I am reading an article, Inflation and CMBR by Charles H. Lineweaver.

https://www.mso.anu.edu.au/~charley/papers/canberra.pdf (Page 5/13)

He explains the inflation period as the shrinking of the event horizon in the comoving coordinate system. Which it makes sense since the inflation was a period of $\Lambda$. And In this period of time event horizon shrinks down to $0$ as time goes to infinity (in future). And in the solution part of the horizon problem, the author defines a new surface last scattering due to the inflation.

I am having trouble to understand how can shrinking event horizon can lead to a new surface of the last scattering and solve the horizon problem.

  • 2
    $\begingroup$ For the "horizon problem" to exist, the universe must have started as asymmetrical. There is no reason for this asymmetry, so there is no 'horizon problem" in the first place. $\endgroup$ – safesphere Feb 11 at 3:31
  • $\begingroup$ @safesphere Yes, you are right. But let us assume it started as asymmetric. I just want to understand how the solution works. In the context of cosmic inflation. $\endgroup$ – Reign Feb 11 at 5:53

Imagine two points, A and B, that are presently at opposite locations on the last scattering sphere. Light emitted from A and from B has only just now reached Earth, and since the proper distance between A and B is twice the last scattering distance, they have never exchanged light signals. In other words, their light cones when projected from the last scattering surface to $\tau = 0$, do not intersect, as shown in the figure. And, yet, all such points on the last scattering sphere are strikingly uniform, suggesting that they were in equilibrium by the time of last scattering. As there is not causal mechanism which could have brought about this equilibrium, this is considered a problem -- the horizon problem.

Inflation addresses this problem by providing such a mechanism. That the proper distance to the event horizon is shrinking in comoving coordinates is just another way of saying that space is expanding at a greater rate than the horizon is. Consider again points A and B, but now suppose that they have had time to exchange light signals before inflation begins, i.e. they are within each other's particle horizon's at the start of inflation. During inflation, since space expands at a greater rate than the horizon, points A and B will be pulled outside of each other's event horizons (as well as Earth's horizon). See the following sequence illustrating how a single point can be pulled outside an observer's horizon on account of the inflating space.

enter image description here

Now, when inflation ends, points A and B will appear to subtend an acausal distance on the last scattering sphere, but in reality they were once in causal contact. This has the effect of moving the last scattering surface ahead in time such that their lightcones indeed intersect at $\tau = 0$, i.e. that they have time to exchange light signals before last scattering.

  • $\begingroup$ Is it right to define a "new last scattering surface" ?. I understand your point but I did not understand why the author defines the new last scattering surface ? From what you said it seems that he just wanted to show that the points were in causal contact once. But then why at that particular time, $a(t)=0.8$ $\endgroup$ – Reign Feb 12 at 16:45
  • $\begingroup$ I think the way to interpret the "new" last scattering surface is as a shift relative to its position in a non-inflationary universe, i.e. there aren't really 2 notions of last scattering in a single spacetime. The LSS is still at a z of 1000 even with inflation, but the amount of expansion that takes place prior to last scattering is much greater with inflation, in the example here, more by a factor of 0.8/0.001. $\endgroup$ – bapowell Feb 12 at 17:04
  • $\begingroup$ I think the graph is wrong $\endgroup$ – Reign Feb 12 at 17:14

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