gonzalo a. palma · gonzalo a. palma first step: the background features of heavy physics in the...
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PASCOS 2011 - Cambridge
Gonzalo A. PalmaDFI - U. de Chile
Subodh Patil (LPTEN & CPTH)
WITH
Ana Achucarro (Leiden)Jinn-Ouk Gong (Leiden & CERN)
Sjoerd Hardeman (Leiden)
Based on: 1005.3848 & 1010.3693
Features of heavy physics in the CMB power spectrum
Gonzalo A. Palma
In this talkFeatures of heavy physics in the CMB power spectrum
PASCOS 2011
What are their effects on the power spectrum and bispectrum?
The status of heavy physics during inflation
The role of heavy physics during inflation
Under which circumstance may we ignore heavy degrees of freedom during inflation?
01
Gonzalo A. Palma
The status of heavy physicsFeatures of heavy physics in the CMB power spectrum
Common lore: If heavy degrees of freedom are sufficiently massive, then we can ignore them...
How massive? M H
They become quickly suppressed on super horizon scales
1 2 3 4 5
60
40
20
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40
60
1 2 3 4 5
60
40
20
20
40
60
02
M2 = 5H
2M2 = 0
PASCOS 2011
Ignored = Truncated
Gonzalo A. PalmaFeatures of heavy physics in the CMB power spectrum
In inflation the v.e.v.’s of massive fields vary as the inflaton evolves!
03PASCOS 2011
The status of heavy physics
Instead of truncating them, we should integrate them out
But:
Difficult (if not impossible) to obtain vacuum expectation values of massive fields independent of the inflaton
Example: SUGRA
ΦM = Φ0(φ)
Gonzalo A. Palma
Multi-field inflationFeatures of heavy physics in the CMB power spectrum
S = √
−g d4x
M2
Pl
2R− 1
2γabg
µν∂µφa∂νφb − V (φ)
04
I will not focus on any specific model
PASCOS 2011
Instead, I will ask myself what happens to adiabatic modes under general “turns” of the inflationary trajectory
V (φ1,φ2)
φ1
φ2
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
D
dtφ
a0 + 3Hφ
a0 + V
a = 0 DXa = dXa + ΓabcX
bdφc
φ1
φ2
Flat valley
05PASCOS 2011
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
D
dtφ
a0 + 3Hφ
a0 + V
a = 0 DXa = dXa + ΓabcX
bdφc
φ1
φ2
Flat valley
Real trayectory
PASCOS 2011 05
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
D
dtφ
a0 + 3Hφ
a0 + V
a = 0 DXa = dXa + ΓabcX
bdφc
φ1
φ2 Na
T a
Flat valley
Real trayectory
PASCOS 2011 05
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
D
dtφ
a0 + 3Hφ
a0 + V
a = 0 DXa = dXa + ΓabcX
bdφc
Tangent and normal vectors
T a ≡ φa0
φ0Na ≡ −
γbc
DT b
dt
DT c
dt
−1/2DT a
dt
φ1
φ2
Flat valley
Real trayectoryNa
T a
PASCOS 2011 05
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
D
dtφ
a0 + 3Hφ
a0 + V
a = 0 DXa = dXa + ΓabcX
bdφc
Tangent and normal vectors
T a ≡ φa0
φ0Na ≡ −
γbc
DT b
dt
DT c
dt
−1/2DT a
dt
φ1
φ2 Na
T aNa
T a
Flat valley
Real trayectory
PASCOS 2011 05
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
D
dtφ
a0 + 3Hφ
a0 + V
a = 0 DXa = dXa + ΓabcX
bdφc
Tangent and normal vectors
T a ≡ φa0
φ0Na ≡ −
γbc
DT b
dt
DT c
dt
−1/2DT a
dt
φ1
φ2
T aNaNa
T aNa
T a
Flat valley
Real trayectory
PASCOS 2011 05
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
ηa ≡ − 1
Hφ0
Dφa0
dt
Slow roll parameters:
ηa = η||Ta + η⊥Na
η|| = − φ0
Hφ0
η⊥ =√
2MPl
κV
φ1
φ2
06PASCOS 2011
≡ − H
H2
Coupling condition
Effects of size ∼ 4η2⊥H
2
M2
See our paper: Achucarro, et. al. (2010)
(Recall talk by Liam McAllister)Groot Nibbelink & van Tent (2000)
Gonzalo A. Palma
First step: The backgroundFeatures of heavy physics in the CMB power spectrum
ηa ≡ − 1
Hφ0
Dφa0
dt
Slow roll parameters:
ηa = η||Ta + η⊥Na
η|| = − φ0
Hφ0
η⊥ =√
2MPl
κ
06PASCOS 2011
≡ − H
H2
Coupling condition
Effects of size ∼ 4η2⊥H
2
M2
1
See our paper: Achucarro, et. al. (2010)
(Recall talk by Liam McAllister)Groot Nibbelink & van Tent (2000)
V
φ1
φ2
Gonzalo A. Palma
Second step: PerturbationsFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
δφa → (T, N)
07PASCOS 2011
d2T
dτ2+
η⊥τ
dN
dτ+
k2 − 2
τ2+
δ
τ2
T + 2
η⊥τ2
N = 0
d2N
dτ2− η⊥
τ
dT
dτ+
k2 − 2
τ2+
M2
H2τ2
N +
η⊥τ2
T = 0
Gonzalo A. Palma
Second step: PerturbationsFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
δφa → (T, N)
07PASCOS 2011
d2T
dτ2+
η⊥τ
dN
dτ+
k2 − 2
τ2+
δ
τ2
T + 2
η⊥τ2
N = 0
d2N
dτ2− η⊥
τ
dT
dτ+
k2 − 2
τ2+
M2
H2τ2
N +
η⊥τ2
T = 0
Tolley & Wayman (2010)Chen & Wang (2010)Cremonini, Lalak & Turzynski (2011)Baumann & Green (2011)
Gonzalo A. Palma
Second step: PerturbationsFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
δφa → (T, N)
07PASCOS 2011
d2T
dτ2+
η⊥τ
dN
dτ+
k2 − 2
τ2+
δ
τ2
T + 2
η⊥τ2
N = 0
d2N
dτ2− η⊥
τ
dT
dτ+
k2 − 2
τ2+
M2
H2τ2
N +
η⊥τ2
T = 0
Flat direction (adiabatic mode)
Gonzalo A. Palma
Second step: PerturbationsFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
δφa → (T, N)
07PASCOS 2011
d2T
dτ2+
η⊥τ
dN
dτ+
k2 − 2
τ2+
δ
τ2
T + 2
η⊥τ2
N = 0
d2N
dτ2− η⊥
τ
dT
dτ+
k2 − 2
τ2+
M2
H2τ2
N +
η⊥τ2
T = 0
Flat direction (adiabatic mode)
Perpendicula direction(massive mode)
Gonzalo A. Palma
Second step: PerturbationsFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
δφa → (T, N)
07PASCOS 2011
d2T
dτ2+
η⊥τ
dN
dτ+
k2 − 2
τ2+
δ
τ2
T + 2
η⊥τ2
N = 0
d2N
dτ2− η⊥
τ
dT
dτ+
k2 − 2
τ2+
M2
H2τ2
N +
η⊥τ2
T = 0
Flat direction (adiabatic mode)
Perpendicula direction(massive mode)
Gonzalo A. Palma
Second step: PerturbationsFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
δφa → (T, N)
07PASCOS 2011
d2T
dτ2+
η⊥τ
dN
dτ+
k2 − 2
τ2+
δ
τ2
T + 2
η⊥τ2
N = 0
d2N
dτ2− η⊥
τ
dT
dτ+
k2 − 2
τ2+
M2
H2τ2
N +
η⊥τ2
T = 0
Flat direction (adiabatic mode)
Perpendicula direction(massive mode)
Gonzalo A. Palma
Second step: PerturbationsFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
δφa → (T, N)
07PASCOS 2011
d2T
dτ2+
η⊥τ
dN
dτ+
k2 − 2
τ2+
δ
τ2
T + 2
η⊥τ2
N = 0
d2N
dτ2− η⊥
τ
dT
dτ+
k2 − 2
τ2+
M2
H2τ2
N +
η⊥τ2
T = 0
Flat direction (adiabatic mode)
Perpendicula direction(massive mode)
Not possible to truncate N = 0
Gonzalo A. Palma
Artificial exampleFeatures of heavy physics in the CMB power spectrum
To make this discussion simple, I consider just two fields:
08
η⊥(N) =η⊥max
cosh2 [2(N −N0)/∆N ]
PASCOS 2011
η⊥
N
∆N
Gonzalo A. Palma
Features in the primordial spectrumFeatures of heavy physics in the CMB power spectrum
PR(k)
kMpc−1
09
0.002 0.005 0.010 0.020 0.050 0.100
0.2
0.4
0.6
0.8
1.0
1.2
1.4
M2/H
2 = 300 ∆N = 1/4 ηmax = 5
η⊥(N) =η⊥max
cosh2 [2(N −N0)/∆N ]
PASCOS 2011
Gonzalo A. PalmaFeatures of heavy physics in the CMB power spectrum
PR(k)
kMpc−1
0.002 0.005 0.010 0.020 0.050 0.100
0.2
0.4
0.6
0.8
1.0
1.2
1.4
M2/H
2 = 300 ∆N = 1/4
η⊥(N) =η⊥max
cosh2 [2(N −N0)/∆N ]
ηmax = 5
∼ 4η2maxH
2
M2
09PASCOS 2011
Features in the primordial spectrum
Gonzalo A. PalmaFeatures of heavy physics in the CMB power spectrum
PR(k)
kMpc−1
0.002 0.005 0.010 0.020 0.050 0.100
0.2
0.4
0.6
0.8
1.0
1.2
1.4
M2/H
2 = 300 ∆N = 1/4 ηmax = 5
η⊥(N) =η⊥max
cosh2 [2(N −N0)/∆N ]
∼ 4η2maxH
2
M2
09PASCOS 2011
Features in the primordial spectrum
∼ H∆N
Gonzalo A. PalmaFeatures of heavy physics in the CMB power spectrum
PR(k)
kMpc−1
0.002 0.005 0.010 0.020 0.050 0.100
0.2
0.4
0.6
0.8
1.0
1.2
1.4
M2/H
2 = 300 ∆N = 1/4 ηmax = 5
η⊥(N) =η⊥max
cosh2 [2(N −N0)/∆N ]
∼ 4η2maxH
2
M2
09PASCOS 2011
Features in the primordial spectrum
∼ H∆N
More realistic situations:Atal, Céspedes, Palma (2011)
Gonzalo A. Palma
Features in the power spectrum?Features of heavy physics in the CMB power spectrum
Tocchini-Valentini, Douspis & Silk (2004)
0.01 0.015 0.02 0.03 0.05 0.07k !Mpc!1"
0
0.5
1
1.5
P0#k$
10PASCOS 2011
For more recent discussions see: Hlozek et. al. (2011)Aich et. al. (2011)
Gonzalo A. Palma
Effective theoryFeatures of heavy physics in the CMB power spectrum
If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns
11
S =12
dτd3x
dϕ
dτ
2
−∇ϕ e−β(τ,−∇2)∇ϕ− ϕ Ω(τ,−∇2)ϕ
Ω(τ, k2) = Ω0(τ)− β
2−
β
2
2
− aHβ(1 + − η||)
Ω0(τ) = −a2H
2(2 + 2− 3η|| − 4η|| − ξ||η|| − 22)
eβ(τ,k2) = 1 +
4η2⊥
M2/H2 − 2 + − η2⊥ + k2/(aH)2
PASCOS 2011
Gonzalo A. Palma
Effective theoryFeatures of heavy physics in the CMB power spectrum
If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns
11
S =12
dτd3x
dϕ
dτ
2
−∇ϕ e−β(τ,−∇2)∇ϕ− ϕ Ω(τ,−∇2)ϕ
Ω(τ, k2) = Ω0(τ)− β
2−
β
2
2
− aHβ(1 + − η||)
Ω0(τ) = −a2H
2(2 + 2− 3η|| − 4η|| − ξ||η|| − 22)
eβ(τ,k2) = 1 +
4η2⊥
M2/H2 − 2 + − η2⊥ + k2/(aH)2
PASCOS 2011
Gonzalo A. Palma
Effective theoryFeatures of heavy physics in the CMB power spectrum
If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns
11
S =12
dτd3x
dϕ
dτ
2
−∇ϕ e−β(τ,−∇2)∇ϕ− ϕ Ω(τ,−∇2)ϕ
Ω(τ, k2) = Ω0(τ)− β
2−
β
2
2
− aHβ(1 + − η||)
Ω0(τ) = −a2H
2(2 + 2− 3η|| − 4η|| − ξ||η|| − 22)
eβ(τ,k2) = 1 +
4η2⊥
M2/H2 − 2 + − η2⊥ + k2/(aH)2
PASCOS 2011
Gonzalo A. Palma
Effective theoryFeatures of heavy physics in the CMB power spectrum
PR(k)
kMpc−1
12
0.002 0.005 0.010 0.020 0.050 0.100
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Effective theory v/s full theory
PASCOS 2011
If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns
Gonzalo A. Palma
Non-GaussianitiesFeatures of heavy physics in the CMB power spectrum
If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns
S =12
dτd3x
dϕ
dτ
2
−∇ϕ e−β(τ,−∇2)∇ϕ− ϕ Ω(τ,−∇2)ϕ
eβ(τ,k2) = 1 +
4η2⊥
M2/H2 − 2 + − η2⊥ + k2/(aH)2
13
c2s
1 +
4η2⊥
M2/H2
−1
Generalisation of Tolley & Wyman (2010)
PASCOS 2011
See also: Cremonini, Lalak, Turzynski (2010)
Gonzalo A. Palma
Non-GaussianitiesFeatures of heavy physics in the CMB power spectrum
If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns
S =12
dτd3x
dϕ
dτ
2
−∇ϕ e−β(τ,−∇2)∇ϕ− ϕ Ω(τ,−∇2)ϕ
eβ(τ,k2) = 1 +
4η2⊥
M2/H2 − 2 + − η2⊥ + k2/(aH)2
Non Gaussianities?
13
c2s
1 +
4η2⊥
M2/H2
−1
Generalisation of Tolley & Wyman (2010)
PASCOS 2011
See also: Cremonini, Lalak, Turzynski (2010)
Gonzalo A. Palma
Non-GaussianitiesFeatures of heavy physics in the CMB power spectrum
14PASCOS 2011
L ⊃√2
H2
4MPl(3+ 2η2⊥)T
3
Achúcarro et. al. (2011)
We find that the most relevant interaction term is of the form
k2/k1
k3/k1
fNL =15
c3s η2⊥
(Preliminary!)
Squeezed shape for non-Gaussianities
See also: Chen & Wang (2010); Baumann & Green (2011)
0.0
0.5
1.0
0.6
0.8
1.0
0
10
20
Gonzalo A. Palma
Non-GaussianitiesFeatures of heavy physics in the CMB power spectrum
14PASCOS 2011
L ⊃√2
H2
4MPl(3+ 2η2⊥)T
3
Achúcarro et. al. (2011)
We find that the most relevant interaction term is of the form
k2/k1
k3/k1
Squeezed shape for non-Gaussianities
fNL =15
c3s η2⊥
(Preliminary!)
See also: Chen & Wang (2010); Baumann & Green (2011)
0.0
0.5
1.0
0.6
0.8
1.0
0
10
20
Gonzalo A. Palma
Concluding remarksFeatures of heavy physics in the CMB power spectrum
Features might offer a direct insight on heavy physics
Fast turns produce features in the primordial spectrum
These features come together with particular non-Gaussian signatures
15PASCOS 2011
Heavy fields allow fast turns to happen under control
Gonzalo A. Palma
Concluding remarksFeatures of heavy physics in the CMB power spectrum
Features might offer a direct insight on heavy physics
Fast turns produce features in the primordial spectrum
These features come together with particular non-Gaussian signatures
15PASCOS 2011
Heavy fields allow fast turns to happen under controlWhy?
Gonzalo A. Palma
Concluding remarksFeatures of heavy physics in the CMB power spectrum
Features might offer a direct insight on heavy physics
Fast turns produce features in the primordial spectrum
These features come together with particular non-Gaussian signatures
15PASCOS 2011
Heavy fields allow fast turns to happen under controlWhy?
And
Gonzalo A. Palma
Concluding remarksFeatures of heavy physics in the CMB power spectrum
Features might offer a direct insight on heavy physics
Fast turns produce features in the primordial spectrum
These features come together with particular non-Gaussian signatures
15PASCOS 2011
Heavy fields allow fast turns to happen under controlWhy?
And
Additionally