Planck Legacy 2018: Definitive CMB Results

• Planck Legacy 2018 (PL18) is a comprehensive data release offering precise full-sky CMB temperature and polarization maps achieved through advanced calibration and systematic control.
• It employs innovative processing techniques like SRoll2 and iterative LFI algorithms to reduce calibration uncertainties and systematic errors, ensuring robust cosmological parameter inference.
• The release sets a new benchmark for precision cosmology by integrating rigorous end-to-end simulations, component separation methods, and tight constraints on the ΛCDM model and its extensions.

Planck Legacy 2018 (PL18) embodies the definitive data release and cosmological analysis products from the ESA Planck satellite, representing the culmination of a decadal effort to map the cosmic microwave background (CMB) with unprecedented precision in temperature and polarization across the full sky. The release incorporates state-of-the-art calibration, systematic control, component separation, power spectrum estimation, and cosmological parameter inference, fixing the benchmark for current and future precision cosmology across the standard $\Lambda$CDM model and its leading extensions.

1. Mission, Data Products, and Processing Improvements

The Planck satellite operated from 2009–2013, collecting data in nine frequency bands ($30$–$857$ GHz). The 2018 "Planck Legacy" (PL18) release presents full-mission sky maps at high angular resolution (to $5'$ at $217$ GHz), with absolute temperature calibration uncertainties at the $10^{-4}$–$10^{-3}$ level, and polarization calibration at the sub-percent regime (Collaboration et al., 2018, Collaboration et al., 2018, Collaboration et al., 2018).

Key instrument and processing advancements in PL18 include:

• SRoll HFI mapmaking: Introduction of the SRoll and later SRoll2 algorithms for the HFI, simultaneously fitting gain, transfer functions, bandpass-mismatch, and ADCNL effects. SRoll2 further models higher-order ADCNL systematics via spline expansions, reducing large-scale polarization residuals to below the detector noise for $\ell\geq2$ over $86\%$ of the sky. End-to-end (E2E) and null-test validation demonstrates suppression of systematics in $I$, $Q$, $U$ maps (Collaboration et al., 2018, Delouis et al., 2019).
• Iterative LFI pipeline: Improved 4$\pi$ calibration incorporating full-sky signal and an emulator for ADC nonlinearity at 30 GHz, with gain solution iterations to self-consistency using Commander sky models (Collaboration et al., 2018).
• End-to-end simulations: Public release of hundreds of full-mission E2E simulations including noise, beam, gain, and all dominant systematic templates, aligned with the actual scanning and instrument behavior.
• Solar dipole determination: Sub-$10^{-4}$ accuracy in amplitude and $<1'$ in direction, validating frequency and detector calibrations (Collaboration et al., 2018).

These processing advances reduced polarization large-scale systematics by factors $>2$ over the 2015 data, enabling robust low-$\ell$ $EE$ analysis and stable determination of the optical depth to reionization, $\tau$ (Collaboration et al., 2018, Delouis et al., 2019).

2. Component Separation and Map Products

PL18 delivers four independent CMB map products in $I$, $Q$, $U$: Commander, NILC, SEVEM, and SMICA (Collaboration et al., 2018). Each uses different statistical methodologies:

Method	Methodology	Output
Commander	Bayesian parametric fitting	CMB, foregrounds
NILC	Needlet, minimum-variance weighting	CMB-only
SEVEM	Template subtraction	CMB-only
SMICA	Blind harmonic-space ICA	CMB, foreground SEDs

Three methods (Commander, GNILC, SMICA) also produce all-sky synchrotron and thermal dust polarization maps. Masks are rigorously derived via four-map standard deviation and individual pipeline masks, yielding $f_{\rm sky} \sim 0.78$ for confident $I$ and $P$ analyses. E2E noise simulations combined with split-map differences (odd-even, half-mission) underpin accurate statistical error estimation.

For the first time, spatially resolved fits of the dust spectral index in polarization yield $\beta_d = 1.55 \pm 0.05$, and for synchrotron, $\beta_s = -3.1 \pm 0.1$, controlling for method variation and systematic uncertainty (Collaboration et al., 2018).

3. CMB Power Spectra and Likelihood Construction

The PL18 power spectrum likelihood employs a hybrid approach (Collaboration et al., 2019):

• Low-$\ell$ regime $(\ell<30)$ uses Commander Gibbs/Blackwell-Rao TEB likelihood and a simulation-based HFI $EE$ cross-spectrum ($100\times143$ GHz), supported by 300 E2E simulations for noise and systematic uncertainty propagation (Collaboration et al., 2018).
• High-$\ell$ regime $(\ell\geq30)$ is modeled via pseudo-$C_\ell$ Gaussian likelihood for mutually cross-half-mission $(100,143,217)$ GHz spectra in $TT$, $TE$, and $EE$, with full analytic covariance including foreground, beam, leakage, subpixel, and correlated noise templates. Polarization-efficiency recalibration leverages sky-based $EE$ and $TE$ cross-spectra, reducing interfrequency scatter by factors of $17$ ($TE$) and $50$ ($EE$) compared to 2015.

Foreground templates and nuisance parameters are jointly fitted or marginalized. End-to-end and analytic covariances are validated internally and via open-source reproductions (PSpipe reproduces $C_\ell$ and covariance to $<0.1\sigma$ and $<10\%$ respectively (Li et al., 2021)).

4. Cosmological Parameters, Model Extensions, and Tensions

PL18 yields definitive $\Lambda$CDM parameters (Collaboration et al., 2018, Collaboration et al., 2018, Valentino et al., 2019):

Parameter	Baseline value ($68\%$ CL)
$\Omega_b h^2$	$0.02237\pm0.00015$
$\Omega_c h^2$	$0.1200\pm0.0012$
$H_0$	$67.36\pm0.54$ km s$^{-1}$ Mpc$^{-1}$
$\tau$	$0.0544\pm0.0073$
$n_s$	$0.9649\pm0.0042$
$\ln(10^{10}A_s)$	$3.044\pm0.014$

The angular acoustic scale is fixed to $0.03\%$ accuracy, and the temperature spectrum is cosmic-variance limited to $\ell\sim1600$.

Model extensions are robustly constrained:

• Total neutrino mass: $\Sigma m_\nu<0.12$ eV (95% CL) with BAO (Collaboration et al., 2018).
• Relativistic species: $N_\mathrm{eff}=2.99 \pm 0.17$, consistent with the Standard Model (Collaboration et al., 2018).
• Spatial curvature: $\Omega_K = 0.0007 \pm 0.0019$, consistent with flat geometry when adding BAO and lensing (Collaboration et al., 2018).

Notable residual anomalies:

• Enhanced lensing amplitude: $A_L=1.18\pm0.065$, $>2.5\sigma$ above $\Lambda$CDM value, traced to smoothing excess in $TT$ at $1100<\ell<2000$. Lensing reconstruction and BAO data do not support $A_L>1$ (Collaboration et al., 2018, Valentino et al., 2019). Some studies demonstrate that this anomaly can be traded for curvature: a closed universe with $\Omega_K\sim-0.044$ yields $A_\mathrm{lens}\sim1$, but then conflicts at $>3\sigma$ with BAO, $H_0$, and low-$z$ probes (Valentino et al., 2019).
• Tension with local $H_0$: Planck's $H_0$ is $3.6\sigma$ below SH0ES (local) determinations (Collaboration et al., 2018). Extensions to $w<-1$ can formally reconcile $H_0$, but are inconsistent with BAO and Type Ia supernovae (Valentino et al., 2019, Pan et al., 2020).
• Low-$\ell$ TT dip and S$_8$ tension: Mild $\sim2\sigma$ preference for low power at $20<\ell<30$ and S$_8$ tension compared to some cosmic shear results; both remain statistically limited.

5. Ancillary Science and Legacy Constraints

PL18 data set unprecedented constraints on:

• Primordial Magnetic Fields: Sub-nanogauss upper limits on field amplitude, $\sqrt{\langle B^2 \rangle} < 0.69$ nG (95% CL), set by E-mode large-scale polarization through ambipolar diffusion and MHD turbulence heating effects (Paoletti et al., 2022).
• Inflationary Models: For instance, Natural Inflation models with cosine potentials are ruled out at $>95\%$ CL for standard reheating; only with a stiff post-inflationary equation of state $w>1/3$ and unphysically low $T_\mathrm{re}$ can they marginally enter the $95\%$–$68\%$ CL allowed region (Stein et al., 2021).
• Cosmic Voids and Lensing: Cross-correlation of DESI LRG voids with the PL18 lensing map detects the void imprint at $>14\sigma$, $A_\kappa=1.016\pm0.054$, fully consistent with $\Lambda$CDM (Sartori et al., 2024).

6. Systematics Control, Simulations, and Public Data Policy

All PL18 map and likelihood products are supplemented by an extensive suite of E2E simulations capturing noise, beams, scanning, and residual systematics—crucial for robust error budget and cosmological parameter inference (Collaboration et al., 2018, Collaboration et al., 2018, Delouis et al., 2019). Each step is validated through cross-checks among multiple map-making pipelines, component-separation methods, and splits (half-mission, detector sets, odd-even rings). The Planck Legacy Archive offers all maps, likelihoods, simulations, and instrument models for community analyses.

7. Impact, Current Status, and Outlook

PL18 stands as the benchmark for full-sky CMB analyses and the reference for cosmic parameter inference. Its internal consistency and high-fidelity simulation set are the gold standard for future datasets from advanced ground-based and satellite CMB efforts. Key lessons include the need for integrated calibration/component separation, the efficacy of systematics-blind end-to-end simulations, and the limits of temperature-dominated cosmic-variance. Remaining issues such as the $A_L$ anomaly and $H_0$ tension delineate targets for future observational and theoretical advance, particularly from next-generation polarization and high-resolution lensing surveys (Collaboration et al., 2018, Collaboration et al., 2018, Valentino et al., 2019).

PL18's cosmological legacy is its precision constraint of the $\Lambda$CDM paradigm, weak limits on new physics, and methodical framework for systematic control and simulation-aided inference that will inform the next decade of observational cosmology.