Constraining Dvali-Gabadadze-Porrati gravity from observational data

The accelerating expansion of our Universe at present could be driven by an unknown energy component (dark energy) or a modification of general relativity (modified gravity). In this paper we revisit the constraints on a phenomenological model which interpolates between the pure $\Lambda \mathrm{CDM}$ model and the Dvali-Gabadadze-Porrati braneworld model with an additional parameter $\alpha$. Combining the cosmic microwave background , baryon acoustic oscillations, and type Ia supernovae, as well as some high-redshift observations, such as the gamma-ray bursts and the measurements of linear growth factors, we obtain the tight constraint on the parameter $\alpha =0.254\pm 0.153$ (68% C.L.), which implies that the flat Dvali-Gabadadze-Porrati model is incompatible with the current observations, while the pure $\Lambda \mathrm{CDM}$ model still fits the data very well. Finally, we simulate the future measurements with higher precisions and find that the constraint on $\alpha$ can be improved by a factor of 2 when compared to the present constraints.

Figure 1

The evolutions of effective energy density ${\Omega }_{\alpha }(z)$ and effective equation of state $w_{\mathrm{eff}}(z)$ for different values of $\alpha$. The black solid lines are for $\alpha =0$ ($\Lambda \mathrm{CDM}$), the red dashed lines are for $\alpha =0.25$ and the blue dotted lines are for $\alpha =1$ (DGP). And the vertical line denotes today ($z=0$).

Figure 2

The evolutions of linear growth $g(a)\equiv \delta (a)/a$ for different values of $\alpha$. The black solid lines are for $\alpha =0$ ($\Lambda \mathrm{CDM}$), the red dashed lines are for $\alpha =0.25$, and the blue dotted lines are for $\alpha =1$ (DGP).

Figure 3

The evolution of the $\beta$ term $(3\beta {)}^{-1}$ when fixing $\alpha =-2$.

Figure 4

One dimensional constraint on the parameter $\alpha$ from the different current data combinations: $\mathrm{CMB}+\mathrm{BAO}+\mathrm{SN}$ (blue dashed lines) and all real data (red solid lines).

Figure 5

68% and 95% constraints in the $({\Omega }_m,\alpha )$ plane from the current observations.

Figure 6

68% and 95% constraints in the $({\Omega }_m,\alpha )$ plane from the future measurements.