Searching for modified growth patterns with tomographic surveys

TL;DR

The paper addresses how upcoming tomographic surveys can test modifications to gravity that alter the growth of cosmic structure beyond GR. It introduces a five-parameter, scale- and time-dependent framework for the potentials via $\mu(a,k)$ and $\gamma(a,k)$, connected to scalar-tensor theories such as $f(R)$ and Chameleon models, and forecasts constraints using a Fisher matrix approach on the combined data from GC, WL, CMB, and SNe. Key findings show that DES already yields non-trivial constraints on the modified-growth parameters and LSST considerably tighter bounds, with characteristic degeneracies between $\mu$ and $\gamma$ and strong sensitivity gains from cross-correlations and bias priors. The results demonstrate the potential of future surveys to detect or significantly limit departures from GR in the linear regime and motivate further, more model-independent analyses (e.g., PCA) and extensions to include neutrinos or dynamical dark energy.

Abstract

In alternative theories of gravity, designed to produce cosmic acceleration at the current epoch, the growth of large scale structure can be modified. We study the potential of upcoming and future tomographic surveys such as DES and LSST, with the aid of CMB and supernovae data, to detect departures from the growth of cosmic structure expected within General Relativity. We employ parametric forms to quantify the potential time- and scale-dependent variation of the effective gravitational constant, and the differences between the two Newtonian potentials. We then apply the Fisher matrix technique to forecast the errors on the modified growth parameters from galaxy clustering, weak lensing, CMB, and their cross-correlations across multiple photometric redshift bins. We find that even with conservative assumptions about the data, DES will produce non-trivial constraints on modified growth, and that LSST will do significantly better.

Figures (11)

• Figure 1: The rescaling of the Newton constant $\mu(a,k)$ and the ratio of Newtonian potentials $\gamma(a,k)$, plotted as a function of the redshift for the four fiducial models used in our Fisher analysis. The contours are lines of constant $\mu$ and $\gamma$. The first two models correspond to $f(R)$ fiducial cases, with $s=4$, the coupling $\beta_1=4/3$ and the mass scale of $\lambda_2^2=10^3 \rm{Mpc}^2$ for model I and $\lambda_2^2=10^4 \rm{Mpc}^2$ for model II. Models III and IV correspond to Chameleon theories with $s=2$, the coupling $\beta_1=9/8$ and the mass scale of $\lambda_2^2=10^3 \rm{Mpc}^2$ and $\lambda_2^2=10^4\rm{Mpc}^2$, respectively.
• Figure 2: A schematic representation of all the $2$-point correlations used in this work. $M$ is the number of redshift bins used for galaxy counts (GC), $N$ is the number of bins used for weak lensing (WL), $T$ and $E$ stand for temperature and E-mode polarization of the CMB. The white blocks corresponding to the cross-correlations between E and G$_i$, and between E and WL$_i$ indicate that those cross-correlations were not considered in this work.
• Figure 3: Some representative growth functions (time evolution divided by the corresponding initial values, set at $z=30$) that contribute to the integration kernels of the $C_{\ell}$'s for ISW, WL, GC, and their cross-correlations. The corresponding $C_{\ell}$'s are shown in Fig. \ref{['fig:fid_cl']}. The solid line corresponds to GR and the other lines are for Model II (an $f(R)$ fiducial model described in Sec. \ref{['theory']}). The different types of line types/colors represent four different $k$ modes and are explained in the legend.
• Figure 4: Dimensionless power spectra $\ell(\ell+1)C_{\ell}^{XY}/2\pi$, where $X,Y=\{T,GC,WL\}$ for GR (solid line) and for our Models I-IV (line types explained in the legend), for Planck and a few representative choices of GC and WL redshift bin pairs expected from LSST. On the plots, $\epsilon_i$ stands for the $i$-th WL bin, and $g_i$ stands for the $i$-th GC bin. The assumed redshift distribution of WL and GC sources for LSST, along with their partition into photometric bins, is shown in Fig. \ref{['Fig:des_lsst_window']}. For each group of spectra, we pick one with the largest deviation from the GR prediction and plot its relative difference w.r.t GR in the lower part of each panel. The straight dashed lines indicate the approximate scale at which non-linear corrections become significant. We have only used the parts of the spectra that can be accurately described by linear theory.
• Figure 5: The assumed redshift distribution and the partition into photometric bins for the galaxy counts (GC) and weak lensing (WL) for DES and LSST. The bias parameter for each GC bin is shown with a thin red solid line in the lower panel.