# What were the dimensions of the universe during Planck epoch?

Wikipedia says:

It is believed that, due to the extraordinarily small scale of the universe at the time, quantum effects of gravity dominated physical interactions.

But I wonder whether there is any indication that the dimensions of the universe were small at the time rather than being infinite?

Undoubtedly it was very dense but very dense does not necessary mean "small".

Is Wikipedia wrong on this point?

• Comment to the question (v1): It seems that OP is essentially pondering if the volume of 3-dimensional space is infinite or finite. Related: physics.stackexchange.com/q/9419/2451 and links therein. Dec 20 '13 at 13:58
• The (visible) universe is currently approximately $10^{27}$ m in diameter. From supernova surveys, we know that the universe is accelerating its expansion. Extrapolate backwards for about 13.8 billion years and you get a diameter that is infinitesimal. Dec 20 '13 at 14:01
• Saying that the scale was small doesn't necessarily imply that the spatial dimensions themselves of the whole universe were small. IMHO, that sentence from Wikipedia would be better if it used the term "scale factor". On a related note, see physics.stackexchange.com/a/136861/123208 Oct 19 '20 at 23:48

If the universe is infinite now, it must also have been infinite during it's earliest phase greater than t=0. If the universe is finite now, it it must also have been finite during it's earliest phase greater than t=0. What happens at t=0 is undefined since the GR equations for the universe have a singularity at t=0.

One of the comments mentioned the finite "visual" universe, also more commonly called the observable universe. This is always finite independently of whether the (whole) universe is finite or infinite.

Sometimes you may see in an article the term "universe" (carelessly) used when the intended meaning is "observable universe".

• Well, given the universe if approaching de Sitter space, there is no question about its finitness (it depends on the choice of the coordinates). Oct 19 '20 at 17:29
• @Anixx I am confused by "approaching de Sitter space". A 3D boundary to a 4D sphere is a de Sitter space. It is a solution of the Friedman equation with $\Omega_\Lambda=0$ and $\Omega_m>1$. It never approaches a de Sittrer space because it is always a de Sitter space.
– Buzz
Oct 30 '20 at 22:22
• @Anixx Is your question about wanting to know the volume of the observable universe at the Planck time? This value depends on whether or not you want to take into account the concept of an early inflation period. If you are willing to omit inflation, I can calculate a roughly approximate volume at Planck time.
– Buzz
Nov 3 '20 at 18:55