Figures below show the differences in the Flux Power Spectrum measured in our simulations compared to the observational data. The differences are quantified by \(\chi^2\) defined as:

\[\chi^{2} = \sum_{i}^N \left[ \frac{ P(k_i)^{\mathrm{observ}} - P(k_i)^{\mathrm{model}} } { \sigma_i^{\mathrm{observ}} } \right]^{2}\]

The reduced error \(\chi^2_{\nu, \mathrm{P19}}\) and \(\chi^2_{\nu, \mathrm{HM12}}\) shown in the figures for each snapshot are computed as:

\[\chi^2_{\nu} = \frac{ \chi^2 }{ N } }\]

For the small scale comparison the scales selected are \(0.01 \leq k \leq 0.1 \, \mathrm{s} \, \mathrm{km}^{-1}\) and the measurements of \(\chi^2\) is computed separately for each of the observational data sets.

The distribution of \(\chi^2_{\nu}\) for the two models is summarized in the following figure:

For \(2\lesssim z \lesssim 4.5\), \(\langle \chi^2_\nu \rangle \sim 2\) for the P19 model compared to \(\langle \chi^2_\nu \rangle \sim 8\) for the HM12 model

Now comparing in the \(k \leq 0.01 \, \mathrm{s} \, \mathrm{km}^{-1}\) range:

For the large scale comparison with the eBOSS data the differences are much larger

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