just enough inflation: power spectrum modifications on large...

Francisco Gil Pedro !

!!

in collaboration with: Michele Cicoli, Bhaskar Dutta,

Sean Downes, and Alexander Westphal

Just enough inflation: power spectrum modifications

on large scales[1407.1048]

Outline:

Observational hints The standard inflationary picture The spectrum of slow-roll inflation Pre-inflation and the power spectrum Degeneracy in power loss Summary

Francisco Gil Pedro, Trieste, 8 July 2014

Observational hints

Francisco Gil Pedro, Trieste, 8 July 2014

Observational hints

Francisco Gil Pedro, Trieste, 8 July 2014

Observational hints

Francisco Gil Pedro, Trieste, 8 July 2014

Observational hints

Francisco Gil Pedro, Trieste, 8 July 2014

large r increases: -significance of power loss

-level of power loss

Tensor modes contribute to TT spectrum on large

scales

Cosmic varianceWe only have one sky

Measurements on largest scales are statistically limited[Planck XV]

Cosmic variance

[1309.4060]

CV can be decreased using LSS data

CV is the simplest explanation for low-

anomaly`

Francisco Gil Pedro, Trieste, 8 July 2014

The standard pictureln aH

Ne

radiation era:

ln aH � �Ne

matter era:

ln aH � �12Ne

60 e-folds of slow-roll:

ln aH � +Ne

tet60Francisco Gil Pedro, Trieste, 8 July 2014

The standard pictureln aH

Ne

radiation era:

ln aH � �Ne

matter era:

ln aH � �12Ne

60 e-folds of slow-roll:

ln aH � +Ne

tet60Francisco Gil Pedro, Trieste, 8 July 2014

The standard pictureln aH

Ne

radiation era:

ln aH � �Ne

matter era:

ln aH � �12Ne

60 e-folds of slow-roll:

ln aH � +Ne

tet60

decays

Francisco Gil Pedro, Trieste, 8 July 2014

The standard pictureln aH

Ne

radiation era:

ln aH � �Ne

matter era:

ln aH � �12Ne

60 e-folds of slow-roll:

ln aH � +Ne

tet60

decays freezes

Francisco Gil Pedro, Trieste, 8 July 2014

The standard pictureln aH

Ne

radiation era:

ln aH � �Ne

matter era:

ln aH � �12Ne

60 e-folds of slow-roll:

ln aH � +Ne

tet60

decays freezes decays

Francisco Gil Pedro, Trieste, 8 July 2014

The Mukhanov-Sasaki Equation

u00 +

✓k2 � z00

z

◆u = 0

z ⌘ ap2✏Hu ⌘ ⇣ zcurvature perturbation: ⇣ with

Useful to use efolds as ‘time’ coordinate

aH ⇠ e⇠NAssume background of the form:

Francisco Gil Pedro, Trieste, 8 July 2014

The Mukhanov-Sasaki Equation

u00 +

✓k2 � z00

z

◆u = 0

z ⌘ ap2✏Hu ⌘ ⇣ zcurvature perturbation: ⇣ with

Useful to use efolds as ‘time’ coordinate

aH ⇠ e⇠NAssume background of the form:

⇠ = 1 +O (✏H , ⌘H)

inflation:

Francisco Gil Pedro, Trieste, 8 July 2014

The Mukhanov-Sasaki Equation

u00 +

✓k2 � z00

z

◆u = 0

z ⌘ ap2✏H

u↵↵ + ⇠ u↵ +

(✓k

aH

◆2

� (1 + ⇠)

)u = 0

u ⌘ ⇣ zcurvature perturbation: ⇣ with

Useful to use efolds as ‘time’ coordinate

aH ⇠ e⇠NAssume background of the form:

⇠ = 1 +O (✏H , ⌘H)

inflation:

Francisco Gil Pedro, Trieste, 8 July 2014

The Mukhanov-Sasaki EquationLhor

⌘ H�1

k < a H $ �phys > H�1

k > a H $ �phys < H�1 inside horizon, decays

outside horizon, freezes

⇣

⇣

Behaviour of curvature pert. depends on during inflation:

Francisco Gil Pedro, Trieste, 8 July 2014

The Mukhanov-Sasaki EquationLhor

⌘ H�1

k < a H $ �phys > H�1

k > a H $ �phys < H�1 inside horizon, decays

outside horizon, freezes

⇣

⇣

Behaviour of curvature pert. depends on

u = C(1) 1p⇠aH

H(1)⌫

✓k

⇠aH

◆+ C(2) 1p

⇠aHH(2)

⌫

✓k

⇠aH

◆

set by ics

during inflation:

Francisco Gil Pedro, Trieste, 8 July 2014

The spectrum of slow-roll inflation

Francisco Gil Pedro, Trieste, 8 July 2014

The spectrum of slow-roll inflation

deep inside horizon modes do not feel curvature

Francisco Gil Pedro, Trieste, 8 July 2014

The spectrum of slow-roll inflation

deep inside horizon modes do not feel curvature

⇠ = 1 +O (✏H , ⌘H)

flat space mode functions

Francisco Gil Pedro, Trieste, 8 July 2014

The spectrum of slow-roll inflation

deep inside horizon modes do not feel curvature

⇠ = 1 +O (✏H , ⌘H)

flat space mode functions

Francisco Gil Pedro, Trieste, 8 July 2014

The spectrum of slow-roll inflation

ns = 0.9603± 0.0073

k⇤ = 0.002 Mpc�1

ln(1010As) = 3.089+0.024�0.027

Scale invariance is excluded by more than 5�

Planck XXII:

Pk = As

✓k

k⇤

◆ns�1

Francisco Gil Pedro, Trieste, 8 July 2014

Pre-inflation and the power spectrum

?? What if inflation was short ??

Francisco Gil Pedro, Trieste, 8 July 2014

Pre-inflation and the power spectrum

?? What if inflation was short ??

theoretically well motivated:

Freivogel et al. 2007 McAllister et al. 2013

Francisco Gil Pedro, Trieste, 8 July 2014

Pre-inflation and the power spectrum

?? What if inflation was short ??

??

Modifies large scale part of spectrum

Can this leave an imprint on the power spectrum?

theoretically well motivated:

Freivogel et al. 2007 McAllister et al. 2013

Francisco Gil Pedro, Trieste, 8 July 2014

ln aH

Ne

slow-roll inflationpre-inflation

?

Pre-inflation and the power spectrum

Francisco Gil Pedro, Trieste, 8 July 2014

ln aH

Ne

slow-roll inflationpre-inflation

? k � a0H0

Pre-inflation and the power spectrum

Francisco Gil Pedro, Trieste, 8 July 2014

ln aH

Ne

slow-roll inflationpre-inflation

? k � a0H0

k ⇠ a0H0

Pre-inflation and the power spectrum

Francisco Gil Pedro, Trieste, 8 July 2014

What pre-inflation?• Fast-roll

• Super inflation

• Climbing scalars

• Radiation domination

• Matter domination

• Curvature domination

⇠ = 2

Contaldi et al. 2003

Liu et al. 2013

Sagnotti et al. 2012/14

Nicholson&Contaldi 2007

Kinney&Powell 2008

⇠ = 0 Linde et al. 1998,…,2011

Francisco Gil Pedro, Trieste, 8 July 2014

What pre-inflation?• Fast-roll

• Super inflation

• Climbing scalars

• Radiation domination

• Matter domination

• Curvature domination

⇠ = 2

Contaldi et al. 2003

Liu et al. 2013

Sagnotti et al. 2012/14

Nicholson&Contaldi 2007

Kinney&Powell 2008

What similarities and what differences?

⇠ = 0 Linde et al. 1998,…,2011

Francisco Gil Pedro, Trieste, 8 July 2014

! = �1 + 2 ⇠

3

What pre-inflation?

⇠ > 1

0 < ⇠ < 1IIIlnaH

Ne

II

IV

�1/2 < ⇠ < 0

w < �1

�1 < w < �1/3

�1/3 < w < 0

w > 0

! ⇡ �1⇠ ⇡ 1

I

⇠ < �1/2 aH ⇠ e⇠N

Francisco Gil Pedro, Trieste, 8 July 2014

What pre-inflation?

⇠ > 1

lnaH

Ne

IV

w < �1

w > 0

! ⇡ �1⇠ ⇡ 1

I

⇠ < �1/2

! = �1 + 2 ⇠

3

aH ⇠ e⇠N

Francisco Gil Pedro, Trieste, 8 July 2014

Type I backgroundsln

aH

Ne

⇠ ⇠ 1

⌫ ⇠ 3/2⇠ < �1/2

⌫ < 3/2

I k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from superhorizon modesDecelerated expansion: decreasesH

Francisco Gil Pedro, Trieste, 8 July 2014

Type I backgroundsln

aH

Ne

⇠ ⇠ 1

⌫ ⇠ 3/2⇠ < �1/2

⌫ < 3/2

I k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from superhorizon modeslarge scales set by pre-inflationary

vacuum

Decelerated expansion: decreasesH

Francisco Gil Pedro, Trieste, 8 July 2014

Type I backgrounds

! Pk ⇠H2

inf

✏H

lnaH

Ne

⇠ ⇠ 1

⌫ ⇠ 3/2⇠ < �1/2

⌫ < 3/2

I k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from superhorizon modeslarge scales set by pre-inflationary

vacuum

Decelerated expansion: decreasesH

Francisco Gil Pedro, Trieste, 8 July 2014

Type I backgrounds

! Pk ⇠H2

inf

✏H

lnaH

Ne

⇠ ⇠ 1

⌫ ⇠ 3/2⇠ < �1/2

⌫ < 3/2

I k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from superhorizon modeslarge scales set by pre-inflationary

vacuum

frozen: decaying: with

⇠ < �2�2 < ⇠ < 0

ns > 1

Decelerated expansion: decreasesH

Francisco Gil Pedro, Trieste, 8 July 2014

Type I backgrounds

! Pk ⇠H2

inf

✏H

lnaH

Ne

⇠ ⇠ 1

⌫ ⇠ 3/2⇠ < �1/2

⌫ < 3/2

I k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from superhorizon modeslarge scales set by pre-inflationary

vacuum

frozen: decaying: with

⇠ < �2�2 < ⇠ < 0

ns > 1 frozen

Decelerated expansion: decreasesH

Francisco Gil Pedro, Trieste, 8 July 2014

Type I backgrounds

! Pk ⇠H2

inf

✏H

lnaH

Ne

⇠ ⇠ 1

⌫ ⇠ 3/2⇠ < �1/2

⌫ < 3/2

I k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from superhorizon modeslarge scales set by pre-inflationary

vacuum

frozen: decaying: with

⇠ < �2�2 < ⇠ < 0

ns > 1 frozen

Decelerated expansion: decreasesH

! Pk ⇠ H2 ⇥✓

k

aH

◆ns�1

deep IR behaviour determined by :ns

Francisco Gil Pedro, Trieste, 8 July 2014

Type I backgrounds

! Pk ⇠H2

inf

✏H

lnaH

Ne

⇠ ⇠ 1

⌫ ⇠ 3/2⇠ < �1/2

⌫ < 3/2

I k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from superhorizon modeslarge scales set by pre-inflationary

vacuum

frozen: decaying: with

⇠ < �2�2 < ⇠ < 0

ns > 1 frozen

Decelerated expansion: decreasesH

! Pk ⇠ H2 ⇥✓

k

aH

◆ns�1

deep IR behaviour determined by :ns

IR power suppression

⌧1z }| {

Francisco Gil Pedro, Trieste, 8 July 2014

Different peak amplitudeDifferent low-k fall-off

Same broad features

red green blue ⇠ = �1

⇠ = �2⇠ = �1/2 matter

fast-roll radiation

background:

0.01 0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

kphysêHinf

P k

Type I backgrounds

Francisco Gil Pedro, Trieste, 8 July 2014

We see what we put in: choice of ICs determines power

on large scales

Type IV backgrounds

⇠ > 11

2< ⌫ <

3

2

lnaH

Ne

IV

⇠ ⇠ 1

⌫ ⇠ 3/2 k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from pre-inf. subhorizon modesAccelerated expansion: is growingH H / e(⇠�1)Ne

Francisco Gil Pedro, Trieste, 8 July 2014

Type IV backgrounds

! Pk ⇠H2

inf

✏H

⇠ > 11

2< ⌫ <

3

2

lnaH

Ne

IV

⇠ ⇠ 1

⌫ ⇠ 3/2 k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from pre-inf. subhorizon modesAccelerated expansion: is growingH H / e(⇠�1)Ne

Francisco Gil Pedro, Trieste, 8 July 2014

Type IV backgrounds

! Pk ⇠H2

inf

✏H

⇠ > 11

2< ⌫ <

3

2

lnaH

Ne

IV

⇠ ⇠ 1

⌫ ⇠ 3/2 k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from pre-inf. subhorizon modesAccelerated expansion: is growingH H / e(⇠�1)Ne

frozen with ns > 1

Francisco Gil Pedro, Trieste, 8 July 2014

Type IV backgrounds

! Pk ⇠H2

inf

✏H

⇠ > 11

2< ⌫ <

3

2

lnaH

Ne

IV

⇠ ⇠ 1

⌫ ⇠ 3/2 k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from pre-inf. subhorizon modesAccelerated expansion: is growingH H / e(⇠�1)Ne

frozenfrozen with ns > 1

Francisco Gil Pedro, Trieste, 8 July 2014

Type IV backgrounds

! Pk ⇠H2

inf

✏H

⇠ > 11

2< ⌫ <

3

2

lnaH

Ne

IV

⇠ ⇠ 1

⌫ ⇠ 3/2 k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from pre-inf. subhorizon modesAccelerated expansion: is growingH H / e(⇠�1)Ne

! Pk ⇠ H2 ⇥✓

k

aH

◆ns�1

frozenfrozen with ns > 1

Francisco Gil Pedro, Trieste, 8 July 2014

Type IV backgrounds

! Pk ⇠H2

inf

✏H

⇠ > 11

2< ⌫ <

3

2

lnaH

Ne

IV

⇠ ⇠ 1

⌫ ⇠ 3/2 k � aH|0

k ⌧ aH|0

k ⇠ aH|0

Large scale spectrum from pre-inf. subhorizon modesAccelerated expansion: is growingH H / e(⇠�1)Ne

! Pk ⇠ H2 ⇥✓

k

aH

◆ns�1

frozenfrozen with ns > 1

Low power on large scales

|{z}⌧H2

inf|{z}⌧1

Francisco Gil Pedro, Trieste, 8 July 2014

0.01 0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

kphysêHinf

P k

⇠ = 3/2⇠ = 2⇠ = 5/2

red green blue

!super-inflation

background:

Type IV backgrounds

Francisco Gil Pedro, Trieste, 8 July 2014

0.01 0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

kphysêHinf

P k

Different peak amplitudeDifferent low-k fall-off

Same broad features

⇠ = 3/2⇠ = 2⇠ = 5/2

red green blue

!super-inflation

background:

Type IV backgrounds

Francisco Gil Pedro, Trieste, 8 July 2014

0.01 0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

kphysêHinf

P k

Different peak amplitudeDifferent low-k fall-off

Same broad features

⇠ = 3/2⇠ = 2⇠ = 5/2

red green blue

!super-inflation

background:

Type IV backgrounds

Francisco Gil Pedro, Trieste, 8 July 2014

More robust than Type I: Insensitive to choice of ICs

Pre-inflation and power loss

Degeneracy: one-parameter family of primordial spectraln

aH

Ne0.001 0.01 0.1 1 10 100 1000

0.0

0.2

0.4

0.6

0.8

1.0

1.2

kphysêHinf

P k

Francisco Gil Pedro, Trieste, 8 July 2014

Pre-inflation and power loss

Interesting hints:[1311.1599] & [1402.1418]

claim these spectra are better fits than simpler monotonic

parametrization 0.001 0.01 0.1 1 10 100 1000

0.0

0.2

0.4

0.6

0.8

1.0

1.2

kphysêHdS

P Q

Degeneracy: one-parameter family of primordial spectraln

aH

Ne0.001 0.01 0.1 1 10 100 1000

0.0

0.2

0.4

0.6

0.8

1.0

1.2

kphysêHinf

P k

Francisco Gil Pedro, Trieste, 8 July 2014

TT Power spectrum

5 10 50 100 500 1000

1000

2000

3000

4000

5000

{

{H{+

1L

2pC {@mK

2 D

10-5 10-4 0.001 0.01 0.10

5. ¥ 10-10

1. ¥ 10-9

1.5 ¥ 10-9

2. ¥ 10-9

2.5 ¥ 10-9

3. ¥ 10-9

k in MPc-1

PHkL

�

�(�+

1)2�

C�[µ

K2]

PQ(k)

k in MPc�1

Francisco Gil Pedro, Trieste, 8 July 2014

Summary

Persistent hints from COBE / WMAP / PLANCK !Short inflation modifies large scale/low- power spectrum

!Different ways to reduce power

!Degeneracy/universality in power loss !Better understanding requires fit to the data

!We might be seeing pre-inflationary phase

`

Francisco Gil Pedro, Trieste, 8 July 2014

Thank you

Francisco Gil Pedro, Trieste, 8 July 2014

[1407.1048]