Hi, this is my first post on the group so hello, and I have no idea how many people may be listening. I want to ask a question and see who may be able to help me test "Inflationary" theory.
In 1981 in order to map observed data to the excellent big bang theory, the idea was invented that in the first fraction of a second of the universe, everything expanded exponentially, before a period lasting 380,000 years in which the cosmic microwave background was emitted. This has held together the mainstream cosmological model and enabled us to make ever more incredible conclusions about the universe.
I have a way to test the theory against reality, as follows:
Firstly, imagine a universe which obeys Hubble's law, i.e. expansion is proportional to distance. Next, go to the point remote you, which is just inside your event horizon, i.e. just so far enough from you that it is receding at slightly less than the speed of light. Light emitted here will take next to forever to reach you since it will always be swimming effectively against the tide, and when it does, its frequency and energy will be next to nothing.
Light emitted slightly closer will reach much sooner, but will have higher energy, until the light emitted very closely will reach instantaneously and, by and large, the highest frequency.
The challenge is this: In such a universe, what CONTINUOUS function of time must Hubble's law obey (i.e. without inflation), for us to observe exactly the following distribution of radiation:
It may initially be easier to assume (probably incorrectly) but as a simplification, that the intensity and frequency of radiation emitted is constant - but that can be changed later.