Fullshape power spectrum for the Symmetron modified gravity model

Abstract

We make use of the perturbation theory for modified gravity models that we developed in previous works and apply it to construct the fullshape galaxy power spectrum for the Symmetron modified gravity model. First, we study the growth rate, that is a scale dependent quantity, and compare our results with those of the $n=1 $ Hu-Sawcki (HS) model, finding that the Symmetron has a growth quite similar to the HS F6 in the wavenumber interval $0.01 \leq k \leq 0.1 $ and for redshifts where Symmetron model is viable. We also propose a growth parametrization that turns to be a good approximation for the HS and Symmetron models, with a deviation less than $0.6 \%$. To compute the RSD multipoles we employ an expansion of the velocity moments generating function that is suitable for general modified gravity models. Later, we apply the fk-Perturbation Theory (fkPT) approximation to reduce the computation time of nonlinear kernels, to find the fullshape galaxy power spectrum for the Symmetron, and study the differences with HS model. The RSD multipoles of the Symmetron result similar to those of the HS F6 model. Next, we integrate this theory to an MCMC sampler and validate our results by fitting our parameters to EZMocks to recover the parameters that bring the model to GR. We found a similar agreement in the model validation between Symmetron and F6 model, recovering the simulation cosmological parameters, and concluding that our pipeline is ready to make cosmological parameters' inference with real data.

Figures (12)

• Figure 1: Function $\mu(k,a)$ for Hu-Sawicki and Symmetron models. Left panel evaluated at $k=0.01$ and the right panel is evaluated at $k=0.1$, in units of $h~{\rm Mpc^{-1} }$. The curves correspond to Symmetron (blue) and F6 (orange) models. The transition value for Symmetron is $z_{ssb}=1$
• Figure 2: $f(k,z)$ for Hu-Sawicki $f(R)$ and Symmetron models for two $k$-bins.
• Figure 3: Comparison of the growth function for $f(R)$ and Symmetron models as function of $k$ in units of $h~{\rm Mpc^{-1} }$, for the $z$-values ($0.8, 0.5, 0$). The black line is the value for $\Lambda$CDM.
• Figure 4: Comparison of the linear growth rate for HS-$f(R)$, Symmetron, and their parametrization (eq. \ref{['fk_parameterization']}) as function of $k \in [10^{-3},0.2]$$h~{\rm Mpc^{-1} }$ at $z=0$. In the right panel we show the relative difference for each model, where the f$_{\text{MG}}$ label is for the modified gravity model and f$_{p}$ is for the parametrization.
• Figure 5: Relative difference between full kernels and fk kernels multipoles for Symmetron model with (dashed lines) and without adding counterterms (solid lines).