Theoretical Priors On Modified Growth Parametrisations

TL;DR

The work addresses how to tell apart modified gravity from dark-energy scenarios using linear growth, by parameterising deviations with $Q(a,k)$ and $\eta(a,k)$ and recasting them into observable quantities $\Sigma$ and $\mu$. It analyzes three theoretical frameworks—Brans-Dicke modified gravity, clustering dark energy, and interacting dark energy—and shows that each yields a characteristic path in the $(\Sigma,\mu)$ plane: BD MG constrains $\Sigma=1$ with a BD-parameter dependent $\mu$, cDE can produce scale-independent but nontrivial $Q$ and $\eta$ along a one-parameter track, and IDE implies $\Sigma=\mu$ due to absence of anisotropic stress. These distinct trajectories provide theoretical priors to interpret future structure-formation data. The results demonstrate how measurements of lensing and velocity fields can reveal the underlying cause of cosmic acceleration by mapping observed $\Sigma$ and $\mu$ onto the predicted planes for MG, cDE, and IDE. This framework aims to optimize the extraction of physical insight from upcoming surveys by connecting observables to fundamental model classes via the $\Sigma$–$\mu$ plane.

Abstract

Next generation surveys will observe the large-scale structure of the Universe with unprecedented accuracy. This will enable us to test the relationships between matter over-densities, the curvature perturbation and the Newtonian potential. Any large-distance modification of gravity or exotic nature of dark energy modifies these relationships as compared to those predicted in the standard smooth dark energy model based on General Relativity. In linear theory of structure growth such modifications are often parameterised by virtue of two functions of space and time that enter the relation of the curvature perturbation to, first, the matter over-density, and second, the Newtonian potential. We investigate the predictions for these functions in Brans-Dicke theory, clustering dark energy models and interacting dark energy models. We find that each theory has a distinct path in the parameter space of modified growth. Understanding these theoretical priors on the parameterisations of modified growth is essential to reveal the nature of cosmic acceleration with the help of upcoming observations of structure formations.

Figures (4)

• Figure 1: The evolution of $Q$ and $\eta$ is presented with varying $c_P^2$ for the case of scale-invariant growth of dark energy perturbations where the anisotropic stress balances the pressure support ($f_{\sigma}=1$). Here we set $w_{de}=-0.8$ as in the sDE reference.
• Figure 2: The scale-dependence of $Q$ and $\eta$ is shown for different values of $f_\sigma$. We include the limiting cases of no anisotropic stress ($f_\sigma=0$, dash-dotted) and scale-independent growth of dark energy perturbations ($f_\sigma=1$, dotted). Here we set $w_{de}=-0.8$ and $c_P^2=1$ as in the sDE reference.
• Figure 3: The time evolution of $Q$ is presented for two different models of IDE. The left-hand side plot corresponds to Model I: $\mathcal{C}=\Gamma_c\rho_c$ with varying $\Gamma_c$ (1/Mpc). The right-hand side plot corresponds to Model II: $\mathcal{C}=\Gamma_{de}\rho_{de}$ with varying $\Gamma_{de}$ (1/Mpc).
• Figure 4: Trajectories on $\Sigma$ and $\mu$ plane of BD type MG models (solid curve), clumping dark energy (dotted curve) and interacting dark energy (dash curve).