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❚❤❡ ❯♥✐✈❡rs❡ ❛❢t❡r P❧❛♥❝❦ ✷✵✶✸

▼❛rt✐♥ ❇❯❈❍❊❘✱ ▲❛❜♦r❛t♦✐r❡ ❆str♦♣❛rt✐❝❧❡s ✫ ❈♦s♠♦❧♦❣✐❡✱ ❯♥✐✈❡rs✐té P❛r✐s ✼ ✭❉❡♥✐s✲❉✐❞❡r♦t✮ ❢♦r t❤❡ P▲❆◆❈❑ ❈♦❧❧❛❜♦r❛t✐♦♥ ✷✶ ❆✉❣✉st ✷✵✶✸✱ ❑②♦t♦✱ ❏❛♣❛♥

❖✉t❧✐♥❡

✶✳ ❲❤❛t ✐s P❧❛♥❝❦❄ ✷✳ ❆ ❜r✐❡❢ ❤✐st♦r② ♦❢ ❈▼❇ ♦❜s❡r✈❛t✐♦♥ ✸✳ ❋✐rst r❡❧❡❛s❡ ♦❢ ❝♦s♠♦❧♦❣② r❡s✉❧ts ✹✳ P♦✇❡r s♣❡❝tr✉♠ ✺✳ ●r❛✈✐t❛t✐♦♥❛❧ ❧❡♥s✐♥❣ ✻✳ ◆♦♥✲●❛✉ss✐❛♥✐t② ✼✳ ❙t❛t✐st✐❝❛❧ ✐s♦tr♦♣② ✽✳ ❲❤❛t✬s ♥❡①t

❲❤❛t ✐s P❧❛♥❝❦❄

❚❤❡ P❧❛♥❝❦ ♠✐ss✐♦♥

P▲❆◆❈❑ ❋♦❝❛❧ P❧❛♥❡

❚❤❡ ✇♦r❦❤♦rs❡ ♦❢ P❧❛♥❝❦✿ s♣✐❞❡r✇❡❜ ❛♥❞ ♣♦❧❛r✐③❛t✐♦♥ s❡♥s✐t✐✈❡ ❜♦❧♦♠❡t❡rs

▼❛❞❡ ❜② ❏P▲✱ ❈❛❧t❡❝❤ ❈♦♦❧❡❞ t♦ ≈ ✶✵✵♠❑

P❧❛♥❝❦ ❈❛♣❛❜✐❧✐t✐❡s

P❧❛♥❝❦ ❈❛♣❛❜✐❧✐t✐❡s

❆ ❜r✐❡❢ ❤✐st♦r② ♦❢ ❈▼❇ ♦❜s❡r✈❛t✐♦♥

❇♦♦♠❡r❛♥❣ ❜❛❧♦♦♥

❇♦♦♠❡r❛♥❣ ♠✉t✐♣♦❧❡ s♣❡❝tr✉♠ ✭♥♦ t❤❡♦r②✮

❇♦♦♠❡r❛♥❣ ♠✉t✐♣♦❧❡ s♣❡❝tr✉♠ ✭✇✐t❤ t❤❡♦r②✮

❲▼❆P ✾✲②❡❛r ❛❧♦♥❡

❲▼❆P ✾✲②❡❛r ✰❙P❚✰❆❈❚

❇❛s✐❝ st❛t✐st✐❝❛❧ ❛♣♣r♦❛❝❤✖✐♥t❡r❡st✐♥❣ ♦✉t❝♦♠❡ ❝❛s❡

✶✳ ◆♦ ♣♦♣✉❧❛r ♠♦❞❡❧ ♣r♦✈✐❞❡s ❣♦♦❞ ✜t t♦ ❞❛t❛✳ ✷✳ ❋♦r♠❡r ❛❣r❡❡♠❡♥t ✇✐t❤ ✏❝♦♥❝♦r❞❛♥❝❡✑ ♠♦❞❡❧ ✭s✉✣❝✐❡♥t t♦ ❡①♣❧❛✐♥ ❲▼❆P ♣♦✇❡r s♣❡❝tr✉♠ ❛♥❞ t❤❡ ❧♦♦s❡ ❝♦♥str❛✐♥ts ❛t ✈❡r② ❧❛r❣❡ ℓ ❢r♦♠ ❆❈❚ ❛♥❞ ❙P❚✮ ❢❛❧❧s ❛♣❛rt ♦✇✐♥❣ t♦ ❢❛❝t♦r ✷ ✐♠♣r♦✈❡♠❡♥t ✐♥ r❡s♦❧✉t✐♦♥ ❛♥❞ ❢❛❝t♦r ✶✵ ✐♠♣r♦✈❡♠❡♥t ✐♥ s❡♥s✐t✐✈✐t② ♦❢ P❧❛♥❝❦✳ ✸✳ ◆♦ s✐♠♣❧❡✱ t❤❡♦r❡t✐❝❛❧❧② ♠♦t✐✈❛t❡❞ ♠♦❞❡❧ ✇♦r❦s✱ ❛❧t❤♦✉❣❤ ❜❛r♦q✉❡ ♠♦❞❡❧s ✇✐t❤ ❡♣✐❝②❝❧❡s ❛♥❞ ♠❛♥② ♣❛r❛♠❡t❡rs ❝❛♥ ❜❡ ♠❛❞❡ t♦ ✇♦r❦✳ ✹✳ ❚❤❡♦r✐sts s❡♥t ❜❛❝❦ t♦ ❞r❛✇✐♥❣ ❜♦❛r❞✳ ❚❤✐s ❞✐❞ ♥♦t ❤❛♣♣❡♥✱ ❜✉t ♣♦❧❛r✐③❛t✐♦♥ ❞❛t❛ st✐❧❧ ❜❡✐♥❣ ❛♥❛❧②③❡❞✳ ❙t✐❧❧ r♦♦♠ ❢♦r s♦♠❡ s✉r♣r✐s❡s ✐♥ ❢✉t✉r❡ r❡❧❡❛s❡s✳

❇❛s✐❝ st❛t✐st✐❝❛❧ ❛♣♣r♦❛❝❤✖❜♦r✐♥❣ ♦✉t❝♦♠❡ ❝❛s❡

✶✳ ❆❢t❡r ❤❛✈✐♥❣ ❝♦♥str✉❝t❡❞ ❛ ❧✐❦❡❧✐❤♦♦❞ ❢✉♥❝t✐♦♥ ✇❤♦s❡ ✐♥♣✉t ✐s t❤❡ ♣r❡❞✐❝t❡❞ t❤❡♦r❡t✐❝❛❧ ♣♦✇❡r s♣❡❝tr✉♠✱ ✜♥❞ t❤❡ s✐♠♣❧❡st ♠♦❞❡❧ ✇✐t❤ ❛ ❣♦♦❞ ✜t t♦ t❤❡ ♣♦✇❡r s♣❡❝tr✉♠✳ ✷✳ ❈♦♥s✐❞❡r ❡①t❡♥s✐♦♥s t♦ t❤✐s ♠♦❞❡❧ ❛♥❞ s❡❡ ✇❤❡t❤❡r t❤❡ ✐♠♣r♦✈❡♠❡♥t ✐♥ t❤❡ q✉❛❧✐t② ♦❢ ✜t ✐s st❛t✐st✐❝❛❧❧② s✐❣♥✐✜❝❛♥t✳ ✭❊✳❣✳✱ ✐s♦❝✉r✈❛t✉r❡ ♠♦❞❡s✱ ❡①tr❛ ♥❡✉tr✐♥♦ s♣❡❝✐❡s✱ ✈❛r②✐♥❣ α, . . . ✸✳ ❙t✉❞② t❤❡ r❡s✐❞✉❛❧s t♦ t❤❡ ♠✐♥✐♠❛❧ ♠♦❞❡❧s t♦ t❡st ❢♦r st❛t✐st✐❝❛❧ s✐❣♥✐✜❝❛♥❝❡✳

❚❤❡ P❧❛♥❝❦ ❚❡♠♣❡r❛t✉r❡✲❚❡♠♣❡r❛t✉r❡ P♦✇❡r ❙♣❡❝tr✉♠ ❈❚❚(ℓ)

❇❛s❡ ♠♦❞❡❧✖s❛♠♣❧✐♥❣ ♣❛r❛♠❡t❡rs

❇❛s❡ ♠♦❞❡❧✖❞❡r✐✈❡❞ ♣❛r❛♠❡t❡rs

P❧❛♥❝❦ ■▲❈ ♠❛♣

P❧❛♥❝❦ ●r❛✈✐t❛t✐♦♥❛❧ ❧❡♥s✐♥❣ s♣❡❝tr✉♠

❯♥❞❡r❧②✐♥❣ q✉❡st✐♦♥✿ ❝♦♥✈❡♥t✐♦♥❛❧ ♣❛r❛♠❡t❡r✐③❛t✐♦♥

❲❤❛t ✐s t❤❡ ♣r✐♠♦r❞✐❛❧ ♣♦✇❡r s♣❡❝tr✉♠❄

◮ ❋♦r ❧❛❝❦ ♦❢ ❛ ❢✉♥❞❛♠❡♥t❛❧ t❤❡♦r②✱ ❡①♣❛♥❞ ✐♥ ♣♦✇❡rs ♦❢ ❧♥(❦) ❧♥ (P(❧♥ ❦)) = P✵

• ❧♥(❦/❦♣✐✈)

✵ + P✶

• ❧♥(❦/❦♣✐✈)

✶ + P✷

• ❧♥(❦/❦♣✐✈)

✷ + . . . P(❦) = ❆(❦/❦♣✐✈)(♥s−✶) ♦r P(❦) = ❆(❦/❦♣✐✈)(♥s−✶)+α ❧♥(❦/❦♣✐✈ )+... ◮ P❧❛♥❝❦ s❡❡♠s t♦ ❜❡ t❡❧❧✐♥❣ ✉s t❤❛t t❤❡ ✜rst t✇♦ t❡r♠s s✉✣❝❡✱

❛♥❞ ✉s✐♥❣ ❥✉st t❤❡ ✜rst t❡r♠ ❝❛♥ ❜❡ r✉❧❡❞ ♦✉t ❛t ❛ r❡s♣❡❝t❛❜❧❡ st❛t✐st✐❝❛❧ s✐❣♥✐✜❝❛♥❝❡✳ ♥❙ = ✶ ✐♠♣❧✐❡s ❡①❛❝t s❝❛❧❡ ✐♥✈❛r✐❛♥❝❡ ♥❡❡❞s t♦ ❜❡ ❞♦✇♥❣r❛❞❡❞ t♦ ❛♥ ❛♣♣r♦①✐♠❛t❡ s②♠♠❡tr②✳ ◆♦ st❛t✐st✐❝❛❧❧② s✐❣♥✐✜❝❛♥t ❡✈✐❞❡♥❝❡ ❢♦r r✉♥♥✐♥❣ ♦❢ t❤❡ s♣❡❝tr❛❧ ✐♥❞❡①✳

❯♥❞❡r❧②✐♥❣ q✉❡st✐♦♥✿ s❡❛r❝❤✐♥❣ ❢♦r ❢❡❛t✉r❡s

◮ ❚✇♦ ❛♣♣r♦❛❝❤❡s

◮ P❛r❛♠❡t❡r✐③❡❞ ❛♣♣r♦❛❝❤❡s ✿ ♠❛❦❡ ❆♥sät③❡ ✇✐t❤ ❛ s♠❛❧❧

♥✉♠❜❡r ♦❢ ❡①tr❛ ♣❛r❛♠❡t❡rs ❛♥❞ ❝♦♠♣❛r❡ q✉❛❧✐t② ♦❢ ✜t t♦ s✐♠♣❧❡r ♠♦❞❡❧ t♦ ❞❡t❡r♠✐♥❡ ✇❤❡t❤❡r ❡①tr❛ ♣❛r❛♠❡t❡rs ❛r❡ ❥✉st✐✜❡❞ ❜② t❤❡ ❞❛t❛ ✭❆✐❦❛❦❡ ■♥❢♦r♠❛t✐♦♥ ❈r✐t❡r✐♦♥✱ ❇❛②❡s✐❛♥ ■♥❢♦r♠❛t✐♦♥ ❈r✐t❡r✐♦♥✱ ❇❛②❡s✐❛♥ ❊✈✐❞❡♥❝❡✱ . . .✮✳ ✭❆♣♣r♦❛❝❤ ❢♦❧❧♦✇❡❞ ✐♥ P❧❛♥❝❦ ♣❛♣❡r ❳❳■■✱ s❡❝t✐♦♥ ✽✮

◮ ◆♦♥✲♣❛r❛♠❡t❡r✐③❡❞ ❛♣♣r♦❛❝❤❡s✿ ♣❡♥❛❧✐③❡❞ ❧✐❦❡❧✐❤♦♦❞s✱✳✳✳✳

❬❉❡t❛✐❧s ♦❢ ❛♣♣r♦❛❝❤ ❢♦❧❧♦✇❡❞ ✐♥ P❧❛♥❝❦ ❳❳■■ ♣❛♣❡r ❢♦❧❧♦✇✿

• ❛✉t❤✐❡r✱ ❈❤r✐st♦♣❤❡r❀ ❇✉❝❤❡r✱ ▼❛rt✐♥❀ ❘❡❝♦♥str✉❝t✐♥❣ t❤❡

♣r✐♠♦r❞✐❛❧ ♣♦✇❡r s♣❡❝tr✉♠ ❢r♦♠ t❤❡ ❈▼❇✱ ❏❈❆P ✶✵✱ ✵✺✵ ✭✷✵✶✷✮ ✭❛r❳✐✈✿✶✷✵✾✳✷✶✹✼✮ ✭❆♣♣r♦❛❝❤ ❢♦❧❧♦✇❡❞ ✐♥ P❧❛♥❝❦ ♣❛♣❡r ❳❳■■✱ s❡❝t✐♦♥ ✼✮

❚❡♥t❛t✐✈❡ ❝♦♥❝❧✉s✐♦♥ ♦❢ P❧❛♥❝❦ P❛r❛♠❡t❡rs ♣❛♣❡r

◮ ❈♦♥❝❧✉s✐♦♥ ❜❛s❡❞ ♦♥ ❧♦♦❦✐♥❣ ❛t ♦✈❡r❛❧❧ χ✷ ✇✐t❤ ❛ ✈❡r② ❧❛r❣❡

♥✉♠❜❡r ♦❢ ❞❡❣r❡❡s ♦❢ ❢r❡❡❞♦♠✳

◮ ❲❡ ✇❛♥t t♦ ❡①❛♠✐♥❡ ✇❤❡t❤❡r t❤✐s ❝♦♥❝❧✉s✐♦♥ ✐s r❡❛❧❧② ❥✉st✐✜❡❞✳

P❡♥❛❧✐③❡❞ ❧✐❦❡❧✐❤♦♦❞

▲❡t P✵(❦) = ❆s(❦/❦∗)♥s−✶ ❜❡ t❤❡ ❜❡st ✜t ♣♦✇❡r s♣❡❝tr✉♠ ♦❢ t❤❡ s✐① ♣❛r❛♠❡t❡r ♠♦❞❡❧✳ ❲❡ ❞❡✜♥❡ ❛ ❣❡♥❡r❛❧ ❆♥s❛t③ ❢♦r t❤❡ ♣♦✇❡r s♣❡❝tr✉♠ ✐♥ t❡r♠s ♦❢ ❛ ❢r❛❝t✐♦♥❛❧ ✈❛r✐❛t✐♦♥✱ ❢ (❦)✱ r❡❧❛t✐✈❡ t♦ t❤✐s ✜❞✉❝✐❛❧ ♠♦❞❡❧✱ s♦ t❤❛t PR(❦) = P✵(❦)

• ✶ + ❢ (❦)
• .

✭✶✮ ❆♥② ❢❡❛t✉r❡s ❛r❡ t❤❡♥ ❞❡s❝r✐❜❡❞ ✐♥ t❡r♠s ♦❢ ❢ (❦)✳ ■♥ t❤✐s ❛♥❛❧②s✐s ✇❡ ✉s❡ t❤❡ P❧❛♥❝❦✰❲P ❧✐❦❡❧✐❤♦♦❞ s✉♣♣❧❡♠❡♥t❡❞ ❜② t❤❡ ❢♦❧❧♦✇✐♥❣ ♣r✐♦r✱ ✇❤✐❝❤ ✐s ❛❞❞❡❞ t♦ −✷ ❧♥ L✿ ❢❚ ❘(λ, α)❢ = λ

• ❞κ

∂✷❢ (κ) ∂κ✷ ✷ + α κ♠✐♥

−∞

❞κ ❢ ✷(κ) + α +∞

κ♠❛①

❞κ ❢ ✷(κ). ✭✷✮ ✇❤❡r❡ κ = ❧♥ ❦✳

❱❛❧✐❞❛t✐♦♥ ♦❢ ♠❡t❤♦❞

❘❡s✉❧ts ♦♥ P❧❛♥❝❦ ✏◆♦♠✐♥❛❧ ♠✐ss✐♦♥✧ ❧✐❦❡❦❧✐❤♦♦❞

10-2 10-1

k (Mpc−1 )

0.15 0.10 0.05 0.00 0.05 0.10 0.15

f(k)

λ =103

10-2 10-1

k (Mpc−1 )

0.05 0.00 0.05 0.10

f(k)

λ =104

10-2 10-1

k (Mpc−1 )

0.03 0.02 0.01 0.00 0.01 0.02 0.03

f(k)

λ =105

10-2 10-1

k (Mpc−1 )

0.02 0.01 0.00 0.01 0.02

f(k)

λ =106

103 104 105 106

λ

0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72

h

103 104 105 106

λ

0.108 0.110 0.112 0.114 0.116 0.118 0.120 0.122 0.124 0.126

Ωch2

103 104 105 106

λ

2.00 2.05 2.10 2.15 2.20 2.25 2.30

100 ×Ωbh2

▼❛①✐♠✉♠ ❡①❝✉rs✐♦♥s ❧♦❝❛❧❧② ✸.✷σ ❛♥❞ ✸.✾σ ❢♦r λ = ✶✵✹ ❛♥❞ ✶✵✸✱ r❡s♣❡❝t✐✈❡❧②✳ ❆❢t❡r ❧♦♦❦✲❡❧s❡✇❤❡r❡✲❡✛❡❝t tr❛♥s❧❛t❡s ✐♥t♦ ♣ = ✶.✼✹% ❛♥❞ ♣ = ✵.✷✶%, ♦r ✷.✹σ ❛♥❞ ✸.✶σ.

❲❤❡r❡ ❞♦❡s t❤✐s ❝♦♠❡ ❢r♦♠ ✐♥ t❤❡ ❈▼❇ ♠✉❧t✐♣♦❧❡ ♣♦✇❡r s♣❡❝tr✉♠❄

500 1000 1500 2000 2500

ℓ

100 50 50 100

∆

ℓ(µK)2

100 GHz

500 1000 1500 2000 2500

ℓ

100 50 50 100

∆

ℓ(µK)2

143 GHz

500 1000 1500 2000 2500

ℓ

100 50 50 100

∆

ℓ(µK)2

217 GHz

500 1000 1500 2000 2500

ℓ

100 50 50 100

∆

ℓ(µK)2

143 x 217 GHz

Pr♦♦❢ t❤❛t s✐❣♥❛❧ ✐s ❢r♦♠ ❛r♦✉♥❞ ℓ ≈ ✶✽✵✵

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

k (Mpc−1 )

0.10 0.05 0.00 0.05 0.10

f(k)

500 1000 1500 2000 2500

ℓ

15 10 5 5 10 15

∆

ℓ(µK)2

✭❊①tr❛❝t ❢r♦♠ ♣❛r❛♠❡t❡rs ♣❛♣❡r✮

✭❊①tr❛❝t ❢r♦♠ ♣❛r❛♠❡t❡rs ♣❛♣❡r✮

✭❊①tr❛❝t ❢r♦♠ ♣❛r❛♠❡t❡rs ♣❛♣❡r✮

❈♦♥str❛✐♥ts ♦♥ ♥❡✉tr✐♥♦ ♣❤②s✐❝s

■♠♣❛❝t ♦❢ ♥❡✉tr✐♥♦s ♦♥ ❈▼❇

✶✳ ❆❝t✉❛❧ ✭♣r❡❝✐s✐♦♥✮ ❛♥❛❧②s✐s ✐s s♦♠❡✇❤❛t ♠✐♥❞❧❡ss✳ ✭✶✮ ■♥❝♦r♣♦r❛t❡ ♥❡✇ ♣❤②s✐❝s ✐♥ ❇♦❧t③♠❛♥♥ s♦❧✈❡r ✭❡✳❣✳✱ ❈❆▼❇✱ ❈▲❆❙❙✱✳✳✳✳✮ ✭✷✮ ❘✉♥ ▼♦♥t❡ ❈❛r❧♦ ▼❛r❝♦ ❈❤❛✐♥ ✭▼❈▼❈✮ ✭✷✮ ❈❤❡❝❦ ❢♦r ❝♦♥✈❡r❣❡♥❝❡✱ ♣r✐♦r ❞❡♣❡♥❞❡♥❝❡✱ ✳✳✳✳✳ ✭✸✮ ❈♦♠♣❛r❡ q✉❛❧✐t② ♦❢ ✜ts✳ ✷✳ Pr❡❝✐s✐♦♥ ❛♣♣r♦❛❝❤ ❣✐✈❡s ♥♦ ✐♥t✉✐t✐♦♥✳ ❉✐✣❝✉❧t t♦ ✉♥❞❡rst❛♥❞ ✇❤❛t ✐s r❡❛❧❧② ❜❡✐♥❣ t❡st❡❞✳ ❉✐✣❝✉❧t t♦ ❦♥♦✇ ✇❤❛t ♥❡✇ ♠♦❞❡❧s t♦ ❧♦♦❦ ❢♦r ✐♥ ♦r❞❡r t♦ ❡①♣❧❛✐♥ ♣♦ss✐❜❧❡ ❛♥♦♠❛❧✐❡s✳ ✸✳ ◆❡✉tr✐♥♦s ❛✛❡❝t ♠♦❞❡❧ ❈▼❇ ♣r✐♠❛r✐❧② ✐♥ t❤r❡❡ ✇❛②s✿ ✭✶✮ ♥✉♠❜❡r ♦❢ r❡❧❛t✐✈✐st✐❝ s♣❡❝✐❡s s❤✐❢ts ♠♦♠❡♥t ♦❢ ♠❛tt❡r✲r❛❞✐❛t✐♦♥ ❡q✉❛❧✐t②✱ ❛✛❡❝t✐♥❣ t❤❡ ❞❛♠♣✐♥❣ t❛✐❧✳ ✭❊❛r❧② r❡❝♦♠❜✐♥❛t✐♦♥ ♠❡❛♥s ♠♦r❡ ✏✈✐s❝♦s✐t②✑✮✱ ✭✷✮ ✏❡❛r❧②✑ ✐♥t❡❣r❛t❡❞ ❙❛❝❤s✲❲♦❧❢❡ ❡✛❡❝t✱ ❡①t❡♥❞✐♥❣ ✈✐s✐❜✐❧✐t② s✉r❢❛❝❡✱ ✭✸✮ ❣r❛✈✐t❛t✐♦♥❛❧ ❧❡♥s✐♥❣ ✭❛❦❛ ❧❛t❡✲t✐♠❡ ✐♥t❡❣r❛t❡❞ ❙❛❝❤s✲❲♦❧❢❡ ❛t ❧❛r❣❡ ℓ✮✳ ❉❡✜❝✐t ♦❢ ❤❛❧♦ str✉❝t✉r❡ ♦♥ s♠❛❧❧✲s❝❛❧❡s✳ ✹✳ ❲❤✐❧❡ ♥♦♥✲❝♦s♠♦❧♦❣✐❝❛❧ ♥❡✉tr✐♥♦ ❡①♣❡r✐♠❡♥ts ❞❡♣❡♥❞ s❡♥s✐t✐✈❡❧② ♦♥ t❤❡ ❝♦✉♣❧✐♥❣ ♦❢ ♥❡✉tr✐♥♦s t♦ t❤❡ ❙t❛♥❞❛r❞ ▼♦❞❡❧✱ ❝♦s♠♦❧♦❣✐❝❛❧ ♣r♦❜❡s ❛r❡ s❡♥s✐t✐✈❡ t♦ ♥❡✉tr✐♥♦ ❜❡❝❛✉s❡ ♦❢ t❤❡ ❣r❛✈✐t❛t✐♦♥❛❧ ❝♦✉♣❧✐♥❣✳ ❚❤✉s ✏❛❝t✐✈❡✑ ❛♥❞ ✏st❡r✐❧❡✑ ♥❡✉tr✐♥♦s ✐♠♣r✐♥t t❤❡ s❛♠❡ ❈▼❇ ❛♥✐s♦tr♦♣✐❡s✳

P❧❛♥❝❦ ♥❡✉tr✐♥♦ ❝♦♥str❛✐♥ts

❲▼❆P ❙❡✈❡♥✲②❡❛r ❝❧❛✐♠✿ ◆❡✛ = ✹.✸✹ ± ✵.✽✼ ❲▼❆P ◆✐♥❡✲②❡❛r ❝❧❛✐♠✿ ◆❡✛ = ✸.✽✹ ± ✵.✹✵ ♠✈ < ✵.✹✹❡❱ ✾✺% ❝♦♥✜❞❡♥❝❡✳ P❧❛♥❝❦✿ ◆❡✛ = ✸.✺✷+✵.✹✽

−✵.✹✺(✾✺%❈♦♥✜❞❡♥❝❡; P❧❛♥❝❦ + ❲P + ❍✵ + ❇❆❖)

♠✈ < ✵.✷✽❡❱ ✾✺% ❝♦♥✜❞❡♥❝❡✳

P❧❛♥❝❦ ✷✵✶✸ ❘❡s✉❧ts✳ ❳❳■❱✳ ❈♦♥str❛✐♥ts ♦♥ ♣r✐♠♦r❞✐❛❧ ♥♦♥✲●❛✉ss✐❛♥✐t②

P❧❛♥❝❦ ❈♦❧❧❛❜♦r❛t✐♦♥✿ P✳ ❆✳ ❘✳ ❆❞❡✱ ◆✳ ❆❣❤❛♥✐♠✱ ❈✳ ❆r♠✐t❛❣❡✲❈❛♣❧❛♥✱ ▼✳ ❆r♥❛✉❞✱ ▼✳ ❆s❤❞♦✇♥✱ ❋✳ ❆tr✐♦✲❇❛r❛♥❞❡❧❛✱ ❏✳ ❆✉♠♦♥t✱ ❈✳ ❇❛❝❝✐❣❛❧✉♣✐✱ ❆✳ ❏✳ ❇❛♥❞❛②✱ ❘✳ ❇✳ ❇❛rr❡✐r♦✱ ❏✳ ●✳ ❇❛rt❧❡tt✱ ◆✳ ❇❛rt♦❧♦✱ ❊✳ ❇❛tt❛♥❡r✱ ❑✳ ❇❡♥❛❜❡❞✱ ❆✳ ❇❡♥♦ît✱ ❆✳ ❇❡♥♦✐t✲▲é✈②✱ ❏✳✲P✳ ❇❡r♥❛r❞✱ ▼✳ ❇❡rs❛♥❡❧❧✐✱ P✳ ❇✐❡❧❡✇✐❝③✱ ❏✳ ❇♦❜✐♥✱ ❏✳ ❏✳ ❇♦❝❦✱ ❆✳ ❇♦♥❛❧❞✐✱ ▲✳ ❇♦♥❛✈❡r❛✱ ❏✳ ❘✳ ❇♦♥❞✱ ❏✳ ❇♦rr✐❧❧✱ ❋✳ ❘✳ ❇♦✉❝❤❡t✱ ▼✳ ❇r✐❞❣❡s✱ ▼✳ ❇✉❝❤❡r✱ ❈✳ ❇✉r✐❣❛♥❛✱ ❘✳ ❈✳ ❇✉t❧❡r✱ ❏✳✲❋✳ ❈❛r❞♦s♦✱ ❆✳ ❈❛t❛❧❛♥♦✱ ❆✳ ❈❤❛❧❧✐♥♦r✱ ❆✳ ❈❤❛♠❜❛❧❧✉✱ ▲✳✲❨ ❈❤✐❛♥❣✱ ❍✳ ❈✳ ❈❤✐❛♥❣✱ P✳ ❘✳ ❈❤r✐st❡♥s❡♥✱ ❙✳ ❈❤✉r❝❤✱ ❉✳ ▲✳ ❈❧❡♠❡♥ts✱ ❙✳ ❈♦❧♦♠❜✐✱ ▲✳ P✳ ▲✳ ❈♦❧♦♠❜♦✱ ❋✳ ❈♦✉❝❤♦t✱ ❆✳ ❈♦✉❧❛✐s✱ ❇✳ P✳ ❈r✐❧❧✱ ❆✳ ❈✉rt♦✱ ❋✳ ❈✉tt❛✐❛✱ ❘✳ ❉✳ ❉❛✈✐❡s✱ ❘✳ ❏✳ ❉❛✈✐s✱ P✳ ❞❡ ❇❡r♥❛r❞✐s✱ ❆✳ ❞❡ ❘♦s❛✱ ●✳ ❞❡ ❩♦tt✐✱ ❏✳ ❉❡❧❛❜r♦✉✐❧❧❡✱ ❏✳✲▼✳ ❉❡❧♦✉✐s✱ ❋✳✲❳✳ ❉és❡rt✱ ❏✳ ▼✳ ❉✐❡❣♦✱ ❍✳ ❉♦❧❡✱ ❙✳ ❉♦♥③❡❧❧✐✱ ❡t ❛❧✳ ✭✶✼✺ ❛❞❞✐t✐♦♥❛❧ ❛✉t❤♦rs ♥♦t s❤♦✇♥✮ ✭❙✉❜♠✐tt❡❞ ♦♥ ✷✵ ▼❛r ✷✵✶✸✮ ❚❤❡ P❧❛♥❝❦ ♥♦♠✐♥❛❧ ♠✐ss✐♦♥ ❝♦s♠✐❝ ♠✐❝r♦✇❛✈❡ ❜❛❝❦❣r♦✉♥❞ ✭❈▼❇✮ ♠❛♣s ②✐❡❧❞ ✉♥♣r❡❝❡❞❡♥t❡❞ ❝♦♥str❛✐♥ts ♦♥ ♣r✐♠♦r❞✐❛❧ ♥♦♥✲●❛✉ss✐❛♥✐t② ✭◆●✮✳ ❯s✐♥❣ t❤r❡❡ ♦♣t✐♠❛❧ ❜✐s♣❡❝tr✉♠ ❡st✐♠❛t♦rs✱ s❡♣❛r❛❜❧❡ t❡♠♣❧❛t❡✲✜tt✐♥❣ ✭❑❙❲✮✱ ❜✐♥♥❡❞✱ ❛♥❞ ♠♦❞❛❧✱ ✇❡ ♦❜t❛✐♥ ❝♦♥s✐st❡♥t ✈❛❧✉❡s ❢♦r t❤❡ ♣r✐♠♦r❞✐❛❧ ❧♦❝❛❧✱ ❡q✉✐❧❛t❡r❛❧✱ ❛♥❞ ♦rt❤♦❣♦♥❛❧ ❜✐s♣❡❝tr✉♠ ❛♠♣❧✐t✉❞❡s✱ q✉♦t✐♥❣ ❛s ♦✉r ✜♥❛❧ r❡s✉❧t ❢ ❧♦❝❛❧

◆▲

= ✷.✼ ± ✺.✽, ❢ ❡q✉✐❧

◆▲

= −✹✷ ± ✼✺, ❛♥❞ ❢ ♦rt❤♦

◆▲

= −✷✺ ± ✸✾ ✭✻✽✪ ❈▲ st❛t✐st✐❝❛❧✮❀ ❛♥❞ ✇❡ ✜♥❞ t❤❡ ✐♥t❡❣r❛t❡❞ ❙❛❝❤s✲❲♦❧❢❡ ❧❡♥s✐♥❣ ❜✐s♣❡❝tr✉♠ ❡①♣❡❝t❡❞ ✐♥ t❤❡ Λ❈❉▼ s❝❡♥❛r✐♦✳ ❚❤❡ r❡s✉❧ts ❛r❡ ❜❛s❡❞ ♦♥ ❝♦♠♣r❡❤❡♥s✐✈❡ ❝r♦ss✲✈❛❧✐❞❛t✐♦♥ ♦❢ t❤❡s❡ ❡st✐♠❛t♦rs ♦♥ ●❛✉ss✐❛♥ ❛♥❞ ♥♦♥✲●❛✉ss✐❛♥ s✐♠✉❧❛t✐♦♥s✱ ❛r❡ st❛❜❧❡ ❛❝r♦ss ❝♦♠♣♦♥❡♥t s❡♣❛r❛t✐♦♥ t❡❝❤♥✐q✉❡s✱ ♣❛ss ❛♥ ❡①t❡♥s✐✈❡ s✉✐t❡ ♦❢ t❡sts✱ ❛♥❞ ❛r❡ ❝♦♥✜r♠❡❞ ❜② s❦❡✇✲❈❧ , ✇❛✈❡❧❡t ❜✐s♣❡❝tr✉♠ ❛♥❞ ▼✐♥❦♦✇s❦✐ ❢✉♥❝t✐♦♥❛❧ ❡st✐♠❛t♦rs✳ ❇❡②♦♥❞ ❡st✐♠❛t❡s ♦❢ ✐♥❞✐✈✐❞✉❛❧ s❤❛♣❡ ❛♠♣❧✐t✉❞❡s✱ ✇❡ ♣r❡s❡♥t ♠♦❞❡❧✲✐♥❞❡♣❡♥❞❡♥t✱ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ r❡❝♦♥str✉❝t✐♦♥s ♦❢ t❤❡ P❧❛♥❝❦ ❈▼❇ ❜✐s♣❡❝tr✉♠ ❛♥❞ t❤✉s ❞❡r✐✈❡ ❝♦♥str❛✐♥ts ♦♥ ❡❛r❧②✲❯♥✐✈❡rs❡ s❝❡♥❛r✐♦s t❤❛t ❣❡♥❡r❛t❡ ♣r✐♠♦r❞✐❛❧ ◆●✱ ✐♥❝❧✉❞✐♥❣ ❣❡♥❡r❛❧ s✐♥❣❧❡✲✜❡❧❞ ♠♦❞❡❧s ♦❢ ✐♥✢❛t✐♦♥✱ ❡①❝✐t❡❞ ✐♥✐t✐❛❧ st❛t❡s ✭♥♦♥✲❇✉♥❝❤✲❉❛✈✐❡s ✈❛❝✉❛✮✱ ❛♥❞ ❞✐r❡❝t✐♦♥❛❧❧②✲❞❡♣❡♥❞❡♥t ✈❡❝t♦r ♠♦❞❡❧s✳ ❲❡ ♣r♦✈✐❞❡ ❛♥ ✐♥✐t✐❛❧ s✉r✈❡② ♦❢ s❝❛❧❡✲❞❡♣❡♥❞❡♥t ❢❡❛t✉r❡ ❛♥❞ r❡s♦♥❛♥❝❡ ♠♦❞❡❧s✳ ❚❤❡s❡ r❡s✉❧ts ❜♦✉♥❞ ❜♦t❤ ❣❡♥❡r❛❧ s✐♥❣❧❡✲✜❡❧❞ ❛♥❞ ♠✉❧t✐✲✜❡❧❞ ♠♦❞❡❧ ♣❛r❛♠❡t❡r r❛♥❣❡s✱ s✉❝❤ ❛s t❤❡ s♣❡❡❞ ♦❢ s♦✉♥❞✱ ❝s ≥ ✵.✵✷(✾✺%❈▲)✱ ✐♥ ❛♥ ❡✛❡❝t✐✈❡ ✜❡❧❞ t❤❡♦r② ♣❛r❛♠❡tr✐③❛t✐♦♥✱ ❛♥❞ t❤❡ ❝✉r✈❛t♦♥ ❞❡❝❛② ❢r❛❝t✐♦♥ r❉ ≥ ✵.✶✺(✾✺%❈▲)✳ ❚❤❡ P❧❛♥❝❦ ❞❛t❛ ♣✉t s❡✈❡r❡ ♣r❡ss✉r❡ ♦♥ ❡❦♣②r♦t✐❝✴❝②❝❧✐❝ s❝❡♥❛r✐♦s✳ ❚❤❡ ❛♠♣❧✐t✉❞❡ ♦❢ t❤❡ ❢♦✉r✲♣♦✐♥t ❢✉♥❝t✐♦♥ ✐♥ t❤❡ ❧♦❝❛❧ ♠♦❞❡❧ τ◆▲ < ✷✽✵✵(✾✺%❈▲). ❚❛❦❡♥ t♦❣❡t❤❡r✱ t❤❡s❡ ❝♦♥str❛✐♥ts r❡♣r❡s❡♥t t❤❡ ❤✐❣❤❡st ♣r❡❝✐s✐♦♥ t❡sts t♦ ❞❛t❡ ♦❢ ♣❤②s✐❝❛❧ ♠❡❝❤❛♥✐s♠s ❢♦r t❤❡ ♦r✐❣✐♥ ♦❢ ❝♦s♠✐❝ str✉❝t✉r❡✳

■♠♣❧✐❝❛t✐♦♥s ❢♦r ✐♥✢❛t✐♦♥✖s✉♠♠❛r② ♣❧♦t

0.94 0.96 0.98 1.00 Primordial Tilt (ns) 0.00 0.05 0.10 0.15 0.20 0.25 Tensor-to-Scalar Ratio (r0.002) Convex Concave Planck+WP Planck+WP+highL Planck+WP+BAO Natural Inflation Power law inflation Low Scale SSB SUSY R2 Inflation V ∝ φ2/3 V ∝ φ V ∝ φ2 V ∝ φ3 N∗=50 N∗=60

❈♦♥str❛✐♥ts ♦♥ ✐s♦❝✉r✈❛t✉r❡ ♠♦❞❡s

❙t❛t✐st✐❝❛❧ ■s♦tr♦♣②❄

❚❤❡ ❋✉t✉r❡

❈♦♥str❛✐♥✐♥❣ ✐♥✢❛t✐♦♥ ✇✐t❤ ❈❖r❊

ns Δφ / mpl r

0.95 1 1 0.1 0.01 10 1.05 10

−4

10

−3

10

−2

10

−1

10

r

10

−5

10

−4

10

−3

10

−2

10

−1

10

power law

WMAP constraints COrE constraints

chaotic p=8 chaotic p=1 chaotic p=0.1 Spontaneous Symmetry Breaking Allowed region if no tensor modes detected with COrE Allowed region if no tensor modes detected with COrE

r = ✶✵−✸ ❛t ✸σ ❛t ❧❡❛st✳