Confronting braneworld cosmology with supernova data and baryon oscillations

Braneworld cosmology has several attractive and distinctive features. For instance the effective equation of state in braneworld models can be both quintessencelike ($w_0\ge -1$) as well as phantomlike ($w_0\le -1$). Models with $w_0\ge -1$ ($w_0\le -1$) are referred to as Brane 2 (Brane 1) and correspond to complementary embeddings of the brane in the bulk. (The equation of state in Brane 1 can successfully cross the “phantom divide“ at $w=-1$.) In this paper we compare the predictions of braneworld models to two recently released supernova data sets: the “Gold” data (Riess et al., 2004) and the data from the Supernova Legacy Survey (SNLS) (Astier et al., 2005). We also incorporate the recent discovery of the baryon acoustic peak in the Sloan Digital Sky Survey (Eisenstein et al., 2005) into our analysis. Our main results are that braneworld models satisfy both sets of SNe data. Brane 1 (with $w_0\le -1$) shows very good agreement with data for values of the matter density bounded from below: ${\Omega }_{0\mathrm{m}}\gtrsim 0.25$ (Gold) and ${\Omega }_{0\mathrm{m}}\gtrsim 0.2$ (SNLS). On the other hand Brane 2 (with $w_0\ge -1$) shows excellent agreement with data for values of the matter density which are bounded from above: ${\Omega }_{0\mathrm{m}}\lesssim 0.45$ (Gold) and ${\Omega }_{0\mathrm{m}}\lesssim 0.35$ (SNLS). The DGP model is excluded at $3\sigma$ by SNLS and at $1\sigma$ by the Gold dataset. Braneworld models with future “quiescent” singularities (at which the Hubble parameter and the matter density remain finite but higher derivatives of the expansion factor diverge) are excluded by both datasets.

Figure 1

The reduced ${\chi }^2$ per degree of freedom as a function of ${\Omega }_{0\mathrm{m}}$, marginalized over ${\Omega }_{\ell }$, ${\Omega }_{{\Lambda }_{\mathrm{b}}}$, $H_0$ for Brane 1 (top) and Brane 2 (bottom). The left panel shows results for the Gold Supernova data while the right panel shows results for the SNLS data. The dashed line is each panel is obtained by using supernova data alone, while the solid line uses both SNe data and the baryon oscillation peak.

Figure 2

The redshift variation of the effective equation of state $w(z)$ for the Brane 1 (top panel) and Brane 2 (bottom panel) models using the Gold $+$ BAO (left panel) and SNLS $+$ BAO (right panel) datasets. The light gray contours denote the $1\sigma$ errors around the best-fit, and the dashed line represents $\Lambda \mathrm{CDM}$, which is the upper (lower) limit for $w(z)$ for the Brane 1 (Brane 2) model. In the top right panel, the thick solid line represents the best-fit for the SNLS $+$ BAO data for the Brane 1 model. For the other three cases, the best-fit is at the $\Lambda \mathrm{CDM}$ line. We see that the behavior of the effective equation of state of the braneworld models can be markedly different from $\Lambda \mathrm{CDM}$ within $1\sigma$ even for the small values of ${\Omega }_{\ell }$ allowed by the data, especially for Brane 1. For the Gold data, which extends to higher redshifts, we can even see the existence of a pole in the effective equation of state for the Brane 1 models.

Figure 3

Confidence levels in the ${\Omega }_{0\mathrm{m}}-{\Omega }_{\ell }$ plane for Brane 1 (top) and Brane 2 (bottom). $H_0$ is marginalized over and ${\Omega }_{{\Lambda }_{\mathrm{b}}}$ is fixed at the best-fit value of ${\Omega }_{{\Lambda }_{\mathrm{b}}}=0$. The left panel shows results for the Gold Supernova data while the right panel shows results for the SNLS data. The solid lines in each panel represent the 1, 2, $3\sigma$ confidence levels obtained by using supernova data alone, while the dashed lines are the 1, 2, $3\sigma$ contours for the baryon oscillation peak. The light gray, medium gray and dark gray contours represent the 1, 2, $3\sigma$ confidence levels when the supernova data is used in conjunction with the baryon oscillation peak. The region to the right of the thick dotted line in the lower panels represents Brane 2 models which will undergo a future “quiescent” singularity. The thick solid line in the lower panels represents the DGP model.