Planck 2018 results
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Table 14.

Constraints on mixed adiabatic and isocurvature models.

100βiso at
Model and data Δn klow kmid khigh 100 cos Δ 100αnon-adi Δχ2 lnB
General models (three isocurvature parameters):
 CDI Planck 2015 TT+lowP 3 4.1 37 57 [ − 30 : 20] [ − 1.48 : 1.91] −2.1
 CDI Planck TT+lowE 3 3.6 38 61 [ − 23 : 27] [ − 0.76 : 2.05] −0.7 −12.6
 CDI CamSpec TT+lowE 3 3.8 35 56 [ − 22 : 23] [ − 0.62 : 2.12] −0.7 −13.4
 CDI Planck TT+lowP 3 4.2 35 56 [ − 25 : 23] [ − 1.03 : 1.98] −0.5 −12.6
 CDI Planck TT + τ prior 3 8.4 27 40 [ − 21 : 29] [ − 0.83 : 5.35]
 CDI Planck 2015 TT+lowP+lensing 3 4.5 [1 : 40] [1 : 62] [ − 28 : 17] [ − 1.05 : 1.86] −1.2
 CDI Planck TT+lowE+lensing 3 4.0 35 57 [ − 28 : 23] [ − 1.20 : 2.04] −0.6 −12.3
 CDI CamSpec TT+lowE+lensing 3 3.7 34 55 [ − 24 : 24] [ − 0.96 : 2.10] −0.5 −12.8
 CDI Planck 2015 TT,TE,EE+lowP 3 2.0 [3 : 28] [5 : 52] [ − 6 : 20] [0.09 : 1.51] −5.3
 CDI Planck TT,TE,EE+lowE 3 2.1 [1 : 31] 58 [ − 11 : 15] [ − 0.18 : 1.24] −3.0 −12.8
 CDI CamSpec TT,TE,EE+lowE 3 2.8 21 38 [ − 12 : 20] [ − 0.20 : 1.67] −1.2 −14.0
 CDI Planck TT,TE,EE+lowP 3 2.4 27 50 [ − 11 : 17] [ − 0.16 : 1.45] −2.3 −13.4
 CDI Planck TT,TE,EE + τ prior 3 6.2 17 30 [ − 13 : 14] [ − 0.48 : 3.94]
CDIPlanckTT,TE,EE+lowE+lensing 3 2.5 [1 : 26] 47 [ − 12 : 15] [ − 0.25 : 1.31] −2.8 −12.8
 CDI CamSpec TT,TE,EE+lowE+lensing 3 3.0 19 33 [ − 16 : 18] [ − 0.38 : 1.54] −0.9 −14.1
 CDI Planck TT,TE,EE+lowP+lensing 3 2.2 [1 : 27] 50 [ − 11 : 16] [ − 0.16 : 1.36]
 CDI WMAP-9 3 20.1 [2 : 50] 66 [ − 38 : 34] [ − 1.79 : 6.46] −0.2 −9.6

 NDI Planck 2015 TT+lowP+lensing 3 15.8 [2 : 24] [2 : 29] [ − 32 : 0] [ − 4.04 : 1.37] −2.8
 NDI Planck TT+lowE+lensing 3 15.3 17 21 [ − 36 : 4] [ − 4.20 : 1.53] −1.9 −10.8
NDIPlanckTT,TE,EE+lowE+lensing 3 7.4 [3 : 17] [2 : 23] [ − 13 : 8] [ − 0.76 : 1.74] −5.3 −10.9

 NVI Planck 2015 TT+lowP+lensing 3 9.8 [1 : 12] 14 [ − 23 : 7] [ − 2.03 : 2.95] −2.5
 NVI Planck TT+lowE+lensing 3 7.1 10 12 [ − 36 : 3] [ − 3.34 : 1.71] −2.5 −12.6
NVIPlanckTT,TE,EE+lowE+lensing 3 6.8 [1 : 8] 10 [ − 20 : 0] [ − 1.66 : 1.29] −5.2 −12.0

 CDI+ALPlanck TT+lowE 4 9.4 28 41 [ − 41 : 10] [ − 2.32 : 2.29] −9.2 −10.1
 CDI+ALPlanck TT+lowE+lensing 4 6.0 36 57 [ − 27 : 18] [ − 1.16 : 2.19] −4.1 −13.1
 CDI+ALPlanck TT,TE,EE+lowE 4 3.3 20 36 [ − 12 : 19] [ − 0.24 : 1.89] −10.6 −11.2
CDI+ALPlanckTT,TE,EE+lowE+lensing 4 2.7 [1 : 27] 49 [ − 10 : 16] [ − 0.12 : 1.53] −8.1 −13.5

Special CDI cases (one isocurvature parameter):
 Uncorrelated, nℐℐ = 1
  “axion I” Planck 2015 TT+lowP+lensing 1 3.9 4.3 4.4 0 [0 : 1.70] 0
  “axion I” Planck TT+lowE+lensing 1 3.5 3.9 3.9 0 [0 : 1.58] 0 −5.7
  “axion I” PlanckTT,TE,EE+lowE+lensing 1 3.5 3.8 3.9 0 [0 : 1.55] 0 −5.5
 Fully correlated, nℐℐ = nℛℛ
  “curvaton I” Planck 2015 TT+lowP+lensing 1 0.2 0.2 0.2 +100 [0.30 : 2.70] 0
  “curvaton I” Planck TT+lowE+lensing 1 0.2 0.2 0.2 +100 [0.09 : 2.91] 0 −8.9
  “curvaton I”PlanckTT,TE,EE+lowE+lensing 1 0.1 0.1 0.1 +100 [0.07 : 1.81] 0 −9.7
 Fully anti-correlated, nℐℐ = nℛℛ
  “curvaton II” Planck 2015 TT+lowP+lensing 1 0.5 0.5 0.5 −100 [ − 4.40 : −0.40] −0.6
  “curvaton II” Planck TT+lowE+lensing 1 0.5 0.5 0.5 −100 [ − 4.40 : −0.35] −0.4 −7.2
  “curvaton II”PlanckTT,TE,EE+lowE+lensing 1 0.1 0.1 0.1 −100 [ − 2.04 : −0.13] 0 −9.2

Special CDI cases (two isocurvature parameters):
 Uncorrelated, nℐℐ free
  “axion II” Planck TT+lowE+lensing 2 2.3 [3 : 43] [6 : 75] 0 [0.03 : 1.24] −0.5 −6.7
  “axion II”PlanckTT,TE,EE+lowE+lensing 2 1.1 [5 : 38] [10 : 77] 0 [0.07 : 0.66] −2.8 −6.3
 Arbitrarily correlated, nℐℐ = nℛℛ
  “curvaton III” Planck TT+lowE+lensing 2 4.7 4.7 4.7 [ − 75 : 28] [ − 3.38 : 1.99] −0.4 −10.0
  “curvaton III”PlanckTT,TE,EE+lowE+lensing 2 3.9 3.9 3.9 [ − 41 : 31] [ − 1.30 : 2.10] 0 −10.5
 Fully correlated, nℐℐ free
  Planck TT+lowE+lensing 2 0.1 4.6 16.0 +100 [0.28 : 2.15] −0.5 −13.2
  PlanckTT,TE,EE+lowE+lensing 2 0.02​​​ 1.5 6.2 +100 [0.14 : 0.99] −0.3 −16.0
 Fully anti-correlated, nℐℐ free
  Planck TT+lowE+lensing 2 0.6 0.9 1.3 −100 [ − 5.56 : −0.53] −1.3 −13.8
  PlanckTT,TE,EE+lowE+lensing 2 0.3 0.2 0.2 −100 [ − 4.56 : −0.16] −0.6 −16.7

Notes. We report 95% CL intervals or upper bounds on the isocurvature fraction βiso at three scales (klow = 0.002 Mpc−1, kmid = 0.050 Mpc−1, and khigh = 0.100 Mpc−1), the scale-independent correlation fraction, cos Δ, and the non-adiabatic contribution to the CMB temperature variance, αnon − adi. Here Δχ2 is the difference between the χ2 of the best-fit mixed and pure adiabatic models. In the last column we give the difference between the log of Bayesian evidences. (A negative lnB means that Bayesian model comparison disfavours the mixed model.) The number of extra parameters compared with ΛCDM is denoted by Δn in the first column. Note that the uniform priors on the primordial powers at two scales lead to non-uniform priors on the parameters reported in this table. This is particularly significant for βiso(kmid), where the prior peaks at a non-zero value. The baseline Planck 2018 TT,TE,EE+lowE+lensing results are highlighted in bold.

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