Paolo Creminelli (ICTP, Trieste). Non-Gaussianities of cosmological perturbations. with N. Arkani-Hamed, D. Babich, L. Boubekeur, S. Mukohyama, A. Nicolis, L. Senatore, M. Tegmark, and M. Zaldarriaga. Is there any correlation among modes?. Slow-roll = weak coupling. V. Friction is dominant.
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Non-Gaussianities of cosmological perturbations
with N. Arkani-Hamed, D. Babich, L. Boubekeur, S. Mukohyama, A. Nicolis, L. Senatore, M. Tegmark, and M. Zaldarriaga
Friction is dominant
To have ~ dS space the potential must be very flat:
The inflaton is extremely weakly coupled. Leading NG from gravity.
Completely model independent
as it comes from gravity
Unobservable (?). To see any deviation you need > 1012 data. WMAP ~ 2 x 106
Maldacena, JHEP 0305:013,2003, Acquaviva etal Nucl.Phys.B667:119-148,2003
Any signal would be a clear signal of something non-minimal
F contains information about the source of NG
Note. We are only considering primordial NGs. Neglect non-linear relation with observables.
Good until primordial NG > 10-5.
see P.C. + Zaldarriaga, Phys.Rev.D70:083532,2004
Bartolo, Matarrese and Riotto, JCAP 0606:024,2006
P.C. JCAP 0310:003,2003
Change inflaton dynamics and thus density perturbations
Potential terms are strongly constrained by slow-roll.
Impose shift symmetry:
Most relevant operator:
3 point function:
In EFT regime NG < 10-5 Difficult to observe
We get large NG only if h. d. terms are important also for the classical dynamics
One can explicitly calculate the induced 3pf:
Alishahiha, Silverstein and Tong, Phys.Rev.D70:123505,2004
Example where higher derivative corrections are important
A probe D3 brane moves towards IR of AdS.
Geometrically there is a speed limit
The dual description of this limit is
encoded in h.d. operators. DBI action:
The scalar is moving towards the origin of the moduli space. H.d. operators come
integrating out states becoming massless at the origin.
(see e.g. S. Kecskemeti etal, hep-th/0605189)
S. Kachru etal. hep-th/0605045
X. Chen, M.x.Huang, S.Kachru and G.Shiu, hep-th/0605045
We want to calculate for a generic:
Let us rephrase the calculation in a way which emphasis symmetries: EFT around FRW
EFT around a given FRW background .
Focus on the perturbation
Goldstone of broken time-translation
At 0th order in derivative I have only:
Tadpole terms to make the given a(t) a solution:
Coefficients can be time dependent:
standard scalar field:
Fix the coefficients from the background:
At 0th derivative level
up to 3rd order in pert:
Only two operators are allowed by symmetries: 2 contributions (up to slow-roll)
The first operator changes the speed of sound
M4 > 0 to avoid superluminality
See P.C., M.Luty, A.Nicolis, L.Senatore,
hep-th/0606090 and Leonardo’s talk
Contribution to NGs:
with Arkani-Hamed, Mukoyama and Zaldarriaga,
has dimension 1/4
Quite large. Close to exp. bound.
Derivative interactions are enhanced wrt standard case by NR relativistic scaling
Every light scalar is perturbed during inflation.
Its perturbations may become relevant in various ways:
Example: variable decay of right-handed neutrinos
with L.Boubekeur, hep-ph/0602052
To match 10-5 we need larger fluctuations and thus larger NGs
The RHN goes out of equilibrium and
decay in ≠ way in ≠ regions of the Universe
Babich, P.C., Zaldarriaga, JCAP 0408:009,2004
Typical for NG produced outside the horizon. 2 field models, curvaton, variable decay…
Derivative interactions irrelevant after crossing.
Correlation among modes of comparable .
F is quite complicated in the various models. But in general
Quite similar in different models
The NG signal is concentrated on different configurations.
J. Maldacena, JHEP 0305:013,2003
P.C. + M. Zaldarriaga, JCAP 0410:006, 2004
Underthe usual “adiabatic” assumption (a single field is relevant),
INDEPENDENTLY of the inflaton Lagrangian
The long wavelength mode is a frozen background for the other two: it redefines spatial coordinates.
In the squeezed limit the 3pf is small and probably undetectable
with Nicolis, Senatore, Tegmark, Zaldarriaga, astro-ph/0509029
WMAP alone gives almost all we know about NG. Large data sample + simple.
Not completely straightforward!
It scales like Npixels5/2 ~ 1016for WMAP!!! Too much…
But if F is “factorizable” the computation time scales as Npixels3/2 ~ 109. Doable!
Use a fact. shape with equilateral properties
CMB signal diagonal in Fourier space (without NG!!). Foreground and noise in real space.
Non-diagonal error matrix + linear term in the estimator
Minimum variance estimator:
Reduces variance wrt WMAP coll. analysis.
N_obs varies across the sky.
Smaller power in more observed regions.
On a given realization it looks like a NG
signal. Bigger variance.
No detection! Limits (1yr):
-27 < fNLlocal < 121 at 95% C.L.
(WMAP 3yr: -54 < fNLlocal < 114 )
-366 < fNLequil. < 238 at 95% C.L.
3 yr data. 1 sigma error for local 37 ----> 33 only 15% improvement
The quite different limits is just a consequence of the definition of fNL
1. Single field models with modified Lagrangian
(single operator, DBI inflation, ghost inflation…)
2. Models with a second field
(curvaton, variable decay width, variable RHN decay…)