The Phenomenology of Dvali-Gabadadze-Porrati Cosmologies

TL;DR

This review analyzes the Dvali–Gabadadze–Porrati braneworld as an infrared modification of gravity that could explain cosmic acceleration via gravity leaking into a large extra dimension. It derives the modified Friedmann equation, describes the brane–bulk geometry, and discusses observational constraints, including how the self-accelerating branch can mimic a dark-energy expansion history. A central focus is the recovery of Einstein gravity through nonlinear brane bending (Vainshtein mechanism) and the resulting phenomenology for solar-system tests, large-scale structure, and gravitational lensing. The work also surveys potential issues such as the VDVZ discontinuity, bulk leakage of perturbations, and ghost instabilities, outlining both promising avenues for empirical discrimination and the theoretical challenges ahead. Overall, DGP provides a provocative framework to test gravity in the infrared and to distinguish modified gravity from dark energy through growth, lensing, and ISW observables.

Abstract

Cosmologists today are confronted with the perplexing reality that the universe is currently accelerating in its expansion. Nevertheless, the nature of the fuel that drives today's cosmic acceleration is an open and tantalizing mystery. There exists the intriguing possibility that the acceleration is not the manifestation of yet another mysterious ingredient in the cosmic gas tank (dark energy), but rather our first real lack of understanding of gravity itself, and even possibly a signal that there might exist dimensions beyond that which we can currently observe. The braneworld model of Dvali, Gabadadze and Porrati (DGP) is a theory where gravity is altered at immense distances by the excruciatingly slow leakage of gravity off our three-dimensional Universe and, as a modified-gravity theory, has pioneered this line of investigation. I review the underlying structure of DGP gravity and those phenomenological developments relevant to cosmologists interested in a pedagogical treatment of this intriguing model.

Figures (22)

• Figure 1: DGP gravity employs the braneworld scenario. Matter and all standard model forces and particles are pinned to a strictly four-dimensional braneworld. Gravity, however, is free to explore the full five-dimensional bulk.
• Figure 2: At distances much smaller than the crossover scale $r_0$, gravity appears four-dimensional. As a graviton propagates, it's amplitude leaks into the bulk. On scales comparable to $r_0$ that amplitude is attenuated significantly, thus, revealing the extra dimension.
• Figure 3: A point source of mass $m$ is located on the brane. The gravitational constant on the brane is $G_{\rm brane} = M_P^{-2}$, whereas in the bulk $G_{\rm bulk} = M^{-3}$ (left diagram). Gravitational equipotential surfaces, however, are not particularly pathological. Near the matter source, those surfaces are lens-shaped. At distances farther from the matter source, the equipotential surfaces become increasingly spherical, asymptoting to equipotentials of a free point source in five-dimensions. I.e., in that limit the brane has no influence (right diagram).
• Figure 4: The solid curve depicts Eq. (\ref{['Fried']}) while the dotted line represents the conventional four-dimensional Friedmann equation. Two cosmological phases clearly emerge for any given spatially-homogeneous energy-momentum distribution.
• Figure 5: A schematic representation of the brane worldsheet from an inertial bulk reference frame. The bulk time coordinate, $T$, is the vertical direction, while the other directions represent all four spatial bulk coordinates, $X^i$ and $Y^5$. The big bang is located along the locus $Y^5 = T$, while the dotted surface is the future lightcone of the event located at the origin denoted by the solid dot. The curves on the brane worldsheet are examples of equal cosmological time, $\tau$, curves and each is in a plane of constant $Y^5 + T$. Figure from Ref. [28].