Figure 1

The left panels show the transfer function $T(k)=|{\Delta }_k/{\Delta }_k^{\Lambda \mathrm{CDM}}(z=2000){|}^2$ evaluated today ($z=0$) for wave number $k$ (in $h{\mathrm{Mpc}}^{-1}$ units) in the range 0.005 to 0.3 for the initial condition sets I, II and III as described in the bulk of this investigation. The transfer functions $T(k)$ on the left panels have been normalized in such a way that the curves coincide on large scales. On the central and right panels we present the corresponding linear matter power spectra $P(k)$ for $\Lambda \mathrm{CDM}$ and $R^n$ models for $n=1.1$, 1.2, 1.27, 1.29, 1.3, 1.31, 1.33 and 1.4. Data correspond to SDSS 2006 [37] (central panel) and SDSS-III data [38] (right panel), respectively. All the power spectra were assumed to have an arbitrary overall normalization at the scale $k=0.01h{\mathrm{Mpc}}^{-1}$ (central panel) and $k=0.02h{\mathrm{Mpc}}^{-1}$ (right panel) in order to find the best fit to the data. Conditions I and II lead to power spectra in complete disagreement with the observed data. Conditions III, due to the almost flatness of the spectra in the range covered by data, present a good fit to the data. On the bottom panels (central and right) we show in a window the relative discrepancy between the $\Lambda \mathrm{CDM}$ and the $R^n$ fits power spectra for every studied exponent. For SDSS 2006 data, the smallest discrepancy in scales $k>3\times {10}^{-2}h{\mathrm{Mpc}}^{-1}$ happens for $n=1.1$, whereas for smaller scales, all the remaining values of $n$ provide a similar relative error around $5\times {10}^{-2}$. For DR9 SDSS-III data, the smallest discrepancy (order ${10}^{-5}$) happens for $n=1.3$ in the whole scale range despite some punctual values of $k$ where other exponents may present smaller relative errors with respect to $\Lambda \mathrm{CDM}$, whereas for smaller scales, all the remaining values of $n$ provide a similar relative error around $5\times {10}^{-2}$.Reuse & Permissions

Figure 2

Saddle-point analysis: scale dependence of the transfer function $T(k)=|{\Delta }_k/{\Delta }_k^{\Lambda \mathrm{CDM}}(z=2000){|}^2$ evaluated today ($z=0$) for wave number $k$ (in $h{\mathrm{Mpc}}^{-1}$ units) in the range 0.0001 to 0.1 for the initial same conditions I, II and III used in the rest of this investigation. The transfer functions have been normalized in such a way that the curves coincide on large scales. Both on very large and on very small scales, the $\Delta$ becomes $k$ independent, so that the evolution of the perturbations does not change as a function of scale and the transfer function is consequently scale invariant. On intermediate scales the curvature fluid causes the oscillations. The result is a considerable loss of power for a relatively small variation of the parameter $n$. As before the shape and amplitudes (i.e., the increasing or decreasing behavior with $k$) of the transfer functions depend on the initial conditions I (left), II (center) and III (right). For example, when $n=1.27$ we have decreasing behavior for I and II but increasing behavior for III.Reuse & Permissions