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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!

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.

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.

This question also occurred in Lecture 4 of Leonard Susskind's Modern Physics in relation to a model that he showed to explain expansion.

"Little bits of space, little bits of newly formed space, that's

one wayto 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). 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}The expanding universe can be described by the Einstein field equations.

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

where $kappa = frac{8pi G}{c^4}$ 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

$egin{array}{rcl} d s^2 &=& g_{mu u} dx^{mu} dx^{ u} &=& d t^2 - R(t) left( frac{d r^2}{1-kr} + r^2(d heta^2 + sin^2 heta d psi^2) ight) end{array}$

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

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

$egin{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.