<p>The expansion of spacetime does not involve the creation of anything. What is happening in the process of expansion is the enlargement of the metric itself of the spacetime. </p>

<p>Imagine this as any arbitrary coordinate system with geometric points a constant distance apart. As spacetime expands, the distance between these geometric points expand for the same distance for every point. Basically every region of spacetime is expanding away from every other region at the same rate and distance no matter where you happen to be situated. </p>

<p>This is why thinking of new matter being "created" as the method of expansion is not just incorrect, but not helpful at all at it introduces the idea that spacetime has a concrete edge where new stuff is always coming into existence that could conceivably be thought of as a certain distance from us. It isn't so. Spacetime expansion is happening everywhere as the distances between every point on our coordinate system expand. </p>

<p>At our scale (and indeed on any scale smaller than galaxy clusters) we don't see this isotropic expansion as gravitational forces between objects overcome following this coordinate expansion. Remember that Andromeda is currently heading towards us as a reminder. Galaxy clusters are following the expansion and are distancing themselves from each other presently. Care should be taken here though. It isn't the distances between the galaxies in the cluster that are expanding, it is the clusters themselves distancing from each other. </p>

<p>During the 'big bang', the distances between coordinates was zero. This is where the idea of the initial singularity comes from, as the density of spacetime instantaneously becomes infinite with the claim of no geometric space existing at all (look up the definition of singularity for further clarification). Most will currently tell you that the notion of the singularity existing is doubtful and that General Relativity's descriptions of spacetime don't adhere to what is happening on the quantum level, but that is outside the scope of this question. </p>

CC BY-SA 4.0
2018-09-03T14:11:19.673Z
You're saying space is stretching. But anything that is stretching must have a limit. Nothing is elastic enough to stretch at faster than light speeds, non-stop, for billions of years.
White Prime
CC BY-SA 4.0
2018-09-03T14:13:39.360Z
(Space is not being created either, of course. You're right about that. The reality is that space itself is infinite, and always has been. And I mean literally infinite).
White Prime
CC BY-SA 4.0
2018-09-03T14:25:42.310Z
Elasticity doesn't apply to spacetime. Elasticity is a property of physical materials. Spacetime is a geometry, not a physical material.
ShroomZed
CC BY-SA 4.0
2018-09-03T13:59:37.400Z
2018-09-03T13:59:37.400Z
ShroomZed
<p>This question also occurred in <a href="https://www.youtube.com/watch?v=KdBrQMkkDz8#t=15m43s" rel="nofollow noreferrer">Lecture 4 of Leonard Susskind's Modern Physics</a> in relation to a model that he showed to explain expansion.</p>

<blockquote>
  <p>"Little bits of space, little bits of newly formed space, that's <em>one way</em> to think about it. The other way to think about it is just trough the equations of general relativity..."</p>
</blockquote>

<p>I believe that it would be wrong to think of space being 'created'. Or at least, that would be more like a metaphysical concept. It raises the question what <em>is</em> space and what <em>is</em> creation? I do not think that it has much place in general relativity (at least not without considering deeper models that try to unify general relativity with quantum field theory). Is space created or is it just stretched (compare with a rubber band, do we create rubber band when we stretch a rubber band)? Those concepts may be ways to think of it but they do not precisely describe what they "are", or at least they go beyond the physics and mathematical description. The current equations (at least to the equations of general relativity) neither tell whether space is stretched or whether space is created. Those concepts are irrelevant.</p>

<p>There isn't some physical mechanism by which we can say 'this or that is creating space'. An interesting contrasting view that puts the expansion and "creation" of space in a different light is the viewpoint that the expanding universe and the relativistic equations can already be derived using only Newtonian dynamics (<a href="https://doi.org/10.1093/qmath/os-5.1.73" rel="nofollow noreferrer">first described by McCrea and Milne mid 30s</a>). That framework, albeit leading to the same equations, is a Newtonian notion and has a different interpretation. Good to mention is that in Newtonian mechanics space is <em>absolute</em> (so when a volume expands then one could say there must be something like creation of space), but in general relativity this is <em>not</em> the case. What looks big to you can look small to a different observer. </p>

<hr>

<p>In General Relativity the expansion of the universe can be described by the Einstein Field equations like any other motion. You could compare it to the Newtonian cosmological model and see the expansion of the universe as described by equations of motion (ie. there is no magical entity that is causing expansion by "creating" space, it is just ordinary motion as described by the Einstein field equations). </p>

<p>These equations can be very briefly stated as: </p>

<ul>
<li><p><sup>Note: the following equations can be written in many different ways. I have used the notation from Jerzy Plebanski Andrzej Krasinski, in <a href="http://www.cambridge.org/ch/academic/subjects/physics/astrophysics/introduction-general-relativity-and-cosmology?format=HB&amp;isbn=9780521856232" rel="nofollow noreferrer">An Introduction to General Relativity and Cosmology</a></sup></p>

<p>The expanding universe can be described by the Einstein field equations.</p>

<p>$ R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R+\Lambda g^{\mu \nu} = G^{\mu \nu} + \Lambda g^{\mu\nu} = \kappa T^{\mu \nu} \\$</p>

<p>where $\kappa = \frac{8\pi G}{c^4}$ is Einstein's constant and $\Lambda$ the (unknown) cosmological constant.</p>

<p>One of many specific solutions are the Friedman equations (for a homogeneous isotropic universe) that use the Robertson-Walker geometry</p>

<p>$\begin{array}{rcl}  d s^2 &amp;=&amp; g_{\mu \nu} dx^{\mu} dx^{\nu} \\
&amp;=&amp; d t^2 - R(t) \left( \frac{d r^2}{1-kr} + r^2(d \theta^2 + \sin^2\theta d \psi^2) \right) \end{array}$</p>

<p>with $R(z)$ a time dependent scale factor and $k$ the curvature index.</p>

<p>This will lead to a solution for the scale factor $R$</p>

<p>$\begin{array}{rcrcl} G_{00} &amp;=&amp; \frac{3k}{R^2} + 3 \frac{\dot R^2}{R^2} &amp;=&amp; \kappa \epsilon - \Lambda \\
 -G_{11} = -G_{22} = -G_{33} &amp;=&amp; \frac{k}{R^2} + \frac{\dot R^2}{R^2} + 2 \frac{\ddot R}{R} &amp;=&amp; -\kappa p + \Lambda \end{array} $</p>

<p>where $p$ is the pressure and $\epsilon$ is the energy density.</p></li>
</ul>

<hr>

<p>The expansion can be seen as a kinematic effect (like with the expansion in Newtonian Cosmology) and is when described by the equations of motion in the framework of general relativity equivalent to a change, in time, of the <em>'metric'</em>. This change of the metric happens to be the way that we can describe motion, gravitation and electromagnetism in a relativistic way. </p>

<p>If you wish you could call that effect something like 'creation of space', but then you would, imo, need to be consistent and call any other relativistic length contraction/stretch as 'space being created/eliminated' (e.g. space is removed from Michelson's and Morley's interferometer when it is moving, or when gravitational waves pass by then we experience a repeated removal and addition of space). </p>

<p>So the next time you see an apple fall from a tree you should imagine that, from the point of view of that apple, space is being contracted, thus space is being removed.</p>

CC BY-SA 4.0
2021-01-30T19:45:40.783Z
I don't think your comparison between relativistic contraction and cosmological expansion is fair or accurate: For one, relativistic contraction is frame-dependent, but even non-comoving observers must agree cosmic expansion is the same
lurscher
CC BY-SA 4.0
2021-01-30T20:06:35.267Z
@lurscher, it remains a relativistic effect. But yes, every observer agrees about the physical rules (that's the point of relativism) just like every observer must agree that the equations of motion for the motions of planets around the sun are the same.
Sextus Empiricus
CC BY-SA 4.0
2021-01-30T20:14:02.320Z
I disagree that the point of my comparison with the relativistic contraction is unfair. It is the *same* principal. Space-time being different for different observers (in the case of cosmic expansion it is the observer now versus the observer around the big bang who have different viewpoints). If one argues that space is 'created' (due to Einstein's laws of motion) when space expansion occurs, then why should this be only the case for cosmological expansion but not for other relativistic expansion (or contraction)? What additional rule is there to Einstein's laws that make this distinction?
Sextus Empiricus
CC BY-SA 4.0
2018-09-06T15:00:46.237Z
2018-09-06T15:11:48.413Z
2018-09-06T15:11:48.413Z
Sextus Empiricus
<p>Yes, space is constantly being created. The new space does not hold any matter (like atoms) or dark matter. This means that the <em>density</em> of normal and dark matter <em>de</em>creases at the same rate as the volume <em>in</em>creases. However, dark <em>energy</em>, which is something completely different and thought to be a property of vacuum itself, is being created with the new space, so the density of dark energy stays constant.</p>

<p>This in turns mean that while the early Universe (i.e. from it was 70,000 years old and until it was almost 10 billion years) was dominated by matter, the Universe is now dominated by dark energy.</p>

<p>And it will only get worse.</p>

CC BY-SA 3.0
2015-08-02T10:45:25.780Z
what do you mean by worse?
Alex Sifuentes
CC BY-SA 3.0
2015-08-02T20:40:59.953Z
@AlexandroSifuentesDíaz: I only meant that the fraction of energy consisting of dark energy will keep increasing forever.
pela
CC BY-SA 3.0
2015-08-02T20:50:03.790Z
Is that bad? sorry, I am curious haha
Alex Sifuentes
CC BY-SA 3.0
2015-08-03T08:38:04.673Z
@AlexandroSifuentesDíaz: If you prefer a cold, barren Universe, with galaxies so far apart that a only a few gravitationally locked ones are visible, with the probability of forming new stars and life approaching zero, then I guess you're good. If on the other hand you prefer galaxies to approach each other, the Universe to get hotter, and eventually everything to collapse in a Big Crunch, with the possibility of starting all over, possibly with new, exciting physical laws, then you should move to a $\Omega_\Lambda=0,\Omega_\mathrm{tot}>1$ universe. As I write this, maybe I prefer the first :)
pela
CC BY-SA 3.0
2018-01-17T18:41:12.083Z
These people write that space is not being created, only expanding, which is contrary to what you are saying. Who is correct? 1) https://www.quora.com/How-does-the-expansion-of-the-universe-create-new-space-time 2) https://physics.stackexchange.com/questions/156249/expansion-of-the-universe-is-new-spacetime-being-created-or-does-it-just-get
Samuel
CC BY-SA 3.0
2018-01-18T09:13:06.377Z
@Samuel A good question, but I think perhaps it boils down to semantics: Space expands, we agree on that. So, when a cube of vacuum grows in size, you have a larger cube of vacuum. Have you now got the same vacuum, only larger, or have you got more vacuum? The atoms and photons that were in your original cube now have more space to roam; their density has decreased, and you may say that space has "just" expanded. But the vacuum energy density, which is a property of space itself, has not decreased. It is constant, so you may say that more space has been created.
pela
CC BY-SA 4.0
2018-09-04T22:37:32.603Z
If your ruler to measure some space shrinks did you 'create' new space? I do not thinks so. I believe that this should not boil down to semantics and a clear unambiguous (formal) answer is possible (except for possible interpretations and simplifications going into different directions).
Sextus Empiricus
CC BY-SA 4.0
2018-09-05T11:40:56.940Z
@MartijnWeterings A shrinking ruler implies neither creation of new space, not expansion of existing space; we agree on that. But that doesn't really apply to this question. Our rulers don't shrink. However, you might still be right that there is an unambiguous answer, I just don't know it.
pela
CC BY-SA 4.0
2019-06-19T13:18:46.297Z
@MartijnWeterings I think the issue boils down to whether or not you have an ambient space to embed things into.  You can fix an object on your desk, describe a metric on it, and then rescale that metric however you see fit, and you know the object isn't growing or shrinking intrinsically. But the universe doesn't have an ambient space it is embedded into (literally, or canonically mathematically).  It is the entirety of what exists by definition. The metric *is* intrinsic to it, and there's no distinction to be made between "just ruler shrinkage" and "literally more space now".
zibadawa timmy
CC BY-SA 3.0
2015-04-22T20:13:40.123Z
2015-04-22T20:13:40.123Z
pela
<p>I am wondering what exactly is meant when it is said the universe expands. Does it simply create new space for matter to fill, does it also create new matter/dark matter to fill that space, or am I way off? Thank you for any help!</p>

<universe><space><expansion><matter>
When the universe expands does it create new space, matter, or something else?
Joey Seibel
# When the universe expands does it create new space, matter, or something else?

(Asked by: username_0 on 2015-04-21)

I am wondering what exactly is meant when it is said the universe expands. Does it simply create new space for matter to fill, does it also create new matter/dark matter to fill that space, or am I way off? Thank you for any help!

**Tags:** universe, space, expansion, matter


---

## 3 answers

### Answer by username_5 on 2015-04-22. Score: 9 | Accepted answer

Yes, space is constantly being created. The new space does not hold any matter (like atoms) or dark matter. This means that the *density* of normal and dark matter *de*creases at the same rate as the volume *in*creases. However, dark *energy*, which is something completely different and thought to be a property of vacuum itself, is being created with the new space, so the density of dark energy stays constant.

This in turns mean that while the early Universe (i.e. from it was 70,000 years old and until it was almost 10 billion years) was dominated by matter, the Universe is now dominated by dark energy.

And it will only get worse.

> **Comments:**
> **username_6**: what do you mean by worse?  
> **username_5**: @AlexandroSifuentesDíaz: I only meant that the fraction of energy consisting of dark energy will keep increasing forever.  
> **username_6**: Is that bad? sorry, I am curious haha  
> **username_5**: @AlexandroSifuentesDíaz: If you prefer a cold, barren Universe, with galaxies so far apart that a only a few gravitationally locked ones are visible, with the probability of forming new stars and life approaching zero, then I guess you're good. If on the other hand you prefer galaxies to approach each other, the Universe to get hotter, and eventually everything to collapse in a Big Crunch, with the possibility of starting all over, possibly with new, exciting physical laws, then you should move to a $\Omega_\Lambda=0,\Omega_\mathrm{tot}>1$ universe. As I write this, maybe I prefer the first :)  
> **username_7**: These people write that space is not being created, only expanding, which is contrary to what you are saying. Who is correct? 1) https://www.quora.com/How-does-the-expansion-of-the-universe-create-new-space-time 2) https://physics.stackexchange.com/questions/156249/expansion-of-the-universe-is-new-spacetime-being-created-or-does-it-just-get  
> **username_5**: @username_7 A good question, but I think perhaps it boils down to semantics: Space expands, we agree on that. So, when a cube of vacuum grows in size, you have a larger cube of vacuum. Have you now got the same vacuum, only larger, or have you got more vacuum? The atoms and photons that were in your original cube now have more space to roam; their density has decreased, and you may say that space has "just" expanded. But the vacuum energy density, which is a property of space itself, has not decreased. It is constant, so you may say that more space has been created.  
> **username_3**: If your ruler to measure some space shrinks did you 'create' new space? I do not thinks so. I believe that this should not boil down to semantics and a clear unambiguous (formal) answer is possible (except for possible interpretations and simplifications going into different directions).  
> **username_5**: @MartijnWeterings A shrinking ruler implies neither creation of new space, not expansion of existing space; we agree on that. But that doesn't really apply to this question. Our rulers don't shrink. However, you might still be right that there is an unambiguous answer, I just don't know it.  
> **username_8**: @MartijnWeterings I think the issue boils down to whether or not you have an ambient space to embed things into.  You can fix an object on your desk, describe a metric on it, and then rescale that metric however you see fit, and you know the object isn't growing or shrinking intrinsically. But the universe doesn't have an ambient space it is embedded into (literally, or canonically mathematically).  It is the entirety of what exists by definition. The metric *is* intrinsic to it, and there's no distinction to be made between "just ruler shrinkage" and "literally more space now".  

---

### Answer by username_1 on 2018-09-03. Score: 2

The expansion of spacetime does not involve the creation of anything. What is happening in the process of expansion is the enlargement of the metric itself of the spacetime.

Imagine this as any arbitrary coordinate system with geometric points a constant distance apart. As spacetime expands, the distance between these geometric points expand for the same distance for every point. Basically every region of spacetime is expanding away from every other region at the same rate and distance no matter where you happen to be situated.

This is why thinking of new matter being "created" as the method of expansion is not just incorrect, but not helpful at all at it introduces the idea that spacetime has a concrete edge where new stuff is always coming into existence that could conceivably be thought of as a certain distance from us. It isn't so. Spacetime expansion is happening everywhere as the distances between every point on our coordinate system expand.

At our scale (and indeed on any scale smaller than galaxy clusters) we don't see this isotropic expansion as gravitational forces between objects overcome following this coordinate expansion. Remember that Andromeda is currently heading towards us as a reminder. Galaxy clusters are following the expansion and are distancing themselves from each other presently. Care should be taken here though. It isn't the distances between the galaxies in the cluster that are expanding, it is the clusters themselves distancing from each other.

During the 'big bang', the distances between coordinates was zero. This is where the idea of the initial singularity comes from, as the density of spacetime instantaneously becomes infinite with the claim of no geometric space existing at all (look up the definition of singularity for further clarification). Most will currently tell you that the notion of the singularity existing is doubtful and that General Relativity's descriptions of spacetime don't adhere to what is happening on the quantum level, but that is outside the scope of this question.

> **Comments:**
> **username_2**: You're saying space is stretching. But anything that is stretching must have a limit. Nothing is elastic enough to stretch at faster than light speeds, non-stop, for billions of years.  
> **username_2**: (Space is not being created either, of course. You're right about that. The reality is that space itself is infinite, and always has been. And I mean literally infinite).  
> **username_1**: Elasticity doesn't apply to spacetime. Elasticity is a property of physical materials. Spacetime is a geometry, not a physical material.  

---

### Answer by username_3 on 2018-09-06. Score: 2

This question also occurred in [Lecture 4 of Leonard Susskind's Modern Physics](https://www.youtube.com/watch?v=KdBrQMkkDz8#t=15m43s) in relation to a model that he showed to explain expansion.

> "Little bits of space, little bits of newly formed space, that's *one way* to think about it. The other way to think about it is just trough the equations of general relativity..."

I believe that it would be wrong to think of space being 'created'. Or at least, that would be more like a metaphysical concept. It raises the question what *is* space and what *is* creation? I do not think that it has much place in general relativity (at least not without considering deeper models that try to unify general relativity with quantum field theory). Is space created or is it just stretched (compare with a rubber band, do we create rubber band when we stretch a rubber band)? Those concepts may be ways to think of it but they do not precisely describe what they "are", or at least they go beyond the physics and mathematical description. The current equations (at least to the equations of general relativity) neither tell whether space is stretched or whether space is created. Those concepts are irrelevant.

There isn't some physical mechanism by which we can say 'this or that is creating space'. An interesting contrasting view that puts the expansion and "creation" of space in a different light is the viewpoint that the expanding universe and the relativistic equations can already be derived using only Newtonian dynamics ([first described by McCrea and Milne mid 30s](https://doi.org/10.1093/qmath/os-5.1.73)). That framework, albeit leading to the same equations, is a Newtonian notion and has a different interpretation. Good to mention is that in Newtonian mechanics space is *absolute* (so when a volume expands then one could say there must be something like creation of space), but in general relativity this is *not* the case. What looks big to you can look small to a different observer.

---

In General Relativity the expansion of the universe can be described by the Einstein Field equations like any other motion. You could compare it to the Newtonian cosmological model and see the expansion of the universe as described by equations of motion (ie. there is no magical entity that is causing expansion by "creating" space, it is just ordinary motion as described by the Einstein field equations).

These equations can be very briefly stated as:

* Note: the following equations can be written in many different ways. I have used the notation from Jerzy Plebanski Andrzej Krasinski, in [An Introduction to General Relativity and Cosmology](http://www.cambridge.org/ch/academic/subjects/physics/astrophysics/introduction-general-relativity-and-cosmology?format=HB&isbn=9780521856232)

  The expanding universe can be described by the Einstein field equations.

  $ R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R+\Lambda g^{\mu \nu} = G^{\mu \nu} + \Lambda g^{\mu\nu} = \kappa T^{\mu \nu} \\$

  where $\kappa = \frac{8\pi G}{c^4}$ is Einstein's constant and $\Lambda$ the (unknown) cosmological constant.

  One of many specific solutions are the Friedman equations (for a homogeneous isotropic universe) that use the Robertson-Walker geometry

  $\begin{array}{rcl} d s^2 &=& g\_{\mu \nu} dx^{\mu} dx^{\nu} \\
  &=& d t^2 - R(t) \left( \frac{d r^2}{1-kr} + r^2(d \theta^2 + \sin^2\theta d \psi^2) \right) \end{array}$

  with $R(z)$ a time dependent scale factor and $k$ the curvature index.

  This will lead to a solution for the scale factor $R$

  $\begin{array}{rcrcl} G\_{00} &=& \frac{3k}{R^2} + 3 \frac{\dot R^2}{R^2} &=& \kappa \epsilon - \Lambda \\
  -G\_{11} = -G\_{22} = -G\_{33} &=& \frac{k}{R^2} + \frac{\dot R^2}{R^2} + 2 \frac{\ddot R}{R} &=& -\kappa p + \Lambda \end{array} $

  where $p$ is the pressure and $\epsilon$ is the energy density.

---

The expansion can be seen as a kinematic effect (like with the expansion in Newtonian Cosmology) and is when described by the equations of motion in the framework of general relativity equivalent to a change, in time, of the *'metric'*. This change of the metric happens to be the way that we can describe motion, gravitation and electromagnetism in a relativistic way.

If you wish you could call that effect something like 'creation of space', but then you would, imo, need to be consistent and call any other relativistic length contraction/stretch as 'space being created/eliminated' (e.g. space is removed from Michelson's and Morley's interferometer when it is moving, or when gravitational waves pass by then we experience a repeated removal and addition of space).

So the next time you see an apple fall from a tree you should imagine that, from the point of view of that apple, space is being contracted, thus space is being removed.

> **Comments:**
> **username_4**: I don't think your comparison between relativistic contraction and cosmological expansion is fair or accurate: For one, relativistic contraction is frame-dependent, but even non-comoving observers must agree cosmic expansion is the same  
> **username_3**: @username_4, it remains a relativistic effect. But yes, every observer agrees about the physical rules (that's the point of relativism) just like every observer must agree that the equations of motion for the motions of planets around the sun are the same.  
> **username_3**: I disagree that the point of my comparison with the relativistic contraction is unfair. It is the *same* principal. Space-time being different for different observers (in the case of cosmic expansion it is the observer now versus the observer around the big bang who have different viewpoints). If one argues that space is 'created' (due to Einstein's laws of motion) when space expansion occurs, then why should this be only the case for cosmological expansion but not for other relativistic expansion (or contraction)? What additional rule is there to Einstein's laws that make this distinction?  

---

