Observational constraints on modified gravity models and the Poincaré dodecahedral topology

We study observational constraints on models that account for the accelerated expansion of the universe via infrared modifications to general relativity, namely, the Dvali-Gabadadze-Porrati braneworld model as well as the Dvali-Turner and Cardassian models. We find that significant constraints can be placed on the parameters of each model using type Ia supernovae data together with the baryon acoustic peak in the large-scale correlation function of the Sloan Digital Sky Survey of luminous red galaxies and the Cosmic Microwave Background Radiation shift parameter data. Moreover, by considering the Poincaré dodecahedral space as the circles-in-the-sky observable spatial topology, we show that the detection of a such a nontrivial topology would provide relevant additional constraints, particularly on the curvature parameter, for all models.

Figure 1

A schematic illustration of two antipodal matching circles in the LSS. These pair of circles come about in all globally homogeneous positively-curved manifolds with a circles-in-the-sky detectable topology. The relation between the angular radius $\gamma$, angular sides $r_{\mathrm{inj}}$ and ${\chi }_{\mathrm{lss}}$ is given by the following Napier’s rule for spherical triangles, $\cos \gamma =\tan r_{\mathrm{inj}}\cot {\chi }_{\mathrm{lss}}$.

Figure 2

Confidence contours (68.3%, 95.4% and 99.7%) in the ${\Omega }_m-{\Omega }_k$ plane for the $\Lambda \mathrm{CDM}$ (top) and DGP (bottom) models obtained with the SNe Ia gold sample plus the SDSS acoustic peak data and CMBR shift parameter (dashed lines). Also shown are the contours obtained assuming in addition a $\mathcal{D}$ space topology with $\gamma =50°\pm 6°$.

Figure 3

Confidence contours (68.3%, 95.4% and 99.7%) for the DT model, in the ${\Omega }_m-\beta$ and ${\Omega }_k-\beta$ planes, obtained with the $\mathrm{SN}+\mathrm{SDSS}+\mathrm{CMB}$ data (first and third plots) and including also a $\mathcal{D}$ space topology with $\gamma =50°\pm 6°$ (second and fourth plots). ${\Omega }_k$ or ${\Omega }_m$ are fixed at the value that minimizes the ${\chi }^2$.

Figure 4

Confidence contours (68.3%, 95.4% and 99.7%) for the Cardassian model, in the ${\Omega }_m-n$ and ${\Omega }_k-n$ planes, obtained with the $\mathrm{SN}+\mathrm{BAO}+\mathrm{CMB}$ data (first and third plots) and including also a $\mathcal{D}$ space topology with $\gamma =50°\pm 6°$ (second and fourth plots). ${\Omega }_k$ or ${\Omega }_m$ are fixed at the value that minimizes the ${\chi }^2$.

Figure 5

Lines of constant angular radius, $\gamma$, in the ${\Omega }_k-{\Omega }_m$ plane for the DGP (solid lines) and $\Lambda \mathrm{CDM}$ (dashed lines) models.