# Dark energy and expansion vs gravity and spatial contraction

• I
Hi all,

A naive question:

My understanding is that dark energy drives the expansion of space - that is, the distance between two points in space increases over time - with the important note that it is space itself that is expanding.

However, when talking about gravity (where one says that matter warps spacetime), the usual description is that gravity causes masses to move towards one another through space.

My question: if dark energy causes space itself to expand, shouldn't gravity have the opposite effect and cause space to contract, perhaps in addition to having masses move towards each other through space? I realize it would be more correct to talk about spacetime, but I'm wondering primarily about the spatial aspect.

Thanks.

phinds
Gold Member
Hi all,

A naive question:

My understanding is that dark energy drives the expansion of space - that is, the distance between two points in space increases over time - with the important note that it is space itself that is expanding.
That is incorrect. Distances are getting larger but there is nothing physical that is expanding. I recommend the link in my signature.

PeterDonis
Mentor
2020 Award
My understanding is that dark energy drives the expansion of space - that is, the distance between two points in space increases over time - with the important note that it is space itself that is expanding.

This viewpoint has significant limitations. One key one is that "space" is not an invariant--it depends on how you choose your coordinates.

A better way of thinking about what dark energy does, although the term can also be easily misunderstood, is "repulsive gravity". That is, suppose we take two small test objects that are initially at rest relative to each other, and let them move freely, i.e., with no forces acting. If dark energy is present, the two objects will move apart with increasing velocity. Furthermore, if we want to be precise, we can define "move apart with increasing velocity" in an invariant way, by having the two objects send light signals back and forth, and having each object carry a clock that measures the round-trip travel times of the signals. If dark energy is present, those round-trip times will increase, and their rate of increase will itself increase (i.e., "accelerate").

Of course, the dark energy density in our universe is very, very small, so this effect is not measurable on local scales; but on cosmological scales, if we view galaxies as "test objects", dark energy does the same thing to them.

when talking about gravity (where one says that matter warps spacetime), the usual description is that gravity causes masses to move towards one another through space.

Here again, "space" is not an invariant, so this viewpoint has limitations.

A better way of thinking about this is to imagine two test objects, as above, but this time with ordinary matter present instead of dark energy. In this case, the two test objects will move towards each other. And again, we can define "move towards each other" in an invariant way in terms of the round-trip travel times of light signals between the objects decreasing. Thus, ordinary matter causes "attractive gravity".

if dark energy causes space itself to expand, shouldn't gravity have the opposite effect and cause space to contract

The question itself is not well posed, because of the limitations in the term "space". See above.

Also, as you can see from the above, a better term to use instead of "gravity" as you use it here would be "ordinary matter".

QuantumQuest
Thanks to both phinds and PeterDonis for your replies.

I realize that my original post had limitations in terms of the use of 'space'. After reading "The Balloon Analogy", I may be able to phrase this slightly more clearly, but I'm not sure.

My primary question is with respect to gravity, as opposed to dark energy: consider the case of the two test masses moving towards each other under gravitational attraction. In this situation, I had always understood (maybe) that the masses would be moving along trajectories bringing them together, but that this did not involve the 'contraction' of space in between them (I'm being very imprecise here, for which I apologize).

Perhaps, after reading "The Balloon Analogy", I can state things this way - there has to be 'something' in between the two test masses (discussion of philosophy aside) - under gravitational attraction, does space undergo metric contraction? I realize I'm again being vague with the notion of 'space'. Said differently, if the entire universe consisted only of those two test masses with some initial spatial separation, when they 'collided' or reached each other (after some time), could the final configuration be described by a single point in spacetime? I.e., would the spacetime manifold at that time be a point with zero spatial extent? Or, would the manifold still have the original spatial extent (perhaps approximately), with the two masses at a position within that spatial extent?

I'm not sure if that's clear (probably not). Here's one more attempt: if I'm skydiving, once I jump out of the plane, I'm falling along a geodesic in spacetime, where the manifold is approximately fixed (since my mass is so much smaller than that of the Earth) ... I'm getting closer to the surface of the Earth because I'm moving through space(time), and not because the space in between myself and the surface is somehow 'contracting'. Am I completely off base?

PeterDonis
Mentor
2020 Award
consider the case of the two test masses moving towards each other under gravitational attraction. In this situation, I had always understood (maybe) that the masses would be moving along trajectories bringing them together, but that this did not involve the 'contraction' of space in between them

Again, it depends on your choice of coordinates, because there is no such thing as "space" in any invariant sense.

Part of the problem here is that our ordinary intuitions are used to a static spacetime. "Static" means roughly this: that the spacetime has a "natural" set of coordinates on it in which "space" does not change with time. For example, if we consider an isolated gravitating body like the Earth, and ignore the effects of all other gravitating bodies, then we can consider spacetime to be static, and we can choose coordinates in which space does not change with time. That allows us to view bodies that are in free fall, feeling no force, as "moving" under the "gravitational attraction" of the Earth alone, without having to worry about space itself changing.

However, it turns out that the scenarios in which we can view spacetime as static are extremely limited. In the case of two masses moving under each other's mutual gravitational attraction, we can consider them as an isolated system to a fairly good approximation, and treat spacetime as static with respect to the center of mass of the system (i.e., of the two masses combined). Then we can treat the motion of each individual mass similar to the way we treat the motion of objects in Earth's gravitational field. But this is only an approximation. Strictly speaking, it's also an approximation in the case of the Earth, but it's a much better one in that case, at least for objects close to the Earth. In the case of two bodies that both have significant masses, there will be additional effects involved that make the spacetime non-static over long enough periods--for example, the emission of gravitational waves by binary pulsar systems.

In the case of the universe as a whole, we can't view spacetime as static, even as an approximation. There are no coordinates we can choose for the universe as a whole in which "space" is not changing with time. So we have no alternative but to include "space expansion" in our model. In other words, the universe as a whole is simply a different kind of spacetime from the kind we're used to, and we just have to deal with that fact.

Imager