I will give two analogies…
The thermal and non thermal CMB are mixed like…
1. Mixed like sand and rice, we have to sieve them/ separate them
2. Like pure water in a bowl. Take out a spoon-full from any where from bowl, define it as thermal, all the remaining is non-thermal…
You are already using analogy 2. But you have defined thermal and non-thermal CMB cannot be combined by laws of physics. Here the spoon of water is different from the bowl, only because that is in your hand. You have taken it out from bowl. Is there any other important physical difference?




