# If the universe didn't expand faster than light, would our nights brighter like day?

There's a common QnA which has amused and inspired many kids:

There are billions of Stars in the sky. If we combine lights received from all stars, wouldn't it beat Sun? Why is night dark really?
It's because speed of light is finite and lights from most of stars are in the way to the Earth.

My Question: If universe didn't expand faster than light in any point of time, would our nights brighter like day?

Common sense says, Yes. But, unfortunately, universe is full of common sense busters. Is there anything else which can affect this?

Note: I am talking about visible light only. I know, night is already bright in other wavelengths.

Update:
I am clarifying the behavior setup of universe in If clause:

• Universe expansion speed is calculated classically with Super Cluster Red Shift. No GR globally separated reference frame glitch here.

• Universe is expanding today, but not accelerating. Similar to original Hubble's discovery except Inflation shouldn't accelerate universe to faster than light.

My common sense reasoning:

• After universe became transparent to light, all luminous objects should continuously illuminate possible position of Earth until their death. As universe is young, death probability should be low.

• Till the time of birth of Earth and till today, light from most of slightly younger stars should reach Earth for continuous illumination.

This is the reasoning of my common sense.

If I am still not clear, let me know.

• The problem is that apparently innocent statement If universe didn't expand faster than light in any point of time. This is fundamentally incompatible with the FLRW metric. For us to give a reasoned answer to your question you'd have to specify what you'll be replacing general relativity and/or the FLRW metric with. – John Rennie Mar 17 '14 at 11:40
• I agree w/ JRennie, but will add this thought: if the universe were expanding much more slowly than it is, or for that matter if we lived close to the center of a dense galaxy, there would be many more stars much closer to us, and the sky would be a lot brighter. Just how much brighter depends on your choice of scenario. (cue the Sci Fi stories..) – Carl Witthoft Mar 17 '14 at 11:46
• @JohnRennie While dealing with GR problems, I don't think we always take universe expansion in account. So, where am I hitting metric? It's same. – Schrödinger's Cat Mar 17 '14 at 11:53
• May be the question should be asked about a static cosmological model. What would the night sky look like in such a universe? – MBN Mar 17 '14 at 12:10
• Sorry I'm mistaken. The resolution of Olbers' paradox in light of the BB requires expansion to red shift the light. See the discussion at wiki en.wikipedia.org/wiki/Olbers'_paradox – innisfree Mar 17 '14 at 13:21

## 2 Answers

Olber's paradox assume infinite and static Universe (infinite life of universe and stars too).

Cosmological redshift due to Universe's expansion shift visible light to infrared or microwave region of electromagnetic spectrum. The CMB radiation is the most clear effect.

Observable Universe is finite (more or less 93 billion light years). This limit the number of galaxies from which we receive radiation.

Stars have finite life.

In addition also some part of universe with recession velocity greater than c could enter (in the future) in the event horizon, but they will red shifted at z more than 1.8, away from visible region.

Reference: arXiv:astro-ph/0310808v2 13 Nov 2003

Peacock Cosmological Physics Cambridge press 2010 (section 12.1)

Davis Linewear Misconceptions about Big Bang Scientific American March 2005

I like this video by MinutePhysics on this topic. It can clarify things as a primer.

When you state that the universe expanded at a speed higher than the speed of light, you have to stop and ask what is actually meant by such a statement. What is moving with respect to what?

In standard cosmology, we describe the universe expansion by the Hubble rate $H(t)$. $H(t)$ is however not a speed, but a "rate" $[H]=time^{-1}$. The "apparent speed" (corresponding roughly to redshift) between two points at a distance $d$ in the rest frame of the universe is then $$v = H(t)d$$ For any given Hubble rate, we can find a $d$ for which the "apparent speed" is formally larger than the speed of light, but also a different $d$ for which it is not. This is just an expression of the fact that for any positive expansion rate and an infinite universe, there will always be only finite regions we can reach since the distance between us and the rest is just growing faster than we can move.

It's because speed of light is finite and lights from most of stars are in the way to the Earth.

This is true, but you also need to consider a second effect - the redshift. If there were no redshift, i.e. no expansion of the universe since it's conception, the stars would constantly be on the background of a dimly glowing orange (temperature $\sim 3000 K$) background of the last scattering of primordial plasma and also we would see much more stars - layer after layer portraying a slice of the history of the universe since every layer farther took more time to get to us. (We see this "primordial plasma glow" as the CMB). However, since our universe has a history of expansion, the lightwaves got "stretched" and thus redshifted beyond visibility.

But yes, if the expansion were much slower, the stars would seem much more brighter, as not so much distance would have grown between us, and more of them would be in the visible spectrum, since they would not be as redshifted by the less expanded universe. If we stretch this a bit further, we could indeed enjoy a lot of light even during the night. But beware what you wish for, this package would also include much more of the power of the cosmic radiation such as gamma ray bursts etc. etc.