Measurement of the CMB temperature power spectrum and constraints on cosmology from the SPT-3G 2018 $TT$, $TE$, and $EE$ dataset

We present a sample-variance-limited measurement of the temperature power spectrum ($TT$) of the cosmic microwave background using observations of a $\sim 1500{\mathrm{deg}}^2$ field made by the SPT-3G in 2018. We report multifrequency power spectrum measurements at 95, 150, and 220 GHz covering the angular multipole range $750\le \ell <3000$. We combine this $TT$ measurement with the published polarization power spectrum measurements from the 2018 observing season and update their associated covariance matrix to complete the SPT-3G 2018 $TT/TE/EE$ dataset. This is the first analysis to present cosmological constraints from SPT $TT$, $TE$, and $EE$ power spectrum measurements jointly. We blind the cosmological results and subject the dataset to a series of consistency tests at the power spectrum and parameter level. We find excellent agreement between frequencies and spectrum types and our results are robust to the modeling of astrophysical foregrounds. We report results for $\mathrm{\Lambda }\mathrm{CDM}$ and a series of extensions, drawing on the following parameters: the amplitude of the gravitational lensing effect on primary power spectra $A_{\mathrm{L}}$, the effective number of neutrino species $N_{\mathrm{eff}}$, the primordial helium abundance $Y_{\mathrm{P}}$, and the baryon clumping factor due to primordial magnetic fields $b$. We find that the SPT-3G 2018 $TT/TE/EE$ data are well fit by $\mathrm{\Lambda }\mathrm{CDM}$ with a probability to exceed of 15%. For $\mathrm{\Lambda }\mathrm{CDM}$, we constrain the expansion rate today to $H_0=68.3\pm 1.5\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and the combined structure growth parameter to $S_8=0.797\pm 0.042$. The SPT-based results are effectively independent of Planck, and the cosmological parameter constraints from either dataset are within $<1\sigma$ of each other. The addition of temperature data to the SPT-3G $TE/EE$ power spectra improves constraints by 8–27% for each of the $\mathrm{\Lambda }\mathrm{CDM}$ cosmological parameters. When additionally fitting $A_{\mathrm{L}}$, $N_{\mathrm{eff}}$, or $N_{\mathrm{eff}}+Y_{\mathrm{P}}$, the posteriors of these parameters tighten by 5–24%. In the case of primordial magnetic fields, complete $TT/TE/EE$ power spectrum measurements are necessary to break the degeneracy between $b$ and $n_s$, the spectral index of primordial density perturbations. We report a 95% confidence upper limit from SPT-3G data of $b<1.0$. The cosmological constraints in this work are the tightest from SPT primary power spectrum measurements to date and the analysis forms a new framework for future SPT analyses.

Figure 1

Relative conditional residuals, $(D_b^{\nu \mu ,\mathrm{cond}}-{\widehat{D}}_b^{\nu \mu })/{\sigma }_b^{\nu \mu ,\mathrm{cond}}$, i.e. the difference between conditional predictions for a given set of multifrequency band powers and the measured data, divided by the square root of the diagonal of the conditional covariance. The blue shaded region corresponds to the $3\sigma$ range and the gray shaded area in the first column indicates the $TT$ angular multipole lower limit. The conditional residuals are consistent with zero, as evidenced by the PTE values indicated in the upper right corner of each panel. This speaks to the interfrequency consistency of the SPT-3G 2018 $TT/TE/EE$ dataset.

Figure 2

Relative conditional residuals, $(D_b^{XY,\mathrm{cond}}-{\widehat{D}}_b^{MV,XY})/{\sigma }_b^{XY,\mathrm{cond}}$ with $XY\in \{TT,TE,EE\}$, i.e. the difference between conditional predictions for a given set of minimum-variance band powers and the measured data, divided by the square root of the diagonal of the conditional covariance. The blue shaded region corresponds to the $3\sigma$ range and the gray shaded area in the first column indicates the $TT$ angular multipole range. The spectra used in the conditional prediction are specified in the bottom right corner of each panel and the PTE values are indicated in the top right corner of each panel. We find good agreement between the different spectra of the SPT-3G 2018 $TT/TE/EE$ dataset.

Figure 3

Parameter constraints from the full SPT-3G 2018 $TT/TE/EE$ dataset (black points) and select subsets (colored points as indicated) in $\mathrm{\Lambda }\mathrm{CDM}$. The gray boxes indicate the expected $1\sigma$ fluctuations between each subset and the full dataset, taking the shared data into account. The observed shifts between subsets and the full data are consistent with statistical fluctuations. During the blind stage of this analysis, the parameter values along the vertical axes were not shown.

Figure 4

SPT-3G 2018 multifrequency $TT/TE/EE$ band powers in colors as indicated in the legend, along with the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model to the SPT data including foregrounds (solid lines of matching color). The SPT-3G data provide a precision measurement of the CMB temperature and polarization anisotropies on intermediate and small angular scales.

Figure 5

SPT-3G 2018 minimum-variance $TT/TE/EE$ band powers (black) along with a selection of contemporary power spectrum measurements: Planck (blue) [11], SPT-SZ (green, top panel only) [42], SPTpol (green, bottom two panels only, horizontally offset for clarity) [45], ACT DR4 (orange) [4], polarbear (pink, bottom panel only) [46]. The SPT-3G 2018 best-fit CMB power spectrum is indicated in gray. The ensemble of CMB data is visually consistent and yields a high signal-to-noise measurement of the power spectrum.

Figure 6

Relative weight of each multifrequency spectrum entering the minimum-variance combination (diagonal elements of the mixing matrix). The gray shaded areas indicate the different ${\ell }_{\min }$ cuts of the $TT$ spectra. Overall, the $95\times 150\mathrm{GHz}$ and $150\times 150\mathrm{GHz}$ spectra contribute the most weight. For $TT$ data, all spectra bar the $220\times 220\mathrm{GHz}$ band powers are non-negligible at intermediate $\ell$ and the $95\times 95\mathrm{GHz}$ $TE$ data are important on large angular scales.

Figure 7

Marginalized one- and two- dimensional posterior distributions for the SPT-3G 2018 $TT/TE/EE$ dataset (blue contours), Planck (black line contours), and ACT DR4 (gray contours) in $\mathrm{\Lambda }\mathrm{CDM}$. The constraints derived from SPT-3G data are in excellent agreement with the Planck constraints, including for $H_0$. The SPT-3G and ACT data have similar constraining power and the differences in their constraints are compatible with statistical fluctuations.

Figure 8

Residuals of the SPT-3G 2018 $TT/TE/EE$ minimum-variance data band powers to the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model. Note that the SPT-3G band powers are correlated by up to 40% for neighboring bins. The standard model fits the data well and we report ${\chi }^2=763$ for 723 degrees of freedom. Residuals for the full array of multifrequency band powers are shown in Appendix pp5.

Figure 9

Ratio of the widths of marginalized posteriors from SPT-3G 2018 $TT/TE/EE$ and $TE/EE$ for select $\mathrm{\Lambda }\mathrm{CDM}$ parameters (left half) and extension parameters (right half). The addition of $TT$ data leads to improvements on core $\mathrm{\Lambda }\mathrm{CDM}$ parameters between 8–27% and the $H_0$ and ${\sigma }_8$ posteriors tighten by 12% and 15%, respectively. For $\mathrm{\Lambda }\mathrm{CDM}+A_{\mathrm{L}}$, $\mathrm{\Lambda }\mathrm{CDM}+N_{\mathrm{eff}}$, and $\mathrm{\Lambda }\mathrm{CDM}+N_{\mathrm{eff}}+Y_{\mathrm{P}}$ we report improvements for extension parameters between 5–24%. In the case of primordial magnetic fields, $\mathrm{\Lambda }\mathrm{CDM}+b$, $TE/EE$ data alone suffers from a degeneracy between $n_{\mathrm{s}}$ and $b$ and only the addition of $TT$ data allows for a meaningful constraint. The vertical axis is split and the improvement on $b$ shown only for visualization purposes.

Figure 10

Compilation of $H_0$ constraints from combinations of different CMB datasets assuming $\mathrm{\Lambda }\mathrm{CDM}$: SPT-3G 2018, Planck [1], WMAP [15], ACT DR4 [5]. The vertical gray band indicates the $2\sigma$ constraint from the most precise supernovae and distance ladder analysis [47]. SPT-3G 2018 data allow for a precision constraint on $H_0$ effectively independent from Planck data that deepens the Hubble tension.

Figure 11

Top panel: constraints in the ${\sigma }_8$ vs ${\mathrm{\Omega }}_{\mathrm{m}}$ plane from SPT-3G 2018 (red), Planck (black line), a joint analysis of DES Y3 galaxy position and lensing data and SPT and Planck CMB lensing data ($6\times 2$, blue) [54], and DES Y3 joint galaxy density and weak lensing data ($3\times 2$, gray) [52]. The combined structure growth parameter, $S_8\equiv {\sigma }_8\sqrt{{\mathrm{\Omega }}_{\mathrm{m}}/0.3}$, varies perpendicular to the degeneracy direction of the DES data. Bottom panel: a compilation of $S_8$ constraints using different cosmological datasets: SPT-3G 2018, Planck [1], WMAP [15], ACT DR4 [5], DES Y3 [52], DES Y3 + SPT [54], and KiDS-1000 [51]. Note that all constraints are produced assuming $\mathrm{\Lambda }\mathrm{CDM}$. The central value of the SPT-3G constraint lies between those of low-redshift analyses and Planck.

Figure 12

Marginalized one-dimensional posterior distributions for the SPT-3G 2018 $TT/TE/EE$ (black solid line), $TT$ (light blue dash-dotted line), and $TE/EE$ (orange long dashed line) on the clumping factor $b$ induced by primordial magnetic fields. We also show the constraints from Planck primary CMB and lensing data (dark blue short dashed line) and ACT DR4 (gray dotted line). The combination of $TT$ and $TE/EE$ spectra allows us to break degeneracies and set a tight constraint on $b$. The SPT-3G and ACT data have similar constraining power.

Figure 13

Marginalized posterior distributions for core $\mathrm{\Lambda }\mathrm{CDM}$ and $H_0$ from the original (black) and updated (blue) SPT-3G 2018 $TE/EE$ likelihood. The posteriors widen slightly; the largest change is a 15% correction to the ${\mathrm{\Omega }}_{\mathrm{c}}{h}^2$ uncertainty. The shift to the central values of parameter constraints are less than the size of the new error bars.

Figure 14

Relative $TT$ difference spectra as indicated by the row and column labels, i.e. difference spectra $\mathrm{\Delta }{\widehat{D}}_b^{\nu \mu ;\kappa \tau }$ divided by the square root of the associated covariance, ${\sigma }_b^{\mathrm{\Delta }\nu \mu ;\kappa \tau }$. The blue shading indicates the range of $1-3\sigma$ fluctuations, while gray indicates data excluded in the analysis. We conservatively exclude all $TT$ data at $\ell <750$. This is motivated by the shape of the transfer function, which slowly rises and plateaus at $\ell \approx 750$; the common-mode filter removes $TT$ power on large and intermediate angular scales. We further exclude $150\times 220\mathrm{GHz}$ and $220\times 220\mathrm{GHz}$ $TT$ spectra at $\ell <1000$, based on our model for correlated atmospheric noise. The PTE values are indicated in the top right corner of each panel. All PTE values are in the 95th percentile and the multifrequency spectra are in good agreement with one another.

Figure 15

Relative $TE$ difference spectra as indicated by the row and column labels, i.e. difference spectra $\mathrm{\Delta }{\widehat{D}}_b^{\nu \mu ;\kappa \tau }$ divided by the square root of the associated covariance, ${\sigma }_b^{\mathrm{\Delta }\nu \mu ;\kappa \tau }$. The blue shading indicates the range of $1-3\sigma$ fluctuations and PTE values are given in the top right corner of each panel. All PTE values are in the 95th percentile and the multifrequency spectra are in good agreement with one another.

Figure 16

Relative $EE$ difference spectra as indicated by the row and column labels, i.e. difference spectra $\mathrm{\Delta }{\widehat{D}}_b^{\nu \mu ;\kappa \tau }$ divided by the square root of the associated covariance, ${\sigma }_b^{\mathrm{\Delta }\nu \mu ;\kappa \tau }$. The blue shading indicates the range of $1-3\sigma$ fluctuations. The multifrequency spectra are in good agreement with one another, as evidenced by the PTE values (given in the top right corner of each panel) which all lie in the 95th percentile.

Figure 17

Relative residuals of the SPT-3G 2018 $TT/TE/EE$ multifrequency band powers to the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model, i.e. difference between the SPT-3G data and the model prediction scaled by the error bar of the band powers measurement. The blue shading indicates the range of $1-3\sigma$ fluctuations. Note that the SPT-3G band powers are correlated by up to 40% for neighboring bins. The residuals are consistent with zero and the standard model provides a good fit to the data.