This looks like a question that actually looks like two questions; namely, &#x27;is the universe infinite&#x27; (and as a side question, what is the actual dimensional and geometric configuration of the universe), and if the first question is true, &#x27;why do we not observe an infinite flux of photons, or really any other type or radiation, bathing our chunk of the universe&#x27;.<p>This one&#x27;s easy.  The first, foundational, assumtion is way easy to knock down, via all the accumulated evidence that we erupted from a singularity 13-some billion years ago.  So.. no infinite time.<p>But we could probably get by with, even with an infinite universe, if we just assume a universal speed, which is most definitely supported by current academic consensus. This is because  of the concept of the light cone, which says that you can&#x27;t be illuminated by things that lie outside your temporal and spacial vicinity, as defined by how long it takes light in a vacuum to reach you.  That&#x27;s a stronger statement than just how bright the sky is... it applies to any conceivable mechanism of information transfer, and it&#x27;s universally supported by any experiments that we&#x27;ve tried (note:  wormholes... possible, super crazy loop hole here... maybe an infinite universe has infinitely many wormholes to pump radiation into our light cone, so basicly multiverse, but we&#x27;ve already talked about the universe having an age).<p>I see no paradox here, but then again the Big Bang and Special Relativity are pretty new as ideas and we all benefit from the shoulders of the giants we stand on.<p>Edit: On further reflection, a truly infinite universe probably would park an infinite number of unstable wormholes on top of our neighborhood, but in that case the the fact that our sky is in fact dark just adds more evidence to the pile that we already have that it&#x27;s not.