Solar system constraints on the Dvali-Gabadadze-Porrati braneworld theory of gravity

A number of proposals have been put forward to account for the observed accelerating expansion of the Universe through modifications of gravity. One specific scenario, Dvali-Gabadadze-Porrati (DGP) gravity, gives rise to a potentially observable anomaly in the solar system: all planets would exhibit a common anomalous precession, $d\omega /dt$, in excess of the prediction of general relativity. We have used the Planetary Ephemeris Program (PEP) along with planetary radar and radio tracking data to set a constraint of $|d\omega /dt{|}_{\mathrm{obs}}<0.02$ arcseconds per century on the presence of any such common precession. This sensitivity falls short of that needed to detect the estimated universal precession of $|d\omega /dt{|}_{\mathrm{DGP}}=5\times {10}^{-4}$ arcseconds per century expected in the DGP scenario. We discuss the fact that ranging data between objects that orbit in a common plane cannot constrain the DGP scenario. It is only through the relative inclinations of the planetary orbital planes that solar system ranging data have sensitivity to the DGP-like effect of universal precession. In addition, we illustrate the importance of performing a numerical evaluation of the sensitivity of the data set and model to any perturbative precession.

Figure 1

Two planets, $M_1$ and $M_2$ (assumed massless), in Keplerian orbits about a common focus (e.g., the Sun). The perihelia are labeled $p_1$ and $p_2$. The longitudes of perihelion, ${\varpi }_1$ and ${\varpi }_2$, are measured with respect to the reference direction $\widehat{\mathit{x}}$, with ${\varpi }_2$ the algebraic sum of noncoplanar angles. The true anomalies, $f_1$ and $f_2$, are measured with respect to their respective perihelia, and the true longitudes are defined by ${\Lambda }_1={\varpi }_1+f_1$ and ${\Lambda }_2={\varpi }_2+f_2$. The inclined orbit has two additional parameters, the longitude of the ascending node, $\Omega$, and the inclination, $i$. In our solar system, the planetary orbits are inclined by only a few degrees with respect to the ecliptic (the plane of the Earth’s orbit about the Sun).

Figure 2

The estimated evolution of the range difference, $\Delta \rho (t)$, between DGP and Newtonian gravity to the planets Mercury (left) and Mars (right). The difference of zero at the start of the time span reflects the freedom of the model to choose the initial anomaly $f$ of each planet independently.