Cosmological Structure Evolution and CMB Anisotropies in DGP Braneworlds

TL;DR

This paper analyzes cosmological structure formation and CMB anisotropies in the DGP braneworld model, where gravity propagates in a 5D bulk and an induced 4D Ricci term leads to a cross-over scale $r_c$ and a self-accelerating branch. The authors derive on-brane field equations, obtain a modified Friedmann equation with a square-root term, and show that linear perturbations act as a density-dependent $G_{ m eff}$, weakening the ISW effect. They perform cosmological simulations with linearized DGP and compare to LCDM, finding a suppressed ISW and modest changes to the matter power spectrum, but SN and CMB distance data jointly favor LCDM over pure DGP. The conclusions stress that, despite some improvements in low-$\ell$ CMB power, the DGP model cannot simultaneously fit expansion-history and CMB observations as well as GR with a cosmological constant.

Abstract

The braneworld model of Dvali, Gabadadze and Porrati (DGP) provides an intriguing modification of gravity at large distances and late times. By embedding a three-brane in an uncompactified extra dimension with separate Einstein-Hilbert terms for both brane and bulk, the DGP model allows for an accelerating universe at late times even in the absence of an explicit vacuum energy. We examine the evolution of cosmological perturbations on large scales in this theory. At late times, perturbations enter a DGP regime in which the effective value of Newton's constant increases as the background density diminishes. This leads to a suppression of the integrated Sachs-Wolfe effect, bringing DGP gravity into slightly better agreement with WMAP data than conventional LCDM. However, we find that this is not enough to compensate for the significantly worse fit to supernova data and the distance to the last-scattering surface in the pure DGP model. LCDM is, therefore, a better fit.

Figures (10)

• Figure 1: Value of scale factor at which the gravity driving evolution transitions from GR to linear DGP. Solid line is for Minkowski bulk ($\Omega_\Lambda = 0$), dashed for $\Omega_\Lambda = -1$. Shape of transition line is a processed dark-matter power spectrum.
• Figure 2: Evolution of Newtonian potential $\Phi$ in GR and DGP (GR--- solid lines, DGP---dashed). In DGP, the growth of the effective Newton's constant leads to a wavelength-dependent growth in the potentials at late times, as opposed to the decay observed in $\Uplambda$CDM. ($\Uplambda$CDM: concordance model; DGP: $\Omega_\Lambda = 0, \beta = 1.38$)
• Figure 3: Transfer functions in $\Uplambda$CDM and DGP ($\Omega_\Lambda = 0$, $\beta = 1.38$). The transfer function is defined here as ratio of size of initial perturbation in $\Phi$ to its final value, renormalized to 1 at large scales. In GR, the growth rate for the potential during dark-energy domination is independent of $k$, so the quantity shown here is equivalent to the usual transfer function. For DGP, the growth rate depends on $k$.
• Figure 4: Plot showing the one sigma (dark color) and three sigma (light color) range for best-fit values of $\beta$ for given values of $\Omega_\Lambda$ for CMB distance (green), SN (blue) and combined (red) For $\Omega_\Lambda$ close to 0 the preferred values for the two data sets are significantly different, leading to a poor overall fit. As $\Omega_\Lambda \rightarrow -\infty$ the preferred parameter spaces increasingly overlap. In this regime DGP is indistinguishable from GR. The table presents values of best-fit $\beta$'s for a selection of $\Omega_\Lambda$ and the $\chi^2$'s of the respective fits to combined CMB-distance and SN data. It can be clearly seen that a positive bulk cosmological constant is strongly excluded.
• Figure 5: Comparison of dark-matter power spectra for $\Uplambda$CDM (solid line) and DGP ($\Omega_\Lambda = 0, \beta = 1.38$, dashed). The spectra have been normalized to unity at $k = 10^{-3} h$ Mpc$^{-1}$. There is excess power at large scales and a power deficiency at low scales.