Planck 2018 results. X. Constraints on inflation

The Honourable Schoolboy

Which inflationary models are best able to account for the
data?
Starting with the 2013 release using only a part of the data,

Planck has substantially tightened the constraints on slow-
roll inflationary models, ruling out hybrid models with ns >

1 and power-law inflation (PCI13). In combination with the
BK14 data, Planck 2018 now strongly disfavours monomial
models with V(φ) ∝ φ
p
and p ≥ 2 and low-scale SUSY
models. Within the representative cases studied in this paper,
inflationary models such as R
2
, T and E α-attractor models,

D-brane inflation, and those having a potential with exponen-
tial tails provide good fits to Planck and BK14 data. We used

two methods to reconstruct the inflaton potential beyond the
slow-roll approximation: by Taylor expanding the inflaton
potential or Hubble parameter in the observable region; and

through a free-form reconstruction of the potential with cu-
bic splines. No statistically significant detection beyond the

second derivative of the potential was found, suggesting that
the slow-roll approximation is adequate for the Planck 2018
likelihood in combination with the BK14 data.





The Planck 2013, 2015, and 2018 releases have substantially im-
proved the constraints on the space of inflationary models, as

described above. Future CMB polarization data will be crucial
for further constraining those inflationary models that currently

provide an adequate fit to Planck and other data. Forthcoming E-
mode polarization data will be decisive for determining whether

the intriguing features in the temperature power spectrum, such
as the deficit at ` ' 20–30, the smaller average amplitude at
` . 40, and other anomalies at higher multipoles require new

physics or whether these features are simply the result of sta-
tistical fluctuations plus instrumental noise. Improved measure-
ments of the B modes promise to constrain inflation even more

tightly and it will be interesting to see how the search for B

modes evolves. One possibility would be a convincing detec-
tion of inflationary gravitational waves, but a tighter upper limit

of r . 10−3

is also an achievable outcome. Either case would

substantially advance our understanding of inflation and the con-
straints on the physics of the very early Universe.