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]