Hello everyone! I have found a pretty interesting problem on the internet about cosmology. I'm new into cosmology and I don't know exactly how to solve it... That's why I need a little help. I wrote under the problem text how I would do it. Measurement of the cosmic microwave background radiation (CMB) shows that its temperature is practically the same at every point in the sky to a very high degree of accuracy. Let us assume that light emitted at the moment of recombination (T r ≈3000 K, t r ≈ 300000 years) is only reaching us now. Scale factor S is defined as such So= S (t=to) = 1 and S t= S (t<to) < 1 Note that the radiation dominated period was between the time when the inflation stopped(t=10^-32 seconds) and the time when the recombination took place, while the matter dominated period started at the recombination time. During the radiation dominated period S is proportional to t ^ 1/2, while during the matter dominated period S is proportional to t ^ 2/3 . a. Estimate the horizon distances when recombination took place. Assume thattemperature T is proportional to 1/ S , where S is a scale factor of the size of the Universe ..Note: Horizon distance in degrees is defined as maximum separation between thetwo points in CMBR imprint such that the points could “see” each other at the timewhen the CMBR was emitted b.Consider two points in CMBR imprint which are currently observed at a separationangle α = 5 ° . Could the two points communicate with each other using photon?(Answer with “YES” or “NO” and give the reason mathematically) c.Estimate the size of our Universe at the end of inflation period. At a. I assume that by knowing the temperatures we could find the scale factor and then related to the radius of universe from the formula R = R o * S(t), where R is the radius at time t and R o is current size At b. I would calculate the rate at wich the radius of the universe is increasing and then comparing it to the speed of a photon (c) At c. I would calculate this rate in the same way as b and then integrate on the given time interval. Thank you!