Constraints on Cosmology from the Cosmic Microwave Background Power Spectrum of the 2500 ${\rm deg}^2$ SPT-SZ Survey

TL;DR

This study leverages the SPT-SZ CMB power spectrum, in combination with WMAP7 and low-redshift probes (BAO, $H_0$, SNe, LRG power spectrum, and SZ clusters), to test extensions to the standard $\Lambda$CDM cosmology. By exploring $\sum m_\\nu$, $dn_s/d\ln k$, $N_{\\rm eff}$, $Y_p$, and $\\Omega_{\\rm e}$ (and key two-parameter combos), the authors diagnose how well current data accommodate a scale-dependent tilt and where tensions among datasets lie. The results show a mild preference for negative running and higher-than-BBN helium in some fits, and a stronger case for extra relativistic species and massive neutrinos when including low-redshift information, with the most consistent cross-dataset picture arising in the $N_{\\rm eff}$+$\sum m_\\nu$ space. Overall, the evidence for new physics beyond $\Lambda$CDM is suggestive but not definitive, highlighting the value of high-resolution CMB data and the potential of Planck and polarization measurements to clarify these hints.

Abstract

We explore extensions to the $Λ$CDM cosmology using measurements of the cosmic microwave background (CMB) from the recent SPT-SZ survey, along with data from WMAP7 and measurements of $H_0$ and BAO. We check for consistency within $Λ$CDM between these datasets, and find some tension. The CMB alone gives weak support to physics beyond $Λ$CDM, due to a slight trend relative to $Λ$CDM of decreasing power towards smaller angular scales. While it may be due to statistical fluctuation, this trend could also be explained by several extensions. We consider running index (nrun), as well as two extensions that modify the damping tail power (the primordial helium abundance $Y_p$ and the effective number of neutrino species $N_{\rm eff}$) and one that modifies the large-scale power due to the ISW effect (the sum of neutrino masses $\sum m_ν$). These extensions have similar observational consequences and are partially degenerate when considered simultaneously. Of the 6 one-parameter extensions considered, we find CMB to have the largest preference for nrun with -0.046<nrun<-0.003 at 95% confidence, which strengthens to a 2.7$σ$ indication of nrun<0 from CMB+BAO+$H_0$. Detectable non-zero nrun is difficult to explain in the context of single-field, slow-roll inflation models. We find $N_{\rm eff}=3.62\pm0.48$ for the CMB, which tightens to $N_{\rm eff}=3.71\pm0.35$ from CMB+BAO+$H_0$. Larger values of $N_{\rm eff}$ relieve the mild tension between CMB, BAO and $H_0$. When the SZ selected galaxy cluster abundances ($\rm{SPT_{CL}}$) data are also included, we obtain $N_{\rm eff}=3.29\pm0.31$. Allowing for $\sum m_ν$ gives a 3$σ$ detection of $\sum m_ν$>0 from CMB+BAO+$H_0$+$\rm{SPT_{CL}}$. The median value is $(0.32\pm0.11)$ eV, a factor of six above the lower bound set by neutrino oscillation observations. ... [abridged]

Figures (20)

• Figure 1: Upper: the SPT bandpowers from S12 (dark blue) and WMAP7 TT bandpowers (red) with $l \in [500, 3000]$. The solid curve shows the best-fit $\Lambda{\rm CDM}$ model including the best-fit extragalactic foreground components with priors for the combination of SPT and WMAP7 data. An additional normalization factor of $l^2$ has been applied to enhance the feature of the CMB damping tail. Lower: the residual between the data and the best-fit $\Lambda{\rm CDM}$ model with extragalactic foregrounds. As discussed in S12, the data are consistent with the standard cosmology.
• Figure 2: This figure illustrates the agreement between parameter values derived from the SPT and WMAP7 bandpowers. For each $\Lambda{\rm CDM}$ parameter, we plot the fractional change in the parameter, defined by ($\alpha_{\rm SPT}/\alpha_{WMAP7} - 1$), and the error bar for this quantity. Following S12, the amplitude of scalar perturbations, $\Delta_R^2$, is evaluated at $k=0.05$ Mpc$^{-1}$. The optical depth to reionization is not plotted, as a WMAP7-based prior is used in the fits to the SPT bandpowers. The most significant shift is to the sound horizon scale which increases by $1.5\,\sigma$.
• Figure 3: Here we illustrate the degree of consistency between the CMB data and the two external datasets which are in the most tension: BOSS and $H_{0}$. The solid lines mark the 1 and $2\,\sigma$ contours from the CMB data in the $H_0 - r_s/D_V(0.57)$ plane, while the color encodes the value of $\Omega_m h^2$, as shown in the color scale on the right. From left to right, the CMB data used is WMAP7, SPT+$\tau$, and SPT+WMAP7. The horizontal solid and dashed lines mark the central value and $1\,\sigma$ region for the BOSS BAO measurement, while the vertical lines do the same for $H_{0}$. The joint 1 and $2\,\sigma$ likelihood regions for BOSS+$H_0$ measurements are denoted by the dark and light grey shaded contours.
• Figure 4: This figure expands Figure \ref{['fig:lcdm_baoh0_ommh2']} to investigate the consistency between the CMB, ${\rm BAO}_{\rm BOSS}$, and $H_{0}$ datasets in one-parameter extensions to $\Lambda{\rm CDM}$. Each panel shows the $H_{0} - r_s/D_V(0.57)$ plane for a different extension. The colored dots are samples drawn from the SPT+WMAP7 MCMC chain, with the color coding reflecting the value of the extension parameter, as shown in the color scales on the right. The horizontal solid and dashed lines mark the central value and $1\,\sigma$ region for the ${\rm BAO}_{\rm BOSS}$ measurement, while the vertical lines do the same for $H_{0}$. The joint 1 and $2\,\sigma$ likelihood region for ${\rm BAO}_{\rm BOSS}$+$H_0$ measurements is denoted by the dark and light grey shaded contours. The blue (red) contours overlaid show the 68% and 95% confidence regions for CMB+BAO (CMB+$H_0$). Varying the effective number of neutrino species leads to the best agreement between the CMB, ${\rm BAO}_{\rm BOSS}$, and $H_{0}$.
• Figure 5: The impact of the angular diameter distance to last scattering, $D_A$, and the lensing information on the curvature constraint from the CMB. The contours show the 68% and 95% C.L. contours when lensing information is included. The colored points are samples from the posterior distribution after marginalzing over $A_L$, which effectively removes all lensing information. The allowed range of $C_{100}^{\phi\phi}$ values remains finite in the absence of lensing information, because the CMB still places (weaker) constraints on the $\Lambda{\rm CDM}$+$\Omega_k$ model parameters. The color reflects the curvature value as indicated by the color bar on the right side of the plot. The lensing sensitivity of the data is clearly crucial to the curvature constraint from the CMB data.