I'd like to introduce a theory math first here.
I'm hoping to come away from this with one of 2 things:
1. Evidence that there is no particular significance to this equation. A comparably simple and accurate equation to the one I am presenting, which would suggest that it is just an easy "fit equation", would definitely do the trick.
2. Help explaining why this equation works as well as it does. I have an explanation which led me to derive the equation, which I can describe in detail, but it is considerably outside the mainstream.
I will be very happy to present my alternative theory here, and hopefully this introductory post isn't too coy or boring; but we don't even need to waste the time on my idea if this equation isn't compelling.
and hey, if you can disabuse me of the notion that this equation is notable, you will save me from getting an embarrassing tattoo.
The equation relates the cosmological redshift to lookback time.
where (z) is the cosmological redshift, and (t) is lookback time where the present equals 0 and the origin equals 1.
The novel equation closely reproduces the relationship of redshift to lookback time in CDM, without any free parameters except the present age of the universe. Because of the relationship of redshift to scale factor, , the cosmological distance scales can also be computed starting from the novel equation. I've included a table of high z supernovas (names, redshifts and peak magnitudes taken from the Perlmutter paper) showing the close fit of this equation, labeled SL, to CDM, using Ned Wright's cosmology calculator with default inputs to generate the CDM values for lookback time, co-moving distance, luminosity distance. Co-moving distance, Luminosity distance and Absolute Magnitude for the SL columns are calculated using standard cosmology equations.
Next is a link to graph plotting the novel equation against two tables spanning a larger range of z values, generated from Ned Wrights CosmoCalc and the Light Cone Calculator.
That's it! Can you help confirm or deny the quantitative efficacy of this equation?