multiple field inflation with additional heavy fields · from multi-field inflation with heavy...
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![Page 1: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/1.jpg)
Multiple field inflation with additional heavy fields
Yvette Welling
Collaborators: Ana Achúcarro, Vicente Atal
Yvette Welling - Leiden University
[Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486] [YW, MSc Thesis 2014, 1502.04369]
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Bottom line
Stabilized heavy fields present during inflation can
affect the dynamics of low energy degrees of
freedom and leave their imprint on observables.
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E.g. the predictions for and
Yvette Welling - Leiden University 3
r snPlot from [Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486]
Stabilized heavy fields present during inflation can
affect the dynamics of low energy degrees of
freedom and leave their imprint on observables.
![Page 4: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/4.jpg)
E.g. the primordial power spectrum
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Plot from [Cespedes, Atal, Palma., JCAP 2012, 1201.4848] [Achúcarro, Gong, Hardeman, Palma, Patil, PRD 2011, 1010.3693]
Stabilized heavy fields present during inflation can
affect the dynamics of low energy degrees of
freedom and leave their imprint on observables.
![Page 5: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/5.jpg)
E.g. features in the bispectrum
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Plot from [Achúcarro, Atal, Ortiz, Torrado, PRD 2013, 1311.2552]
Stabilized heavy fields present during inflation can
affect the dynamics of low energy degrees of
freedom and leave their imprint on observables.
![Page 6: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/6.jpg)
Single field inflation fits data well.
However there could be more fields present during inflation..
Consider single field inflation as EFT
Coming from multi-field inflation with heavy fields
Do heavy fields influence the observables?
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Motivation: signatures of new physics
![Page 7: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/7.jpg)
Single field inflation fits data well.
However there could be more fields present during inflation..
Consider single field inflation as EFT
from multi-field inflation with heavy fields.
Do heavy fields influence the observables?
Yvette Welling - Leiden University 7
Motivation: signatures of new physics
[Cheung, Creminelli, Fitzpatrick, Kaplan, Senatore, JHEP 2007, 0709.0293]
![Page 8: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/8.jpg)
Single field inflation fits data well.
However there could be more fields present during inflation..
Consider single field inflation as EFT
from multi-field inflation with heavy fields.
Do heavy fields influence the observables?
Yvette Welling - Leiden University 8
Motivation: signatures of new physics
[Cheung, Creminelli, Fitzpatrick, Kaplan, Senatore, JHEP 2007, 0709.0293]
![Page 9: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/9.jpg)
Do they…?
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We mean stabilized heavy fields
Ok, their effects in the low energy EFT should be suppressed by , right..?
NO! There are three scales of importance:
1. mass heavy field
2. curvature target space
3. curvature inflationary trajectory
2 2M H
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Do they…?
Yvette Welling - Leiden University 10
We mean stabilized heavy fields
Ok, their effects in the low energy EFT should be suppressed by , right..?
NO! There are three scales of importance:
1. mass heavy field
2. curvature target space
3. curvature inflationary trajectory
2 2M H
2 2H M
![Page 11: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/11.jpg)
We mean stabilized heavy fields
Ok, their effects in the low energy EFT should be suppressed by , right..?
Yes, but.. prefactor can be large!
There are three scales of importance:
1. mass heavy field
2. curvature target space
3. curvature inflationary trajectory
Do they…?
11
2 2M H
2 2H M
[Achúcarro, Gong, Hardeman, Palma, Patil, JCAP 2011, 1005.3848] [Burgess, Horbatch, Patil, JHEP 2013, 1209.5701]
![Page 12: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/12.jpg)
Do they…?
12
We mean stabilized heavy fields
Ok, their effects in the low energy EFT should be suppressed by , right..?
Yes, but.. prefactor can be large!
In particular inflationary trajectory can be curved. This couples perturbations.
Integrate out heavy modes with care.
2 2M H
2 2H M
[Achúcarro, Gong, Hardeman, Palma, Patil, JCAP 2011, 1005.3848 / PRD 2011, 1010.3693 / JHEP 2012, 1201.6342 ] [Achúcarro, Atal, Cespedes, Gong, Palma, Patil, PRD 2012, 1205.0710]
[Cespedes, Atal, Palma., JCAP 2012, 1201.4848] [Burgess, Horbatch, Patil, JHEP 2013, 1209.5701]
For a recent review see [Chluba, Hamann, Patil, 1505.01834]
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Intuitive example: a sudden turn
13
A sudden turn in the inflationary trajectory induced by a bend in the potential.
[Achúcarro, Gong, Hardeman, Palma, Patil, PRD 2011, 1010.3693] [Cespedes, Atal, Palma., JCAP 2012, 1201.4848]
![Page 14: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/14.jpg)
Search for features:
Intuitive example: a sudden turn
14
Power spectrum
A sudden turn gives rise to oscillations in the power spectrum (and bispectrum).
Effects of heavy fields cannot be ignored!
[Achúcarro, Gong, Hardeman, Palma, Patil, PRD 2011, 1010.3693] [Cespedes, Atal, Palma., JCAP 2012, 1201.4848]
[Achúcarro, Atal, Ortiz, Torrado, PRD 2013, 1311.2552] See recent review [Chluba, Hamann, Patil, 1505.01834]
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Turn = Not Geodesic
There could be “hidden” turns if field metric is non-trivial
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4 1( )( )
2ab
a bx GS d g V
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Turn = Not Geodesic
There could be “hidden” turns if field metric is non-trivial
Mismatch between geodesics field space and valley potential?
Curved trajectory
16 Yvette Welling - Leiden University
4 1( )( )
2ab
a bx GS d g V
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Tangent and normal decomposition
17 Measures deviation from geodesic
Turn rate
Tangent + normal vector
Curvature perturbation
Isocurvature perturbation
a
a
HT
a
aN
[Gordon, Wands, Bassett, Maartens, PRD 2001, hep-ph/0107272], [Groot Nibbelink, van Tent, CQG 2002, hep-ph/0107272], for a recent review see [YW, MSc Thesis 2014, 1502.04369]
2
22
2
2
2
(3 2 2 ) 2 (3 )
3 ( ) 2
k HH H
a
kH M
a H
2Ra b
ab HN N V
Field speed Radius of curvature
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Coupled oscillators with derivative coupling
Integrate out heavy modes
18 Measures deviation from geodesic
Curvature perturbation
Isocurvature perturbation
cH
a
aN
Turn rate
Following [Achúcarro, Atal, Cespedes, Gong, Palma, Patil, PRD 2012, 1205.0710] See also [Achucarro et al., JCAP 2011, 1005.3848], [Baumann, Green, JCAP 2011, 1102.5343], [Shiu, Xu, PRD 2011, 1108. 0981], [Cespedes et al., JCAP 2012, 1201.4848], [Gwyn, Palma, Sakellariadou, Sypsas, JCAP 2013, 1210.3020]
2
2
22 2
2
2
2 c
c c
k
a
kM
a
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Coupled oscillators with derivative coupling
High and low frequency solutions
Integrate out heavy modes
19
i t
c
i t
e
e
Turn rate
2
2
22 2
2
2
2 c
c c
k
a
kM
a
2
2
2 2
22
23
s
k
ac
M
2
2 2
2 41s
Mc
Following [Achúcarro, Atal, Cespedes, Gong, Palma, Patil, PRD 2012, 1205.0710] See also [Achucarro et al., JCAP 2011, 1005.3848], [Baumann, Green, JCAP 2011, 1102.5343], [Shiu, Xu, PRD 2011, 1108. 0981], [Cespedes et al., JCAP 2012, 1201.4848], [Gwyn, Palma, Sakellariadou, Sypsas, JCAP 2013, 1210.3020]
![Page 20: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/20.jpg)
Coupled oscillators with derivative coupling
Integrate out heavy modes
Integrate out heavy modes
20
2
2
2 2
22
23
s
k
ac
M
2
2 2
2 41s
Mc
Turn rate
2
2
22 2
2
2
2 c
c c
k
a
kM
a
i t
c
i t
e
e
Following [Achúcarro, Atal, Cespedes, Gong, Palma, Patil, PRD 2012, 1205.0710] See also [Achucarro et al., JCAP 2011, 1005.3848], [Baumann, Green, JCAP 2011, 1102.5343], [Shiu, Xu, PRD 2011, 1108. 0981], [Cespedes et al., JCAP 2012, 1201.4848], [Gwyn, Palma, Sakellariadou, Sypsas, JCAP 2013, 1210.3020]
![Page 21: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/21.jpg)
Integrate out heavy modes
Coupled oscillators with derivative coupling
Constraints on validity
21
2 2 1M H
2 1 2 2
20
M
H
Massive enough Adiabatic condition: Turn not too sharp
Stability condition: Turn not too strong
Turn rate
2
2
22 2
2
2
2 c
c c
k
a
kM
a
See [Cespedes, Atal, Palma., JCAP 2012, 1201.4848]
2 2M
Following [Achúcarro, Atal, Cespedes, Gong, Palma, Patil, PRD 2012, 1205.0710] See also [Achucarro et al., JCAP 2011, 1005.3848], [Baumann, Green, JCAP 2011, 1102.5343], [Shiu, Xu, PRD 2011, 1108. 0981], [Cespedes et al., JCAP 2012, 1201.4848], [Gwyn, Palma, Sakellariadou, Sypsas, JCAP 2013, 1210.3020]
![Page 22: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/22.jpg)
Low energy EFT
Integrating out heavy modes yields EFT for
From here compute power spectrum and higher order correlation functions
22
2 234 3
22
2 3
( )/ )
( )(eff
s
PS aM d xa Oc t a
Turn rate
Yvette Welling - Leiden University
2
2 2
2 41s
Mc
See recent review [Chluba, Hamann, Patil, 1505.01834]
![Page 23: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/23.jpg)
Low energy EFT
Integrating out heavy modes yields EFT for
Example: transient reduced speed of sound
23
Turn rate
2 234 3
22
2 3
( )/ )
( )(eff
s
PS aM d xa Oc t a
2
2 2
2 41s
Mc
[Cespedes, Atal, Palma., JCAP 2012, 1201.4848]
See recent review [Chluba, Hamann, Patil, 1505.01834]
![Page 24: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/24.jpg)
Low energy EFT
Integrating out heavy modes yields EFT for
Always compute turn rate to find how observables are affected
24
Turn rate
Yvette Welling - Leiden University
2 234 3
22
2 3
( )/ )
( )(eff
s
PS aM d xa Oc t a
2
2 2
2 41s
Mc
See recent review [Chluba, Hamann, Patil, 1505.01834]
![Page 25: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/25.jpg)
Summary
• Stabilized heavy fields can influence dynamics of low energy degrees of freedom
Yvette Welling - Leiden University 25
[YW, MSc Thesis 2014, 1502.04369], [Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486]
![Page 26: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/26.jpg)
Summary
• Stabilized heavy fields can influence dynamics of low energy degrees of freedom
• This happens whenever the inflationary trajectory is curved (= non-geodesic)
Yvette Welling - Leiden University 26
[YW, MSc Thesis 2014, 1502.04369], [Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486]
![Page 27: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/27.jpg)
Summary
• Stabilized heavy fields can influence dynamics of low energy degrees of freedom
• This happens whenever the inflationary trajectory is curved (= non-geodesic)
• Integrate out heavy modes with care
Yvette Welling - Leiden University 27
[YW, MSc Thesis 2014, 1502.04369], [Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486]
![Page 28: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/28.jpg)
Summary
• Stabilized heavy fields can influence dynamics of low energy degrees of freedom
• This happens whenever the inflationary trajectory is curved (= non-geodesic)
• Integrate out heavy modes with care
• This could result in reduced speed of sound
Yvette Welling - Leiden University 28
[YW, MSc Thesis 2014, 1502.04369], [Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486]
![Page 29: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/29.jpg)
Summary
• Stabilized heavy fields can influence dynamics of low energy degrees of freedom
• This happens whenever the inflationary trajectory is curved (= non-geodesic)
• Integrate out heavy modes with care
• This could result in reduced speed of sound
• Check how observables are affected
Yvette Welling - Leiden University 29
[YW, MSc Thesis 2014, 1502.04369], [Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486]
![Page 30: Multiple field inflation with additional heavy fields · from multi-field inflation with heavy fields. Do heavy fields influence the observables? Yvette Welling - Leiden University](https://reader034.vdocuments.us/reader034/viewer/2022042620/5f47295050758345ab6e7ad0/html5/thumbnails/30.jpg)
Summary
• Stabilized heavy fields can influence dynamics of low energy degrees of freedom
• This happens whenever the inflationary trajectory is curved (= non-geodesic)
• Integrate out heavy modes with care
• This could result in reduced speed of sound
• Check how observables are affected
• Vicente’s talk (next one)
30 Yvette Welling - Leiden University
[YW, MSc Thesis 2014, 1502.04369], [Ana Achúcarro, Vicente Atal, YW, JCAP 2015, 1503.07486]