# Did cosmological inflation occur at speeds greater than $c$?

If cosmological inflation occurred at speeds less than $c$, wouldn't we see the CMB right in front of our noses (or not at all) instead of at 13.7 billion light years?
And if it happened faster than $c$, does that mean inflation occurred before the current laws of physics (read the four basic forces) precipitated, was $c$ greater then than it is now?

• As far as I know CMB isn't at 13.7 Bly from us, it's actually everywhere in the universe, but dramatically redshifted to 2.73K microwaves. – Joan.bdm Sep 17 '14 at 14:44
• @Joan.bdm - But the CMB is the remains of the opacity wall at 60(?)ky after the big bang, isn't it? And since the BB occurred 13.7By ago, that light has traveled 13.7Bly, right? What am I doing wrong? Thanks for your reply, though. – stevenvh Sep 17 '14 at 14:53
• I think that is a common misconception, it wasn't an opacity wall (like the surface of a bubble), the whole universe was opaque and became transparent leading to the CMB we see today everywhere we look. – Joan.bdm Sep 17 '14 at 14:59
• Yes, inflation did occur at speeds greater than $c$. Joan's point about the CMB is also spot-on. – HDE 226868 Sep 17 '14 at 15:05
• Also note that while all light waves in a vacuum travel at c as measured by local inertial observers, in a cosmological context the "speed of light" defined in terms of (proper distance traveled)/(cosmological time) may be different than c, as explained in the proper distance subsection of the comoving distance article on wikipedia. – Hypnosifl Sep 18 '14 at 18:43

The simple answer to your question is "yes" - the universe expanded at much greater speeds than $c$ during the inflationary epoch. This period of time was very quick but very dramatic, lasting from about $10^{-36}$ to $10^{-32}$ seconds. The universe expanded, in this very short period, by a factor of $10^{26}$. That's pretty incredible, when you think about it.

Inflation was originally proposed to solve, among other things, the horizon problem - that is, why the universe is isotropic and homogenous (on a large scale). This would mean that all the parts of the universe were in "causal contact" at one point in time. Inflation is the explanation for this.

Now, what does this all have to do with the CMB? Well, the temperature of the CMB is the same throughout the universe - a toasty 2.7 Kelvin. For the temperature to be uniform, all the regions of the universe would have had to be in causal contact in some point in time; hence, inflation explains the uniform temperature of the CMB.

However, the CMB was not around during the inflationary epoch. Far from it. It formed a lot later, when the universe was at the ripe old age of $379,000$ years. But the reason that it was formed (photon decoupling) equally throughout the universe is because the conditions were roughly equal, because of inflation. The CMB was, and still is, everywhere. It was never around during inflation, and as such was not otherwise affected by it.

I hope this helps.

My sources for the times:

Inflationary epoch

NASA

does that mean inflation occurred before the current laws of physics (read the four basic forces) precipitated, was c greater then than it is now?

NO Already the very concept of an expansion velocity is flawed. Expansion means that elements of the medium move away from each other with a relative velocity that is proportional to their distance (for small distances). The constant of proportionality, the expansion rate, is the sensible concept here and has dimension of a frequency. Currently the universe expands at about 73km/s/Mpc, which is the smallest natural frequency known. At the epoch of infation, the expansion rate was just much larger.

Of, course, over large sufficiently distances, any expansion results in superluminal velocities, but the laws of phyiscs only constrain the relative velocities of objects in close vicinity.

• +1 for addressing some of the core misconceptions, although this stops short of addressing the follow-up question. – Stan Liou Sep 18 '14 at 21:12

Yes, although we usually do not say the "expansion occurs faster than light." In General Relativity space can be created between all points and that can result in points that were in causal contact (ie, they were able to see each other) before inflation, being, after inflation, farther away than light could travel in the age of the universe. Basically, the rules in General Relativity are a bit more complicated than that of special relativity (which forbids accelerating an object to speeds greater than the speed of light).

Right now, since the local spacetime is not expanding as quickly as is the visible universe (that which we can see because it is within the distance that light travels in the age of the universe, c*t0), we are coming back into contact with regions of space that were out of contact since the inflationary period. As time passes, we will be able to see a larger cosmic microwave background (CMB) surface. Spots on the CMB surface were not in contact with us (or each other) if they are more than 7 degrees apart since before the inflationary period.

• Can you expand your last paragraph a bit? Regions that we were out of contact with before inflation are still moving away very fast. – HDE 226868 Sep 17 '14 at 22:41
• Gravity has been slowing things down, so now things just outside of the visible universe are expanding away more slowly and light from them can eventually reach us. – eshaya Sep 18 '14 at 17:48
• While that may be the case, the expansion of the universe is accelerating. – HDE 226868 Sep 18 '14 at 22:20
• I was trying to keep the cosmological constant out of this to keep it simple, but ... True, since there is a cosmological constant, then there is some, minimum distance today at which everything is receding at c and that distance is shrinking. It would be interesting to calculate that distance, but not necessary for this discussion. You see, the visible universe continues to grow because tomorrow we will be able to see more distant galaxies than ever before because their light is, today, only one light-day away and that is well within that minimum distance. – eshaya Sep 19 '14 at 4:18
• I should have said in the last sentence that we will be able to see a larger CMB surface, not more galaxies, because near the edge of the visible universe galaxies have not yet formed. Spots on the CMB surface were not in contact with us (or each other if they are more than 7 degrees apart) since before the inflationary period. – eshaya Nov 7 '14 at 17:21