N-Body Simulations of DGP and Degravitation Theories

TL;DR

The paper investigates infrared-modified gravity from infinite-volume extra dimensions (DGP and cascading gravity) using N-body simulations to study structure formation with a $\Lambda$CDM background. Gravity is modified by a density-dependent scalar longitudinal mode $\pi$, yielding a fifth force encoded by a propagator $\frac{1}{k^2 + r_c^{-2(1-\alpha)}k^{2\alpha}}$ and filtered by the Vainshtein mechanism; the study demonstrates enhanced clustering across a broad range of scales, especially in mildly nonlinear regimes. A standard nonlinear fitting approach (Smith et al.) overpredicts power in these models, but a recalibrated Halofit fit with new coefficients captures the simulated power spectra, while bias uncertainties can still reconcile the models with SDSS data for plausible $r_c$. The results provide a practical framework for testing higher-dimensional gravity with large-scale structure, highlighting the role of global and local Vainshtein screening and suggesting observational avenues such as bulk flows and weak lensing for future constraints.

Abstract

We perform N-body simulations of theories with infinite-volume extra dimensions, such as the Dvali-Gabadadze-Porrati (DGP) model and its higher-dimensional generalizations, where 4D gravity is mediated by massive gravitons. The longitudinal mode of these gravitons mediates an extra scalar force, which we model as a density-dependent modification to the Poisson equation. This enhances gravitational clustering, particularly on scales that have undergone mild nonlinear processing. While the standard non-linear fitting algorithm of Smith et al. overestimates this power enhancement on non-linear scales, we present a modified fitting formula that offers a remarkably good fit to our power spectra. Due to the uncertainty in galaxy bias, our results are consistent with precision power spectrum determinations from galaxy redshift surveys, even for graviton Compton wavelengths as small as 300 Mpc. Our model is sufficiently general that we expect it to capture the phenomenology of a wide class of related higher-dimensional gravity scenarios.

Figures (14)

• Figure 1: Fractional difference between the power spectra for degravitation/cascading models ($\alpha = 0$) with graviton Compton wavelength of $r_c=300$ Mpc (blue dashed) and $r_c = 500$ Mpc (black solid) and that of standard gravity, without normalizing to data. The dash-dotted line is the expected difference from linear perturbation theory. The dotted line is the expected difference assuming the Smith et al. procedure Smith:2002dz for including nonlinear effects.
• Figure 2: Kinetic energy density at $z=0$ in a slice of depth 31.25 $h^{-1}$Mpc from a pair of 400 $h^{-1}$Mpc simulations with the same initial conditions, evolved according to standard gravity on the left and a degravitation/cascading model ($\alpha = 0$, $r_c = 300$ Mpc) on the right. The units displayed on the scale are arbitrary but common to both panels. We plot kinetic energy density, rather than simple overdensity, because the density enhancement in these models is too subtle to detect readily by eye in such a plot. Kinetic energy density, however, is enhanced significantly by the greater gravitational force felt by the particles.
• Figure 3: Power spectra for $r_c=300$ Mpc (blue dashed), $r_c = 500$ Mpc (black solid) and standard gravity (red dash-dotted), each separately normalized to the Sloan Digital Sky Survey main galaxy data sloan (data points).This figure demonstrates that the apparent difference among the power spectra, as viewed via galaxy redshift surveys, is small, given the uncertainty in galaxy bias. Compared with the bias of the standard gravity power spectrum, the modified spectra biases for $r_c=$ 300 (500) Mpc are 57% (65%) relative to that needed for the standard gravity results.
• Figure 5: Different growth regimes as function of scale factor $a$ and comoving wavenumber $k$. Colored regions correspond to modes inside the horizon today. At early times, $H > r_c^{-1}$, growth proceeds as in general relativity (Green region); for $H < r_c^{-1}$ and on scales smaller than the graviton Compton wavelength ($k> a/r_c$), growth is enhanced thanks to the helicity-0 mode (Blue region); on large scales, $k> a/r_c$, the graviton mass suppresses growth (Red region). The Vainshtein effect is not included here.
• Figure 6: This plot demonstrates how a full range power spectrum is assembled from our four overlapping simulation boxes. The vertical dashed lines indicate the half Nyquist frequencies for the four boxes. The orange, black, blue, and red circles represent the averaged power spectra for the 800, 400, 200, and 100 $h^{-1}$Mpc boxes, respectively. The simulation pictured is that for $r_c=500$ Mpc in the degravitation model ($\alpha = 0$).