Probing Newton's Constant on Vast Scales: DGP Gravity, Cosmic Acceleration and Large Scale Structure

TL;DR

This work probes whether Dvali–Gabadadze–Porrati (DGP) gravity can explain cosmic acceleration without dark energy and how it alters large-scale structure. It derives the subhorizon gravitational force law in a cosmological DGP background, showing a residual repulsive contribution that suppresses growth via an effective, time-dependent Newton constant $G_{\rm eff}=G\left(1+\frac{1}{3\beta}\right)$ and a modified expansion history $H^2 \pm \frac{H}{r_0} = \frac{8\pi}{3M_P^2}\rho$. Linear growth is suppressed relative to GR and dark-energy models with the same expansion history, while nonlinear collapse resembles GR predictions but with different critical density thresholds; importantly, the late-time ISW effect remains unchanged relative to a dark-energy mimic on subhorizon scales. The authors find that matching acceleration in DGP tends to drive the present-day fluctuation amplitude $\sigma_8$ to $\lesssim 0.8$, which is in tension with observations such as galaxy clustering, suggesting a robust challenge for DGP as a unified explanation for both acceleration and structure formation. Overall, the paper provides a framework to test DGP gravity against large-scale structure data and highlights potential observational tensions that require more detailed modeling.

Abstract

The nature of the fuel that drives today's cosmic acceleration is an open and tantalizing mystery. The braneworld theory of Dvali, Gabadadze, and Porrati (DGP) provides a context where late-time acceleration is driven not by some energy-momentum component (dark energy), but rather is the manifestation of the excruciatingly slow leakage of gravity off our four-dimensional world into an extra dimension. At the same time, DGP gravity alters the gravitational force law in a specific and dramatic way at cosmologically accessible scales. We derive the DGP gravitational force law in a cosmological setting for spherical perturbations at subhorizon scales and compute the growth of large-scale structure. We find that a residual repulsive force at large distances gives rise to a suppression of the growth of density and velocity perturbations. Explaining the cosmic acceleration in this framework leads to a present day fluctuation power spectrum normalization sigma_8 <= 0.8 at about the two-sigma level, in contrast with observations. We discuss further theoretical work necessary to go beyond our approximations to confirm these results.

Figures (3)

• Figure 1: The top panel shows the ratio of the growth factors $D_+$ (dashed lines) in DGP gravity [Eq. (\ref{['growth']})] and a model of dark energy (DE) with an equation of state such that it gives rise to the same expansion history (i.e. given by Eq. (\ref{['Fried']}), but where the force law is still given by general relativity). The upper line corresponds to $\Omega_m^0=0.3$, the lower one to $\Omega_m^0=0.2$. The solid lines show the analogous result for velocity perturbations factors $f$. The bottom panel shows the growth factors as a function of redshift for models with different expansion histories, corresponding to (from top to bottom) $\Lambda$CDM ($\Omega_m^0=0.3$), and DGP gravity with $\Omega_m^0=0.3,0.2$ respectively.
• Figure 2: Numerical solution of the spherical collapse. The left panel shows the evolution for a spherical perturbation with $\delta_i=3\times 10^{-3}$ at $z_i=1000$ for $\Omega_m^0=0.3$ in DGP gravity and in $\Lambda$CDM. The right panel shows the ratio of the solutions once they are both expressed as a function of their linear density contrasts.
• Figure 3: The linear power spectrum normalization, $\sigma_8$, for DGP gravity as a function of $\Omega_m^0$. The vertical lines denote the best fit value and $68\%$ confidence level error bars from fitting to type-IA supernovae data from Deffayet:2002sp, $\Omega_m^0=0.18^{+0.07}_{-0.06}$. The other lines correspond to $\sigma_8$ as a function of $\Omega_m^0$ obtained by evolving the primordial spectrum as determined by WMAP by the DGP growth factor. See text for details.