# How can the 13.8 billion years old universe have a radius of 46 billion light years?

The universe is about 13.8 billion years old. Assume at the big-bang it starts from a small region and the maximum possible speed according Einstein is the speed of light how can the universe got a radius of 46 billion light years? According my understanding it could have a max. radius of 13.8 billion light years only. Can someone explain to a non-astrophysicists.

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It's called expansion. Why a universe X years old could not be Y light-years big? Einstein's maximum velocity limit applies to things travelling through space, is does not impose a limit on space itself. –  harogaston Jun 9 at 0:01

You assumption is wrong. Universe can( and is ) expand faster than the speed of light.

The photon emitted towards our planet in the early universe, had to traverse a universe that is expanding. That photon experienced redshift, that means his wavelenght increased and frequency decreased. We measure that photon's wavelength, compare it to a photon that was not redshifted and calculate the scale, which is then applied to the radius of the observable universe.

http://en.wikipedia.org/wiki/Observable_universe

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But if space was expanding when the photon started moving, then how do we know how much distance it has already traveled ? –  Yashbhatt Jun 9 at 10:23
@Yashbhatt I don't understand what are you asking. –  this Jun 9 at 13:06
Sorry. I forgot that photons also get redshift due to expansion of space. But I have another question. If the universe was and it's still expanding at the speed of light, then how can we see the early universe? –  Yashbhatt Jun 9 at 17:59
Also, what do we mean by expansion of space? I am asking this because space is apparently "nothingness". –  Yashbhatt Jun 9 at 18:08
@Yashbhatt You should really do this: astronomy.stackexchange.com/questions/ask –  this Jun 9 at 18:43

To expand on self.'s answer -

Derek from Veritasium on Youtube explains the "(and is)" portion -

...This doesn't violate Einstein's theory of relativity since nothing is moving through space faster than light, it's just that space itself is expanding such that far away objects are receding rapidly from each other. ...

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Far away galaxies are receding from us faster than $c_{0}$ = 299 792 458 m/s, but it does not mean that they are breaking the speed of light limit. These galaxies would still measure the speed of light locally to be $c_{0}$ (assuming the speed of light and the laws of physics are the same throughout the universe), and they would never catch up and move faster than photons moving past them: photons passing by these galaxies in the direction away from us still recede from us faster than these galaxies.

We observe that on average the further away a galaxy is the faster it recedes from us. If we consider that our galaxy is not in a special place in the universe (just like our Sun is not in a special place in our galaxy and like Earth is not a planet around which the rest of the universe revolves), then we think any other galaxy should make the same observation than ours, that is that other galaxies recede away from them and that the further away the faster they are seen receding. We call that the expansion of the universe.

Some people will tell you that this expansion is due to space being "stretched" or "created" between the galaxies, as if space was an entity or substance actually being stretched or created. To me this is a poor explanation because no one has ever detected that entity or substance we call space, for now it is a theoretical abstraction rather than something having a tangible reality.

In case you're wondering, the story as it goes is that the furthest matter we see (the Cosmic Microwave Background or CMB for short) was 42 million light years away from us 380 000 years after the big bang, back when it emitted the light we are detecting now, and this matter is now 46 billion light years away (which we call the radius of our observable universe).

The reason we cannot see light from further back than 380 000 years after the big bang is that before that time, the universe is thought to have been too dense to allow for light to travel freely without being constantly reabsorbed by the surrounding matter.

The reason it took so long for this light to reach us is that 380 000 years after the big bang, the matter that was 42 million light years away (the matter which emitted the light that we call the CMB) was receding much faster than $c_{0}$ from the soon-to-be Milky Way, hence the light it emitted towards us was in fact getting further away.

And the reason this light reached us at all is that during the first 9 billion years following the big bang, the universe is thought to have been decelerating (as opposed to the last 5 billion years when it is thought to have been accelerating). What this means is that galaxies (or soon-to-be galaxies) were moving away from each other at a decelerating velocity during the first 9 billion years. The matter which emitted the CMB didn't slow down enough to recede at less than $c_{0}$ from us, but the light that it emitted 380 000 years after the big bang eventually reached a point where galaxies receded from us slower than $c_{0}$ , i.e. a point where that light started to get closer to us (in other words, the spherical region inside which galaxies recede from us slower than $c_{0}$ enlarged fast enough so that the light of the CMB eventually entered it), and 13.8 billion years later we receive it at last.

The values for the age of the universe and the radius of the observable universe are calculated by solving the equations of Einstein's theory of general relativity, assuming the universe is homogeneous and isotropic, and using cosmological observations to estimate the various parameters in the equations.

If you want to learn more, this is a useful read about galaxies receding from us faster than the speed of light and the expansion of the universe: Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe

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