Stable Islands of Weak Gravity

Abstract

We present an exploration of the phenomenology of Horndeski gravity, focusing on regimes that produce weak gravity compared to General Relativity. This letter introduces a novel method to generate models of modified gravity theories that produce a specific observational behaviour while fulfilling stability criteria, without imposing a fixed parametrisation. We start from the inherently stable basis of linear Horndeski theory, implemented in the recently released Einstein-Boltzmann solver mochi_class. The time evolution of the basis functions is designed with Gaussian processes that directly include the stability and phenomenology criteria during the generation. Here, we focus on models with weak gravity that suppress the growth of Large-Scale Structure at late times. To achieve this behaviour, we mainly focus on the design of a dynamical effective Planck mass for theories with a vanishing fifth force. We find a broad range of weak-gravity islands in Horndeski theory space. We also include additional features, like a vanishing modification to gravity at $z=0$, and extend the exploration to islands of gravity with a non-zero fifth force. Finally, we show that replacing the $Λ$CDM expansion model by the DESI $w_0w_a$CDM best fit also produces stable islands of weak gravity.

Figures (4)

• Figure 1: Testing gradient stability: Terms entering \ref{['eq:cs2-terms-noSlip']} for the local-value weak-gravity model. To achieve a stable theory with $c_s^2>0$ we require the sum of all the plotted terms (in blue) to be positive at all times.
• Figure 2: $\bm{M^2}$ curves of stable no-slip models that produce weak gravity: Selection of $\Delta M^2 \equiv M^2-1$ basis functions that lead to stable weak gravity with the no-slip condition $\alpha_B = - 2 \alpha_M$. The models are built with a $\Lambda$CDM background and $\alpha_K=10^{-2}$. All curves are stable against ghost, gradient, and mathematical instabilities as tested in mochi_class. The amplitude of each $\Delta M^2$ curve is scaled to produce $\sim 12 \%$ suppression of the linear matter power spectrum (top right panel) compared to GR at $z=0$. They are shown with the corresponding no-slip quantities and the generated suppression.
• Figure 3: No-slip and beyond-no-slip models: Stable basis functions and the corresponding suppression $\mu_\infty$ from \ref{['eq:mu']} for the local-value $M^2$ model. Blue curves represent the no-slip model (with $\alpha_B = -2 \alpha_M$). We compare it to the beyond no-slip model (orange) where the sound speed $c_s^2$ is modified with a GP curve -- inducing a fifth force -- while $M^2$, $D_\mathrm{kin}$ and $\alpha_{B0}$ are kept unchanged. The dotted lines represent a beyond-no-slip local-convergence model with $M^2\approx1$ and $\alpha_M\approx0$ today.
• Figure 4: Suppression for $\Lambda$CDM and $\bm{w_0w_a}$CDM backgrounds: Effects of the no-slip (left side) and beyond-no-slip (right side) models for the local-value Planck mass shown in \ref{['fig:mu_M2_example']} on the CMB TT power spectrum and linear matter power spectrum. We show the mochi_class outputs of the MG models for two different backgrounds that are always normalised to the GR model with a $\Lambda$CDM background. Dotted lines represent a MG model with $w_0w_a$CDM background for the DESI best-fit values ($w_0 = -0.752$, $w_a = -0.86$). Coloured solid lines are used for MG models with a $\Lambda$CDM background.