A Comparison of Cosmological Parameters Determined from CMB Temperature Power Spectra from the South Pole Telescope and the Planck Satellite

TL;DR

The paper tests the robustness of ΛCDM by comparing cosmological parameters inferred from Planck full-sky and SPT-SZ CMB temperature bandpowers within the overlapping sky region and a restricted multipole range. It finds a modest tension when using full data, but demonstrates strong consistency when analyses are confined to common modes, suggesting no significant systematics in either dataset for those modes. The residual differences originate from high-ℓ SPT data and sky-area differences, with the tilt between in-patch and full-sky spectra largely affecting A_s e^{-2τ} and n_s, and high-ℓ data driving shifts in Ω_m h^2, Ω_b h^2, and H0. Overall, the results support ΛCDM within the tested regime, though mild tensions in broader comparisons motivate future CMB polarization observations to further test the model.

Abstract

The Planck cosmic microwave background (CMB) temperature data are best fit with a LCDM model that is in mild tension with constraints from other cosmological probes. The South Pole Telescope (SPT) 2540 $\text{deg}^2$ SPT-SZ survey offers measurements on sub-degree angular scales (multipoles $650 \leq \ell \leq 2500$) with sufficient precision to use as an independent check of the Planck data. Here we build on the recent joint analysis of the SPT-SZ and Planck data in \citet{hou17} by comparing LCDM parameter estimates using the temperature power spectrum from both data sets in the SPT-SZ survey region. We also restrict the multipole range used in parameter fitting to focus on modes measured well by both SPT and Planck, thereby greatly reducing sample variance as a driver of parameter differences and creating a stringent test for systematic errors. We find no evidence of systematic errors from such tests. When we expand the maximum multipole of SPT data used, we see low-significance shifts in the angular scale of the sound horizon and the physical baryon and cold dark matter densities, with a resulting trend to higher Hubble constant. When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky data but keep the multipole range restricted, we find differences in the parameters $n_s$ and $A_se^{-2τ}$. We perform further checks, investigating instrumental effects and modeling assumptions, and we find no evidence that the effects investigated are responsible for any of the parameter shifts. Taken together, these tests reveal no evidence for systematic errors in SPT or Planck data in the overlapping sky coverage and multipole range and, at most, weak evidence for a breakdown of LCDM or systematic errors influencing either the Planck data outside the SPT-SZ survey area or the SPT data at $\ell >2000$.

Figures (7)

• Figure 1: The parameter estimates for S13, S13* (obtained from the same bandpowers as S13 but with the likelihood modifications discussed in Section \ref{['sec:likechange']}), and $150\times 150$ (H17). The vertical bars are the $1\sigma$ PlanckFS parameter constraints. The estimates are based on the multipole range of $650\leq \ell \leq3000$. The shift in $A_se^{-2\tau}$ and the reduction in the error bar on that parameter combination, between S13 and S13*, come from a combination of the new calibration constraint from H17 and the correction of a bias in the calibration uncertainty treatment. The shift in $n_s$ comes from the correction of the beam uncertainty bias. The shift in $\theta_{MC}$ is primarily due to the inclusion of aberration effects.
• Figure 2: The parameter estimates for the three sets of in-patch bandpowers for various $\ell_{\rm{max}}$ values. The estimates are based on the multipole range of $650\leq\ell\leq\ell_{\rm{max}}$. There is a noticeable trend in the $150\times150$ density parameters towards better agreement with PlanckFS as $\ell_{\rm{max}}$ is lowered.
• Figure 3: The fractional difference between the in-patch bandpowers and a PlanckFS best-fit model. The two panels are split at $\ell=1800$ to accommodate the growth in the $143\times143$ and $150\times143$ errorbars beyond this point. The solid curves are the best-fit models of the in-patch bandpowers divided by the best-fit PlanckFS model. Foregrounds have been subtracted. Foreground and beam uncertainty are not included in the error bars.
• Figure 4: The $\chi^2$ distributions for the three simulation differences. The vertical purple line marks the $\chi^2$ value from the data. The dashed line is a $\chi^2$ distribution for five degrees of freedom. The $\chi^2$ values are based on the multipole range of $650\leq \ell \leq2000$.
• Figure 5: This plot shows posterior distributions for parameter differences for several different tests. In all cases, contours indicate the 68$\%$ and 95$\%$ confidence regions. The dashed lines correspond to $\Delta=0$. Lower triangle: The posterior distributions for $150\times150$, $150\times143$, both with $\ell_{\rm{max}} = 2000$, and PlanckFS. Each distribution has the PlanckFS best-fit values subtracted. Upper triangle: Contours indicate the posterior distributions from simulations for $150\times150 - 150\times143$ with $\ell_{\rm{max}} = 2000$, and black stars indicate the parameter difference values from the same comparison in the data. It is visually apparent that this comparison constitutes a much more stringent consistency test than comparing to PlanckFS; in fact, this comparison reduces the parameter volume by a factor of $300$ (see text for details). The observed consistency provides strong evidence against a systematic difference in the modes measured in common between the two experiments.