How the cosmic inflation solves the horizon problem (an exact solution)?

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

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.

• 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. – safesphere Feb 11 at 3:31
• @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. – 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. 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.
• 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, $a(t)=0.8$ – Reign Feb 12 at 16:45