Final Planck Results

These final results from the Planck mission are likely to be the definitive Cosmic Microwave Background (CMB) measurements for the foreseeable future. 

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. 

We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ωch2=0.120±0.001, baryon density Ωbh2=0.0224±0.0001, scalar spectral index ns=0.965±0.004, and optical depth τ=0.054±0.007 (in this abstract we quote 68%confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ∗=1.0411±0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. 

Assuming the base-ΛCDM cosmology, the inferred late-Universe parameters are: Hubble constant H0=(67.4±0.5)km/s/Mpc; matter density parameter Ωm=0.315±0.007; and matter fluctuation amplitude σ8=0.811±0.006. We find no compelling evidence for extensions to the base-ΛCDM model. 

Combining with BAO we constrain the effective extra relativistic degrees of freedom to be Neff=2.99±0.17, and the neutrino mass is tightly constrained to ∑mν<0.12eV. 

The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the base-ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. 

The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001±0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r_0.002 < 0.07. 

Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data. 

From here.

Neutrino Physics Implications

These constraints strongly disfavor the existence of a light sterile neutrino (under 10 eV in mass, a heavier sterile neutrino would be degenerate in the CMB data with dark matter) that oscillates with active neutrinos (the expected value of Neff is 3.046 if there are three active neutrino flavors), a light sterile neutrino is disfavored at the six sigma level. Weak force decay measurements already strongly disfavor more than (or less than) three active neutrino flavors.

The data also favor a "normal" neutrino mass hierarchy. The 0.12 eV cap for the sum of the three neutrino masses is more than the minimum mass in an inverted hierarchy scenario, but that is the 95% probability upper limit, so a significantly lower value, which would be inconsistent with an inverted hierarchy, is favored by the data.

The body text notes that:

The normal hierarchy, in which the lowest two mass eigenstates have the smallest mass splitting, can give any P mν >∼ 0.06 eV; an inverted hierarchy, in which the two most massive eigenstates have the smallest mass separation, requires P mν >∼ 0.1 eV. A constraint that P mν < 0.1 eV would therefore rule out the inverted hierarchy. . . . This is consistent with constraints from neutrino laboratory experiments which also slightly prefer the normal hierarchy at 2–3σ[.]

Cosmological Inflation and the Topology of the Universe

The scalar spectral index value of n_s=0.965±0.004 (which corresponds to the vertical yellow lines in the figure below) and the tensor-scalar ratio of less than 0.064 tightly constraints the parameter space of cosmological inflation theories. Basically, the parameter space allowed by the latest observations corresponds to the dark blue hump in the bottom center of the figure below. 

Earlier Planck results combined with other data indicated that the best fit tensor-scalar ratio is zero (i.e. no primordial gravitational waves (i.e. at the very bottom center boundary of the figure below) and a one sigma value from the best fit value is probably 0.032 or less.

The constraint that the universe is flat is also very strong. The body text states that "our Universe is spatially flat to a 1σ accuracy of 0.2 %."

A separate final Planck result paper on cosmological inflation says this in its abstract:

We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be ns=0.9649±0.0042 at 68% CL and show no evidence for a scale dependence of ns. Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r0.002<0.10, is further tightened by combining with the BICEP2/Keck Array BK14 data to obtain r0.002<0.064. 

In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, V"(ϕ)<0,  are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.

From the body text:

– The inflationary predictions (Mukhanov & Chibisov 1981; Starobinsky 1983) originally computed for the R 2 model (Starobinsky 1980) to lowest order, 

ns − 1 is approximately equal to − 2/N,  r  is approximately equal to 12 N^2,   (48) 

are in good agreement with Planck 2018 data, confirming the previous 2013 and 2015 results. The 95% CL allowed range 49 < N∗ < 58 is compatible with the R^2 basic predictions N∗ = 54, corresponding to Treh ∼ 10^9 GeV (Bezrukov & Gorbunov 2012). A higher reheating temperature Treh ∼ 10^13 GeV, as predicted in Higgs inflation (Bezrukov & Shaposhnikov 2008), is also compatible with the Planck data. 

– Monomial potentials (Linde 1983) V(φ) = λM4 Pl (φ/MPl) p with p ≥ 2 are strongly disfavoured with respect to the R^2 model. For these values the Bayesian evidence is worse than in 2015 because of the smaller level of tensor modes allowed by BK14. Models with p = 1 or p = 2/3 (Silverstein & Westphal 2008; McAllister et al. 2010, 2014) are more compatible with the data. 

– There are several mechanisms which could lower the predictions for the tensor-to-scalar ratio for a given potential V(φ) in single-field inflationary models. Important examples are a subluminal inflaton speed of sound due to a nonstandard kinetic term (Garriga & Mukhanov 1999), a nonminimal coupling to gravity (Spokoiny 1984; Lucchin et al. 1986; Salopek et al. 1989; Fakir & Unruh 1990), or an additional damping term for the inflaton due to dissipation in other degrees of freedom, as in warm inflation (Berera 1995; Bastero-Gil et al. 2016). In the following we report on the constraints for a non-minimal coupling to gravity of the type F(φ)R with F(φ) = M2 Pl + ξφ2 . To be more specific, a quartic potential, which would be excluded at high statistical significance for a minimally-coupled scalar inflaton as seen from Table 5, can be reconciled with Planck and BK14 data for ξ > 0: we obtain a 95 % CL lower limit log10 ξ > −1.6 with ln B = −1.6. 

– Natural inflation (Freese et al. 1990; Adams et al. 1993) is disfavoured by the Planck 2018 plus BK14 data with a Bayes factor ln B = −4.2. 

– Within the class of hilltop inflationary models (Boubekeur & Lyth 2005) we find that a quartic potential provides a better fit than a quadratic one. In the quartic case we find the 95 % CL lower limit log10(µ2/MPl) > 1.1. 

– D-brane inflationary models (Kachru et al. 2003; Dvali et al. 2001; Garc´ıa-Bellido et al. 2002) provide a good fit to Planck and BK14 data for a large portion of their parameter space. 

– For the simple one parameter class of inflationary potentials with exponential tails (Goncharov & Linde 1984; Stewart 1995; Dvali & Tye 1999; Burgess et al. 2002; Cicoli et al. 2009) we find ln B = −1.0. 

– Planck 2018 data strongly disfavour the hybrid model driven by logarithmic quantum corrections in spontaneously broken supersymmetric (SUSY) theories (Dvali et al. 1994), with ln B = −5.0. 

– Planck and BK14 data set tight constraints on α attractors (Kallosh et al. 2013; Ferrara et al. 2013). We obtain log10 α E 1 < 1.5 and log10 α E 2 < 1.2 at 95 % CL for the Emodel. We obtain slightly tighter 95 % CL bounds for the T-model, i.e., log10 α T 1 < 1.1 and log10 α T 2 < 1.0. Given the relation |RK| = 2/(3α) between the curvature of the Kahler ¨ geometry RK and α in some of the T-models motivated by supergravity, Planck and BK14 data imply a lower bound on |RK|, which is still in the low-curvature regime. The discrete set of values α = i/3 with an integer i in the range [1, 7] motivated by maximal supersymmetry (Ferrara & Kallosh 2016; Kallosh et al. 2017) is compatible with the current data.