### How can an infinite universe expand?

• Justin Waters

6 years ago

I understand the expansion of the universe as actually an increase in the ratio of space to matter. Is this a correct understanding? Otherwise, I don't understand how an infinite structure can expand. Infinities come in different sizes: https://en.wikipedia.org/wiki/Aleph_number @WayfaringStranger, thats true, but irrelevant in this context Possible duplicate of How can the universe be infinite? universe not is infinite *Observable* universe is not infinite. Hubble's law gets things receding faster than light, unobservable, at 40 some billion light years right now. We tend to assume that an observer on that last planet receding at just under c sees a universe that looks just like ours, but with us receding at just under c. That assumption will get you close to an infinite universe.

• 6 years ago

Expansion means that distances are increasing as a function of time. Say if the distance between two galactic clusters is \$D\$, then in an expanding Universe the distance is governed by some strictly increasing function of time \$a(t)\$ called the scale factor where

\$\$D=a(t)D_0\$\$

where \$D_0\$ is the distance at the present time and by definition \$a(t_{0})=1\$.

Cosmology assumes that the Universe is on large scales the same everywhere (homogeneous) and the same in all directions (isotropic) so the above applies to all distances above a certain scale. The scale factor \$a(t)\$ can be found from the Friedmann equations and initial conditions.

Expansion is possible in Universes of both finite and infinite spatial extent.

As the volume of a (large enough) region of space increases in proportion to \$[a(t)]^3\$, but the amount of matter remains constant, the matter density changes in proportion to \$[a(t)]]^{-3}\$. Expansion however also decreases the kinetic energy of of its contents, so the energy density decreases by a greater factor if the contents has kinetic energy. But if the universe is infinite, how can it expand? Saying _it just can_ does not answer the question. Before I made that statement I explained how expansion is the increase of distances between (comoving) objects. Clearly there is no dependence on the space being finite for distances to increase.  @Florin Andrei : IMHO it says nothing useful about the real universe. See my answer below for my own thoughts on the matter. "Expansion is possible in Universes of both finite and infinite spatial extent". This implies the universe to be held within a space. So, space is not part of the universe, but the universe is just one part of space? Seems quite debatable.