# Hypergeometrical Universe

## Second Peer Review - 3

But putting all of that aside, I will take a narrow view of the manuscript. It proposes a distance(redshift) relation, and we can quantitatively see how well this matches the data. The proper way to do this is not by making plots, it is to compute chi^2 values from the distance moduli (mu) and covariance matrix in Union2.1:

chi^2 = (mu_observed - M - mu_theory)^T . (covariance matrix^-1) . (mu_observed - M - mu_theory)

where M is a constant that can be fit (the host-mass relation can also be fit, but failing to do so won’t affect the results much). After computing chi^2 values for LambdaCDM and HU, you can see if HU is favored or disfavored by the data compared to LambdaCDM. By my eye, HU is significantly worse, but the chi^2 values will say for sure.

Answer: In trying to give current Cosmology their best shot, I tried to use the newest Cosmological Model I could find. I was directed to use Planck-15 python package. Here is the fitting code:

from astropy.cosmology import Planck15

from astropy import constants, units

def d_planck15(z):

R0 = (constants.c)/(Planck15.H0)

d_L = (Planck15.luminosity_distance(z))/R0.to(units.Mpc)

plt.plot(z, d_L)

R0=http://R0.to(units.lyr)/1e9

return R0, d_L

z = np.arange(0.0,1.5,0.01)

R0, d_L=d_planck15(z)

This was an honest attempt to represent Friedmann-Lemaitre Model applied to the Supernova Survey. From my research, it implements this equation:

with six parameters (if one excludes H${}_{0}$). By comparison, HU predicts the data without any parameters (if one excludes H${}_{0}$, which I took from the literature as being 72).

The quality of the Friedmann-Lemaitre fitting is not relevant since the main thrust of my article is to consider that that data might be wrong (biased by the lack of an epoch-dependent G).

In any event, here is the results from the requested calculation:

The Power Divergence is 1.33 and the p-value is 1.0.

The nice but uninformative figures are here:

To my unbiased eyes..:) These predictions (not fittings) are better that the six parameters Friedmann-Lemaitre fitting. One should emphasize that HU has no parameters and FL has six!

I have to say that this is a semi-log plot and shouldn’t be compared with the distance vs z plot below.

Below are the two placed in the same plot:

I suspect the reviewer thought that HU data was intended to fit the raw data (with x). They might not had realized that I corrected the data and displayed it below.

PS - By the way, I know that it is incorrect to say that a data analysis is wrong or biased because it didn’t consider an epoch-dependent G. The reason I say that is because the theory has been censored for 12 years without a peer-review and thus not using my epoch-dependent G is a matter of choice. This is my first one and I am thankful I can reply to it here.

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