Metric expansion misunderstanding

[Lanniakea]

Here is the second paragraph from the article on metric expansion of space from Wikipedia

Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the FLRW metric, and is a generic property of the Universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above). At smaller scales matter has become bound together under the influence ofgravitational attraction and such things do not expand at the metric expansion rate as the Universe ages. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the Universe given the matter density and average expansion rate.

1.Why is the model only valid on large scales?

This is worded in a way to suggest that gravity somehow influences expansion. My understanding is that the 'coordinate system' expands and gravity is irrelevant? So if two particles stay bound or are separated is only dependent on whether the force between them overcomes this expansion or not. Is it not the case that the expansion continues equally everywhere (so even between two atoms in my arm), but gravitationally bound objects are in this perpetual 'tug of war' with expansion?

 

[Loren]

Here is the second paragraph from the article on metric expansion of space from Wikipedia

Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the FLRW metric, and is a generic property of the Universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above). At smaller scales matter has become bound together under the influence ofgravitational attraction and such things do not expand at the metric expansion rate as the Universe ages. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the Universe given the matter density and average expansion rate.

1.Why is the model only valid on large scales?

This is worded in a way to suggest that gravity somehow influences expansion. My understanding is that the 'coordinate system' expands and gravity is irrelevant? So if two particles stay bound or are separated is only dependent on whether the force between them overcomes this expansion or not. Is it not the case that the expansion continues equally everywhere (so even between two atoms in my arm), but gravitationally bound objects are in this perpetual 'tug of war' with expansion?

It's not valid on only large scales. Gravity's effect is of a higher magnitude than the forces that cause the expansion of space as space is not gravitationally bound.

While space is expanding, it is not impacting the size of our galaxy because the collective effect of gravity maintains the system at its current size. Space is still expanding.

The same holds true with your body. You are not expanding because the chemical and atomic bonds are too strong. Well, you might be expanding if there is an imbalance in your caloric intake versus calories burned, but that's a different process altogether.

 

[phinds]

1.Why is the model only valid on large scales

I think of it this way. Dark Energy inside a galaxy is like an ant pushing on a house. It's not that the any just has a really small effect, it's that he has no effect at all. He just isn't pushing hard enough to shift the house on its foundations.

 

[Lanniakea]

It's not valid on only large scales. Gravity's effect is of a higher magnitude than the forces that cause the expansion of space as space is not gravitationally bound.

While space is expanding, it is not impacting the size of our galaxy because the collective effect of gravity maintains the system at its current size. Space is still expanding.

The same holds true with your body. You are not expanding because the chemical and atomic bonds are too strong. Well, you might be expanding if there is an imbalance in your caloric intake versus calories burned, but that's a different process altogether.

So my understanding is correct - the wiki article is misleading then! How dare you call me fat!

Since we're roughly in this topic, allow me another semi-related question. The fundamental source for gravity is ultimately energy correct? When we say 'mass' we mean the magnitude of four-momentum vector of which energy and momentum are components of. So is it possible that the energy that is responsible for the metric expansion of space (what we call dark energy) is also creating some sort of gravitational effect? Or am I being confused here?

 

[bapowell]

The fundamental source for gravity is ultimately energy correct? When we say 'mass' we mean the magnitude of four-momentum vector of which energy and momentum are components of. So is it possible that the energy that is responsible for the metric expansion of space (what we call dark energy) is also creating some sort of gravitational effect? Or am I being confused here?

The source of gravity in Einstein's Equations is the stress-energy tensor $T_{\mu \nu}$; it includes the energy density ($T_{00}$), momentum ($T_{0i}$), pressure ($T_{ii}$), and shear stress ($T_{ij}$, $i\neq j$).

Wouldn't you consider the metric expansion of space a "gravitational effect"? You put the stress-energy on the RHS of Einstein's Equations and the LHS gives you the geometry, which includes the expansion of space in cosmological settings.

 

[Geofleur]

The same holds true with your body. You are not expanding because the chemical and atomic bonds are too strong.

Is the metric expansion then analogous to what happens in a spaceship that is falling freely toward a planet, except in reverse? Two objects placed far apart in the spaceship will start to converge as they both head toward the center of the planet. But the passengers of the ship will not shrink because of the mutual repulsion among the atomic constituents of their bodies.

 

[Lanniakea]

The source of gravity in Einstein's Equations is the stress-energy tensor $T_{\mu \nu}$; it includes the energy density ($T_{00}$), momentum ($T_{0i}$), pressure ($T_{ii}$), and shear stress ($T_{ij}$, $i\neq j$).

Wouldn't you consider the metric expansion of space a "gravitational effect"? You put the stress-energy on the RHS of Einstein's Equations and the LHS gives you the geometry, which includes the expansion of space in cosmological settings.

Hmm! I think of gravitational effects as deformations of space-time. So all objects follow geodesics in this deformed space-time, whereas the expansion of space I perceive as the literal expansion of space-time, or the coordinate system that defines it. Am i correct in thinking this? Is there some sort of difference in the way this energy manifests itself? Does this imply that dark energy is in some sense 'negative'? Or that dark energy and say particles are deforming the geometry of spacetime in the same way, except that the metric expansion is happening to the whole space, whereas the particle's deformation is sort of localized?

 

[Geofleur]

The situation I was describing could happen even with a static metric. I was just trying to relate the discussion to something I think I already understand...

 

[bapowell]

Hmm! I think of gravitational effects as deformations of space-time. So all objects follow geodesics in this deformed space-time, whereas the expansion of space I perceive as the literal expansion of space-time, or the coordinate system that defines it. Am i correct in thinking this? Is there some sort of difference in the way this energy manifests itself? Does this imply that dark energy is in some sense 'negative'? Or that dark energy and say particles are deforming the geometry of spacetime in the same way, except that the metric expansion is happening to the whole space, whereas the particle's deformation is sort of localized?

You can view spatial expansion as a "curvature" of space-time, just like you would view spatial deformation as curvature of space. From the perspective of the 4D space-time, both expansion and spatial curvature are manifestation of space-time curvature and are, hence, gravitational effects broadly speaking.

 

[Lanniakea]

You can view spatial expansion as a "curvature" of space-time, just like you would view spatial deformation as curvature of space. From the perspective of the 4D space-time, both expansion and spatial curvature are manifestation of space-time curvature and are, hence, gravitational effects broadly speaking.

This is absolutely blowing my mind right now. I have at least 6 million questions. I always thought of gravitational effects and metric expansion as something exclusive, or at least not directly related.

What determines if energy will contribute towards 'expanding' or 'deforming' space? At least to me these two seem to be very different ways of affecting space. Where the former seems to be global and weak on small scales and the latter localized and strong on small scales?

I'm struggling to visualize how curvature can translate into expansion, you wrote:
"You can view spatial expansion as a "curvature" of space-time, just like you would view spatial deformation as curvature of space."
I guess those are the key terms? So a curvature of a hypothetical 3D spacetime could be seen as expansion in 2D space? Is this possible to visualize?

Woww my brain is on meltdown right now, thanks!

 

[bapowell]

What determines if energy will contribute towards 'expanding' or 'deforming' space? At least to me these two seem to be very different ways of affecting space. Where the former seems to be global and weak on small scales and the latter localized and strong on small scales?

It mostly depends on the symmetries of the energy distribution. A uniform energy density leads to homogeneous cosmological expansion/contraction: it is known as the Friedmann cosmology and is described by the Friedmann Equations (which one derives from the Einstein Equations for the case of a uniform energy density). Meanwhile, static, spherically symmetric energy density distributions give you the Schwarzschild black hole solution. But in between these special cases are all manner of inhomogeneous, non-symmetric, rotating, flailing, pulsing objects and distributions that lead to correspondingly interesting spactime geometries.

I'm struggling to visualize how curvature can translate into expansion, you wrote:
"You can view spatial expansion as a "curvature" of space-time, just like you would view spatial deformation as curvature of space."

This is because the spacetime manifold of general relativity is 4-dimensional, with one of the dimensions corresponding to time. But as a geometry, we can still talk about curvatures and other features of the 4D manifold just as we would a manifold in any other dimension, like the more familiar 3D space. There are mathematical descriptions of curvature (the Riemann curvature tensor, Ricci curvature tensor, and scalar curvature are the three common mathematical measures of curvature) that in the 4D universe are nonzero even in the case of flat 3D space; in other words, a flat space (zero 3D curvature) that is expanding has a nonvanishing 4D curvature.

 

[Jonathan Scott]

Here's a paper I found interesting: "A diatribe on expanding space" by J.A.Peacock: http://arxiv.org/abs/0809.4573

Also see Sean Carroll's blog entry "Does Space Expand?": http://www.preposterousuniverse.com/blog/2008/10/06/does-space-expand/

I've also found a particular simple conceptual model interesting, which is a universe in the shape of a paper cone, where the distance from the apex is time and circles around the cone represent space (one-dimensional) at a given point in time. On that model, anything small sees space as flat, and parallel lines remain parallel without experiencing any forces (imagine the wheel tracks of a toy car driving down the cone), but new space is being created everywhere with time.

 

[wolram]

Here's a paper I found interesting: "A diatribe on expanding space" by J.A.Peacock: http://arxiv.org/abs/0809.4573

Also see Sean Carroll's blog entry "Does Space Expand?": http://www.preposterousuniverse.com/blog/2008/10/06/does-space-expand/

I've also found a particular simple conceptual model interesting, which is a universe in the shape of a paper cone, where the distance from the apex is time and circles around the cone represent space (one-dimensional) at a given point in time. On that model, anything small sees space as flat, and parallel lines remain parallel without experiencing any forces (imagine the wheel tracks of a toy car driving down the cone), but new space is being created everywhere with time.

Is new space created? i only ask because i have not seen this before.

 

[Jonathan Scott]

I was only using "new space" to highlight the fact that the on the cone, the space is somehow getting bigger as one moves down from the apex, yet any local patch of it is still staying the same size.

If I understand Peacock's "diatribe" correctly, this is actually quite a close analogy to what is happening in the universe, at least to the approximation that the expansion can be considered linear.

A major source of confusion (as Carroll points out) is that there are many different ways to describe the same effect.