How can light reach us from 14 billion light years away?

One thing that I can't quite wrap my head around is how light is traveling to Earth from 14 billion light years away, aka the beginning of the universe.

The way I see it, the universe itself was very small 14 billion years ago and has been steadily accelerating in size since. So the photons that left a star that existed 14 billion years ago couldn't travel for 14 billion years because the universe itself was probably only a few million light years total in diameter. The universe is not expanding faster than the speed of light, so that photon should have hit the end of the universe before now.

What piece of this puzzle am I missing?

• A comment to the general public: Why have there been so many expansion-of-the-universe-related questions recently? Sep 18, 2014 at 22:52
• Doesn't astronomy=study of the universe? Sep 18, 2014 at 22:53
• I'm not saying your question doesn't fit here; it fits fine. I'm just surprised at the frequency of the questions related to the expansion of the universe because so many other topics are in scope. Astronomy is the study of the universe on a large scale and many objects in it - stars, galaxies, black holes. It just seemed odd to find so many questions asked recently related to the expansion of the universe. But your question fits here fine. Sep 18, 2014 at 22:55
• @Scottie - No. The study of the universe is cosmology. Astronomy is the study of the life of stars, which is a much smaller field. Astronomy doesn't include the Big Bang, the CMB or the formation of early galaxies, for instance. Sep 19, 2014 at 11:05
• Regardless, the question is definitely on-topic. But astronomy does include the study of galaxies and other celestial objects. Sep 20, 2014 at 20:20

If a star 300,000 km away from you explodes, it'll normally take the radiation from that explosion one second to start vaporizing you. If the space between you and that exploding star inflates to 2.6X10^23km (28 billion ly) one half second after the explosion, the radiation will take 14 billion years, plus a half second, to reach you, and won't vaporize you. Of course the expansion need not be instantaneous. You can plug in about any function you want there. The important thing is not the distance between you and the star at the time of explosion, but the total distance the photon must travel on its path to you. That distance must take into account the expansion of space between the emitted radiation and you, the observer.

• That's a hypothetical number you're using as an example. The expansion occurs at escape velocity, and that's lower than $c$. The explanation comes from the inflation epoch. Sep 19, 2014 at 11:08
• @Wayfaring, from your hypothetical, space would instantly grow 2.6X10^23km. Space is NOT instantly growing, it is growing at a rate slower than the speed of light. So, while I understand that it would take light longer than the original distance, I don't understand why light 14 billion light years away could possibly just now be reaching us. How big do we estimate the universe was 14 billion years ago? Sep 19, 2014 at 14:09
• @Scottie During inflationary epoch en.wikipedia.org/wiki/Inflationary_epoch spatial expansion occured at far above speed of light. Given the distance given in the initial question, that superluminal growth is the major factor involved. Hubble expansion (68 km/sec mpc) isn't going to get anything out to 14 billion light years in 13.8 billion years. Sep 19, 2014 at 14:16
• @Wayfaring: That is cool! I knew there was a period of time where the universe expanded faster than c, but I didn't know it was that long! Thanks! Sep 19, 2014 at 14:20
• @Scottie - since recession velocity increases with distance, even today there are galaxies with recession velocity > c -- and in some cases a light ray from such a galaxy can even reach us, since despite the acceleration of the expansion, the Hubble parameter is continually decreasing with time (as mentioned in the deceleration parameter wiki page), meaning that the recession velocity at a fixed distance is continually decreasing. So, such a light ray can in some cases end up in a region of space with recession velocity < c. Sep 19, 2014 at 21:56