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.
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
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
Smoking gun for “new physics”
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
Higher derivative terms
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:
E.g. this is all for a
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
Perturbations generated by a second field
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
The shape of non-Gaussianities
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.
Consistency relation for 3-p.f.
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
Analysis of WMAP data
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
Real space VS Fourier space
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…)