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# System prepended metadata

title: 'The fit to redshift evolution of $\delta_F$-$\rho_{DM}$:'

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# The fit to redshift evolution of $\delta_F$-$\rho_{DM}$:




$\rm \left(\frac{\rho_{\rm DM}}{\langle \rho_{\rm DM} \rangle}\right)^{sm} = p^0  \ {\delta^{sm}_F}\ {}^2 \ + \ p^1 \ \delta^{sm}_F + p^2$


The fits are :

|z| $p^0$ | $p^1$ | $p^2$ |
|--|--|--| --|
|2.3 | 18.9 +- 0.7 | 5.7 +- 0.1 | 0.96 +- 0.01 |
|2.4 | 11.5 +- 0.5 | 4.60 +- 0.05 | 0.97 +- 0.01 |
|2.6 | 13.0 +- 0.8 | 4.98 +- 0.06 | 0.99 +- 0.0  |


Fitting each coefficient with redshift :

|    | $p^0$ | $p^1$ | $p^2$ |
|----|---|---| --- |
| linear | $-23.15 \ (z-2.45) + 13.51 $ | $2.27 \ (z-2.45) - 4.98 $ | $0.12 \ (z-2.45) + 0.98$ |
| 2nd deg| $274.9 \ (z-2.45)^2 -22.12 (z-2.45) + 11.34$ | $-42 (z-2.45)^2 + 2.66 (z-2.45) + 11.34$ | $0.296 (z-2.45)^2 + 0.116 (z-2.45) + 0.97$


- The linear fit overestimates the coefficient for z = 2.45 and the second degree polynomial overfits the data points (which was expected).