Does CMB rule out that the universe is infinite?

If the universe were infinite, the energy of the big bang would have been long dissipated, and very little or nothing would hit us. Does the fact that CMB still comes roughly the same from every direction prove that the Universe is bounded and that the radiation keeps bouncing at the boundaries?

EDIT

The question was not clear enough or it has been misunderstood:

• I did not specify if I referred to space or time because the theory says that BB occurred some 10 billions years ago
• by infinite I intend a universe in which you can travel forever from a point in any direction and distance ever grows from that point
• if you after any time get back to the starting point, then space is not infinite but finite and boundless.

Now, if we spin back the 10 billion years, we find that the universe was a few cm wide, if the universe is infinite the energy liberated by the BB traveled in all directions and never came back. Can we conclude that there would be scarce or no CMB? How do you explain radiation coming from all direction if most energy was dissipated?

• This is related to Olber's paradox, en.wikipedia.org/wiki/Olbers%27_paradox – innisfree Jun 20 '19 at 6:53
• When you say 'If the universe were infinite', could you clarify whether you mean infinitely big or infinitely old or both. – innisfree Jun 20 '19 at 6:54
• @innisfree, what is relevant here is un/bounded – user157860 Jun 20 '19 at 6:58
• "If the universe were infinite, the energy of the big bang would have been long dissipated, and very little or nothing would hit us." What is your basis for that claim? I don't see why that follows logically. – PM 2Ring Jun 20 '19 at 9:19
• CMBis not diluted enough, yet. It is not bouncing back nor travelling around and coming back, though I think the latter aspect might be under fine examination and relates to curvature. – Alchimista Jun 20 '19 at 11:56

As has been discussed already, the term infinity is ambiguous and needs clarification to give a proper answer.

No, the CMB does not rule out an infinity of the spacial nature of the universe. Space can be infinite ›although‹ we see the CMB in all directions in the same strength and with the overall same features. Space itself isn't involved in the creation of the CMB, the CMB was created by the matter in this space.

No, the CMB does also not rule out the infinity of matter and energy in the universe, nor does it prove that the universe is bounded at some point and operating with reflections which would dissipate the origin of the CMB enough to make it shine from all directions likewise.

The CMB is arriving from all directions because we were inside the blob of matter which created the CMB. That blob of matter produced photons in all directions, not just directed to the outside. Instead, all the heat and events happening at that time created a fluid of photons from all points in that cloud to all directions (statistically speaking), so also to its own inside. Most of the photons will of course never arrive at where we are now because they are directed elsewhere. But some were already pointed exactly to the point in space where we are today (which is a point which was, at the time when the CMB was emitted, inside that area where the CMB happened; whether this point is today still inside that said area is rather a matter of reference).

Some of these photons have been very close to us when they started their journey, maybe just some light years in distance, so they should have arrived at where we are now just some years later, so we should not be able to see them today. But space took them with it when it expanded (that's the idea of space expansion: It takes everything with it, also photons). This expansion also reduced the energy and frequency of the photons by expanding their wavelengths as well. That's why we today see the originally high energy gamma ray photons as mere infrared photons which are extremely hard to detect.

With the emission of these photons a race was started between the photons moving with light speed towards us and the expansion of space itself. Had they been a little further off, the expansion would have won and these photons would never reach us. What we see today are exactly those photons which had been started in the sphere around us which had exactly the correct distance to us so that these photons today win this race. Tomorrow we will see the photons which were emitted in the sphere around us which was just a tiny bit larger and thus further away.

The diagram attached shows this expansion. We are located in the black spot, the green ring is the sphere which emitted the photons we see today, the triangles are the photons flying directly towards us. They change color over time to indicate their change of wavelength. When they arrive at the black spot they are dark red to indicate infrared.

So no, there is no bouncing necessary to explain our observations. The photons have been on their way for about 13.8 billion years but the green ring which emitted them is now much further away than just 13.8 light years and they were much closer than the 13.8 light years when they were being emitted.

The blob of matter which created the CMB may or may not be infinite, we wouldn't know, at least not by looking at the CMB. The diagrams display it as a circle of finite size and we are located not too close to the border (otherwise we would see a difference in the CMB in varying directions). But the circle might be an infinite field of such matter, getting stretched out by the expanding universe. We would see the exact same CMB.

This all doesn't mean the universe is actually infinite. It just states that this cannot be determined by looking at the CMB.

It might be interesting to mention that our whole observable universe, all photons which arrive at the Earth, are emitted inside the expanding green circle. Anything emitted just outside of it will reach us in the future (but really just a tiny bit of more layers will do so because they have been expanded along with space to immense measures), and anything far enough outside the green ring does not win the race against the expansion and will never reach us. That's the reason we call the microwave photons we see a ›background‹ (the B in CMB).

There are a few things to clarify:

1. the universe is not infinite in age, the big bang happened 13.8 billion years ago

2. the universe might be infinite in size, but what we mean by that is that the universe is practically endless

There are two ways to say if something (our universe for example) is infinite:

1. infinite spatial extension (or infinite 4D extension in our universe), meaning that it extends (for example as a sphere in 3D) infinitely, so its axes would be infinitely long, meaning it is unlimited in spatial extension

2. infinite meaning endless, that is, you can travel in space forever without hitting the edge (that possibly does not exist in our universe)

Now in our universe, the case is possibly 2., infinite, meaning endless, you can travel in space without hitting the edge forever.

Now the good example is the surface of Earth for an ant. The ant can travel on the surface of Earth forever without hitting an end, there is no end of road sign. Does this mean that the Earth has infinite spatial extension in space? No. The earth has a limited spatial extension in space (you could put/limit the Earth in a cube for example).

Yet, the Earth is infinite for the ant (who does not understand the bigger picture), who only lives in 2D on the surface.

Analogously, the universe is infinite for us, who live in 3D space, meaning, we can travel infinitely without hitting the edge.

Does this mean that the universe is infinite in age (in 4D in both directions, back in time and forward)? No.

Analogously, the universe is limited in 4D, so that the dimension of time is limited in one direction, back to the big bang, and it does not make sense to go back before the big bang, there is no such thing as before the big bang.

The very important thing is to understand that the infinity (in this case endlessness) of space does not require infinite time.

Based on the comments, the question is rather why we see the CMB if the universe is infinite in size and all the radiation has diluted.

Now some people might make you confused asking questions like "why is the nightsky not dark then?"

It all comes back to the time dimension. The reason we still see light coming from other galaxies, and we see the CMB is that the universe is not infinite aged. The universe according to our currently accepted theory, the SM, is 13.8 billion years old.

To have what you suggest, that the CMB radiation has all diluted (and analogously the night sky is dark), the universe would have to be infinite aged, meaning the universe would have had existed for an infinite time.

This is not the case, CMB, radiation, just like other photons (like visible) are coming from all direction in the universe, and the farthest we see could have been emitted only as much as 13.8 billion years ago (but again this is for the whole universe, not only for the observable).

If we would see no CMB radiation (and no visible photons either coming from galaxies), that could mean two things:

1. the universe has existed for infinite time

2. the expansion's rate has exceeded a certain limit, where every other galaxy is so far, that no photons (not visible, nor CMB) will ever reach us

• Infinite means that you travel as long as you wish from a point and distance from there is ever increasing. the earth is finite and unbounded. When cosmologists consider the possibility that the universe is infinite mean infinite and not finite-unbounded. I asked my question to clarify this ambiguity; does CMB rile out that it is infinite, that is that you travel forever and do not return to the staring point? – user157860 Jun 20 '19 at 8:40
• In our universe, it's probably case 1, that it's infinite in spatial extent. Case 2 would be true if the global curvature is positive, so that the universe is closed, but current observations indicate that the curvature is very close to zero, and possibly negative. It might have a slight positive curvature, but that curvature would be so small that you'd have to travel at least 1000 times the radius of the observable universe to return to your starting point (and that's not including expansion while you travel). – PM 2Ring Jun 20 '19 at 9:33
• In addition to the comment by PM 2Ring, this doesn't address directly the OP concern about CMB. This is just a description of what can be intended by infinite and assigns our universe to the, presumably, wrong scenario, namely that of a close one. – Alchimista Jun 20 '19 at 11:52
• @user157860 I did already upvote it. I am the only one though who upvoted. Yes you are right, you can see in the comments that it drew a lot of attention and still was downvoted unfairly. – Árpád Szendrei Jun 21 '19 at 10:07