spacetime at very large scales. The gravitational effect of regular mass (baryonic and dark both) is to generate local positive curvature of spacetime, which causes the geodesics of nearby objects to bend toward the mass aka falling inward. If you have a large amount of mass sprinkled throughout the universe, the positive curvature generated by that mass will partially offset the negative curvature effect caused by dark energy, slowing expansion.

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etherified t1_jal6iga wrote

Total layman jumping in here, but in the past I've wondered why the expanding space factor doesn't need to be included in calculating local mass-mass interactions. Even though the expansion is something exceedingly small (like 60 km/3 million light years every second or so?), it seemed that it should be included for precision in calculating how masses will move with respect to each other.

The typical answer (summarized) is that "local mass interaction totally overcomes spatial expansion, so only the gravitional effect exists in local systems", but it still seems that there would still have to be some accounting that some of the gravitional "pull" is having to be "used up" to counteract the expansion.

Your explanation above appears to make this even more necessary, since if we think of the expansion as negative curvature (which is in fact really the case), then even local space is, however minutely, curved in a negative way due to expansion. Therefore, any positive curvature of space is being exerted on that already negatively curved background, and hence the positive curvature of space would necessarily have to be minus whatever that negative curvature was (however miniscule).

Unless I should have been interpreting the typical answer to mean "local mass-mass interactions are of course affected by the expansion of space, but the local mass interaction is simply so large with respect to local spatial expansion, that the local effect of spatial expansion, while not zero, can be ignored for calculations". Or something to that effect.

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Aseyhe t1_jalhw7a wrote

> The typical answer (summarized) is that "local mass interaction totally overcomes spatial expansion, so only the gravitional effect exists in local systems", but it still seems that there would still have to be some accounting that some of the gravitional "pull" is having to be "used up" to counteract the expansion.

This is indeed the typical answer but it's not correct. Expansion of space doesn't affect particle dynamics at all. It's just a mathematical convention.

See for example this entry of the askscience FAQ

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FatSilverFox t1_jal7nh6 wrote

Alright I have no idea about anything, but I read your post and my first thought was “good question, but wouldn’t local interactions be identically impacted by expansion, thus negating expansion as a variable?” In other words: would it not be a constant applied to both masses?

Unless the local bodies are 2 different galaxies, in which case now I want to know too.

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BentonD_Struckcheon t1_jakhyfp wrote

Yeah I haven't thought much about this since college but I do remember curved geometries being introduced and the idea that the issue with whether or not the universe would eventually collapse in on itself was a function of which way the universe was curved.

Probably not remembering it right, but your comment jogged my memory.

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Aseyhe t1_jaliccb wrote

That's a bit different because that idea refers to the curvature of space, not spacetime. Space is a 3D surface in 4D spacetime. There are lots of possible choices of spatial surface, but there is a unique choice that makes the universe homogeneous (statistically the same everywhere on the surface). The curvature of this particular choice of spatial surface can indeed inform us as to whether the universe will eventually collapse.

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mfb- t1_jak8qrn wrote

It's a direct consequence of general relativity. The same equations that tell you how orbits around the Sun work also predict that matter slows down the expansion of the universe. Applied to cosmology you get the Friedmann equations.

It's interesting that Newtonian physics predicts the same thing here if you use a finite mass distribution and then consider the limit to infinite size, but that's not how it was derived of course.

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ferrdek t1_jar0rcj wrote

> matter slows down the expansion of the universe

I can't understand it. If large masses like stars etc cause stretching of space, why not assume that galaxies, clusters and filaments also stretch space between them, which would cause the expansion of the universe? Process of transforming energy into matter would fuel that expansion of space on a large scale.

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mfb- t1_jar92k5 wrote

> If large masses like stars etc cause stretching of space

That's a popular science analogy. Don't use it literally.

Every mass contributes to a slowing of the expansion, doesn't matter if we consider a proton, a star or a galaxy.

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ferrdek t1_jarayvg wrote

>That's a popular science analogy. Don't use it literally.

um, so what does it really means when scientists say that gravity warps the spacetime

>Albert Einstein proposed that massive objects warp and curve theuniverse, resulting in other objects moving on or orbiting along thosecurves—and that this is what we experience as gravity

https://www.science.org.au/curious/space-time/gravity

edit: what I'm saying if the bending of space we experience as gravity, we can experience simultaneous stretching of space as expansion

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mfb- t1_jarqhow wrote

It means spacetime is no longer the simple Minkowski space of special relativity. "Warped" does not mean "expanding". It's more of a local deformation.

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ferrdek t1_jarv0ep wrote

>"Warped" does not mean "expanding". It's more of a local deformation

Lets assume we have some point in space and we travel through it twice. First time the space is empty and the second time some massive object appear on our path (for instance a star) and we travel close to it, going through space warped by its gravity.

is the time needed to travel from point A to point B in warped space longer than time needed to travel that distance through unwarped space? Or the opposite? Or there is no difference?

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mfb- t1_jas94ee wrote

That depends on where A and B are and what your trajectory is in the case with the star.

> Lets assume we have some point in space and we travel through it twice.

If you consider travel from A to B then looking at a single point isn't sufficient.

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ferrdek t1_jasif3h wrote

>That depends on where A and B are and what your trajectory is in the case with the star

The star is located between A and B the trajectory goes through gravitational field of the star. Through space "warped" by the star.

By "point" I mean region of space. English is not my first language, sorry for misunderstandings

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Aseyhe t1_jaka1l0 wrote

Cosmic expansion really does just mean that things are moving apart in a uniform way. There is nothing fundamentally physical about the idea that space itself is expanding; that's just a mathematical convention that is convenient in some contexts. (It's a coordinate choice.)

Thus, the gravitational attraction of the matter in the universe slows the expansion precisely as it would slow the expansion of a distribution of matter inside the universe. Indeed, Newtonian gravity predicts exactly the correct expansion dynamics for a matter-dominated universe. Similarly, the gravitational repulsion of the dark energy accelerates the expansion (although there is some subtlety to this).

Further reading on expanding space not being a physically real phenomenon:

Further reading on cosmological dynamics with Newtonian gravity:

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Resaren t1_jam94cw wrote

This is the answer I’ve been looking for after years of having this concept explained only with vague references to expanding balloons, or allusions to the expansion of space being some sort of intrinsic property. Thank you! This quagmire of a concept reminds me a lot of the confusion around ”relativistic mass”, which has thankfully fallen out of usage.

A follow up question to this, does this mean there is some unique Center Of Momentum frame, or is this precluded by SR? And how is this related to the CMBR rest frame?

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Aseyhe t1_jamb3p2 wrote

The CMB rest frame is the frame of a comoving observer, that is, one who is at rest with respect to their (cosmologically) immediate surroundings. At different locations, the CMB rest frames are different. There's no global "center of momentum frame" if the universe is homogeneous, only local ones.

(I should also note that in curved spacetimes, reference frames only make sense locally. However, this is more minor consideration, in a certain technical sense. While the impact of the difference in the velocities of different comoving observers scales linearly with their separation, the impact of curvature scales as the square of the separation. So the latter only becomes important at very large separations.)

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dphseven t1_jakrf04 wrote

This blows my mind a bit, thanks to the steady diet of documentaries I've had for years.

If I'm reading Diatribe correctly, there would be no "big rip" scenario because local gravity would overcome large scale expansion. And there are lots of similar implications... Am I getting that right?

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Aseyhe t1_jalbzp5 wrote

Not quite because as I noted, dark energy supplies gravitational repulsion. In the big rip, the energy density of dark energy increases over time, and so does the repulsive force. That is what rips everything apart.

(Observations currently do not support that the energy density of dark energy is increasing.)

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theotherquantumjim t1_jamo41v wrote

Recent study suggests otherwise doesn’t it? Yet to be confirmed independently I guess, but hasn’t it very recently been posited (maybe also evidenced) that black holes are driving expansion by returning energy to the quantum vacuum? Does this not mean expansion would indeed be physical?

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Aseyhe t1_jampj7l wrote

Indeed, that's one reason to be highly skeptical of that study. The "cosmological coupling" doesn't make sense in the context of general relativity. The global scale factor is not locally even a thing. In certain cosmological spacetimes, the scale factor isn't even uniquely defined globally.

The authors motivate the cosmological coupling by citing the behavior of black holes placed in otherwise homogeneous universes. Such black holes grow over time, but they grow by accreting the surrounding fluids (which are present due to the assumption of homogeneity), not by magically eating the scale factor, as the authors seem to suggest.

The only interpretation of the black-holes-as-dark energy idea that might make sense relativistically is that black holes have a negative-pressure coupling to other black holes. Then as the black holes separate from each other due to cosmic expansion, the negative pressure feeds them mass. This achieves the same outcome without positing a magical coupling to the global expansion factor.

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Any-Broccoli-3911 t1_jak0o38 wrote

The expansion of the universe is proportional to t^(2/3) in a matter dominated universe and t^(1/2) in a radiation dominated universe. Both have power less than 1, so the universe is decelerating.

In a dark energy dominated universe, the expansion is proportional to e^t, so it's exponentially growing, and exponentially accelerating.

https://en.m.wikipedia.org/wiki/Friedmann_equations

In the current universe (which is mostly dark energy, but has still a lot of matter), it's slowly accelerating.

Those equations come from general relativity and are harder to understand and follow though.

To understand the principle, it's best to think of the universe from an observer point of view with newtonian gravity.

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Any-Broccoli-3911 t1_jajtiak wrote

The expansion of the universe is kinetic energy. The matter is going farther from you (the observer) at a given observed speed and you can compute an energy for that, that's an accurate measure of the kinetic energy. Father things go faster, so they have more energy. Also, the observed speed is always less than the speed of light, so everything has a finite energy.

All the mass between you and a far object cause a gravitational pull towards you which slows down objects. The mass distribution is approximately spherical, so all the mass that is farther than a object gets its gravitational pull on that object canceled.

Things get more complicated when you consider général relativity, and a constant energy that doesn't get diluted by the expansion (cosmological constant, dark energy or vacuum energy) accelerate the expansion of the universe rather than slowing down.

However, for the effect of ordinary matter, Newtonian gravity works fine to explain why it makes the expansion decelerate. General relativity agrees with it.

All observers see themselves in the center, and agree that galaxies decelerate (if only ordinary matter is involved) which correspond to the deceleration of the expansion. It doesn't need a center in the comoving coordinates (the coordinates in which there's no center and no specific observer) to get the same result.

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crazunggoy47 OP t1_jajwm2d wrote

>The expansion of the universe is kinetic energy. [...] Also, the observed speed is always less than the speed of light, so everything has a finite energy.

Is that true? I thought that for distant galaxies, the recessional speed was often greater than c, since c is only a local speed limit, and does not apply to space time inflation.

Consider the rapid inflation of the universe, which went from electron-sized to golf-ball sized in 10–35 seconds; applying a naïve speed calculation would yield speed = distance / time = 43 mm / 10^(–35) seconds >>>>>> 3 x 10^(–8) m/s.

This is all to say, I'm mostly questioning whether the perceived recessional velocity can really correspond to kinetic energy.

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Aseyhe t1_jakbf7x wrote

Relative velocities of distant objects aren't well defined in curved spacetimes. It's often said that distant objects are receding faster than light, and there are standard ways of writing down their distance such that the distance grows faster than the speed of light. However, there is no relativistically meaningful sense in which these objects are moving faster than light in relation to us. Also, the distance isn't uniquely defined either.

In intuitive terms, the relative velocity is the angle between two vectors in spacetime. Imagine drawing two arrows on a sheet. If those arrows are in the same place, you can measure the angle between them. If they are in different places, but the sheet is flat, you can also define the angle between them uniquely. However, if they are in different places and the sheet is not flat, the angle between the arrows is not uniquely defined.

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Any-Broccoli-3911 t1_jajx0tj wrote

The observed speed is always less than c.

The comoving speed is not limited. If you consider ont special relativity, it's equal to gamma*v so as v goes towards c, the comoving speed goes to infinity. Even with general relativity, it's still true that the comoving speed goes to infinity as the observed speed goes to c.

gamma is the Lorentz factor 1/sqrt(1-v2/c2)

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crazunggoy47 OP t1_jajyba4 wrote

Hmm. So if I understand you correctly, you're saying that an object that's moving away from us due to cosmic expansion has a finite kinetic energy (relative to us). So, from our perspective we should "expect" that kinetic energy to be falling, as our own gravity pulls them back in.

And then that galaxy, will also see the exact same thing. From its perspective every other galaxy is fleeing *it*. And if every galaxy sees this, and it just so happens that every trajectory has too little KE, then every galaxy would see the other galaxies crashing down on them.

Is that right?

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Any-Broccoli-3911 t1_jajymds wrote

Yes, though the galaxies that are outside the local group have enough energy not to crash into us even if we don't consider dark energy which will push them away even faster. Without dark energy, they would decelerate relative to us, but still always going away.

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Inside_Olive5504 t1_japjy77 wrote

This is a nice Newtonian explanation, but I've always felt that there is more subtly than it acknowledges. It relies on Gauss' law applied to a frame centered on us, but why is that the correct frame? An argument can be made that gravity exerts no net force, just using Newton's law and symmetry.

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Any-Broccoli-3911 t1_japkex4 wrote

All inertial frames are correct in special relativity. Special relativity works well in this case.

Though we aren't perfectly inertial due to the acceleration of the sun and the galaxy, it's still close enough. Those accelerations are relatively small.

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Inside_Olive5504 t1_japr7ao wrote

You make an interesting point. I believe (possibly wrongly) that you are saying that one should only consider mass that is within the local Hubble volume to compute the force on test galaxies, in which case we are at the gravitational center of the frame (because it truly is a finite sphere centered on us). One should not compute the force from the test galaxy's frame, since it is non-inertial to us. I think I can buy that argument. To me, it hinges on the finiteness of the Hubble volume and the speed of gravity. If the universe is infinite and if Newtonian gravity acted instantly, I think one could still argue that the test galaxy would feel no gravitational force, even in our inertial frame.

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Aseyhe t1_jaqbsge wrote

> An argument can be made that gravity exerts no net force, just using Newton's law and symmetry.

That's what Newton believed, but a more careful look reveals that the integral over all space that determines the gravitational force does not converge to a well defined value. See for example the dynamics of Newtonian cosmology.

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Inside_Olive5504 t1_jaqjuco wrote

Thanks, I appreciate the response. I like the discussion of convergence and the care to consider the shape of the volume in the limit of infinite size.

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awawe t1_jamdsb2 wrote

Complete layman, so take this with a grain of salt, but isn't the relativistic view of gravity that it bends space-time? So when you're in free fall you appear to be accelerating with respect to the ground, but you're actually in an innersial reference frame, while the ground is accelerating upwards through ever contacting space.

If gravity contacts space, then of course it will counteract the expansion of space.

You seem to be thinking relativistically about the expansion of the universe, but Newtonianly about gravity.

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