Robust model comparison disfavors power law cosmology

Late-time power law expansion has been proposed as an alternative to the standard cosmological model and shown to be consistent with some low-redshift data. We test power law expansion against the standard flat $\mathrm{\Lambda }\mathrm{CDM}$ cosmology using goodness-of-fit and model comparison criteria. We consider type Ia supernova (SN Ia) data from two current compilations (JLA and Union2.1) along with a current set of baryon acoustic oscillation (BAO) measurements that includes the high-redshift Lyman-$\alpha$ forest measurements from BOSS quasars. We find that neither power law expansion nor $\mathrm{\Lambda }\mathrm{CDM}$ is strongly preferred over the other when the SN Ia and BAO data are analyzed separately but that power law expansion is strongly disfavored by the combination. We treat the $R_{\mathrm{h}}=ct$ cosmology (a constant rate of expansion) separately and find that it is conclusively disfavored by all combinations of data that include SN Ia observations and a poor overall fit when systematic errors in the SN Ia measurements are ignored, despite a recent claim to the contrary. We discuss this claim and some concerns regarding hidden model dependence in the SN Ia data.

Figure 1

Fits to an isotropic-only version of the BAO data (black points), where we use the direct isotropic measurement from BOSS CMASS ($z=0.57$) and an isotropic measurement derived from the $\mathrm{Ly}\alpha \mathrm{F}$ anisotropic measurements ($z=2.34$). We show the best fit to this modified BAO set for $\mathrm{\Lambda }\mathrm{CDM}$ with ${\mathrm{\Omega }}_m$ and $r_d$ varied (solid black), power law cosmology with $n$ and $r_d$ varied (solid blue), and power law cosmology with $n=1.5$ and only $r_d$ varied (dashed red), where the value $n=1.5$ is roughly the value required to fit the SN Ia data.

Figure 2

Hubble diagram for the JLA SN compilation, where the measured distance moduli have been standardized separately for $\mathrm{\Lambda }\mathrm{CDM}$ (blue points) and the $R_{\mathrm{h}}=ct$ cosmology (red points). The best-fit (${\mathrm{\Omega }}_m=0.29$) $\mathrm{\Lambda }\mathrm{CDM}$ model (solid blue) is plotted along with the $R_{\mathrm{h}}=ct$ model (dashed red). We show the SN data without (left panel) and with (right panel) systematic errors included. The distance moduli are binned in redshift with inverse-covariance weights.