Download what can we learn about fundamental physics?

Paolo Creminelli (ICTP, Trieste)
Inflationary observables: what
can we learn about fundamental
physics?
Alessandria, 15th December 2006
Slow-roll inflation
V
Friction is dominant
To have ~ dS space the potential must be very flat:
• This gives a period of inflation:
diluted away. For
• For
Curvature, inhomogeneities and relics are
we have a completely smooth Universe.
we have quantum fluctuations of all the light degrees of freedom
. Inflaton itself (scalar perturbations) and graviton (tensor modes).
The study of perturbations gives information about this early cosmological era.
Data on quantum fluctuations during inflation
WMAP3:
+ other experiments at shorter
scale: CMB+LSS+Lyman
• Clear evidence of coherence and ~ scale invariance:
modes are already there out of Hubble scale, with ~ scale invariant spectrum
• Polarization: E-modes (already detected) + B-modes (smoking gun of GW contribution)
Inflationary observables
1. Tilt of the spectrum.
Very recently:
(Do not take too seriously: wait!)
Experimental evidence of deviation from dS!
In most models:
2. Tensor modes. Contribution of spin-2 modes in the CMB map.
Now: r < 0.5 Planck (2009?): r < 0.05 Future (?): r < 0.01
3. Non-gaussianities. It describes the interaction among (scalar) modes.
Now: NG < 10-3 Very close to a free field!
Future: NG < 10-5
What are the implication of a GW signal?
Lyth’s bound.
We need ~ 60 e-folds of inflation
Observation of GWs implies (in model indep. way):
How difficult is this?
Typical simple example:
Why should V remains
flat over such a large range?
One expects:
Cfr. Hybrid Models:
Something abrupt at the end of inflation
No observable gravitational waves
Toy model in field theory
Arkani-Hamed, Cheng, P.C. , Randall etal 2003
Take a PNGB, approximate shift symmetry:
To inflate:
How can I get f >> MP ? Gravity will give terms violating the symmetry:
Abelian gauge field in 5d, compactified on S1
R
AM
Cannot write down a gauge invariant potential for A5.
Charge matter will induce a non-local potential for the Wilson line:
No problem in having f >> MP
I can make f as large as I want making g4 small:
weak coupling limit!
For R >> Ms no problem with quantum gravity corrections: gauge symmetry + locality.
Extra dimensions help!
Working out the details we get all the predictions: detectable GWs!
Taylor expanding…
~
The effective field theorist is not afraid of trans-Planckian VEV
… and the string theorist?
f >> MP in string theory?
Banks, Dine, Fox, Gorbatov, hep-th/0303252
In all known examples, we cannot get f >> MP
Example: Type I on a 6-torus
Wilson line:
Naively we can go to a radius R << Ms-1.
T-dual picture: Wilson line is the distance between D8-branes in type I’
R’
Easy?
But in this 1-d geometry I have a
linear growth of the dilaton:
Strong coupling for:
Same thing in higher codimension + for large g dualize to heterotic: NO WAY!
GWs in the swampland?
Arkani-Hamed, Motl, Nicolis, Vafa, hep-th/0601001
Conjecture: we cannot take the limit g --> 0. There must be a distinction between a global
and a gauge symmetry!
If
for an extremal BH. There must be states:
Looking at magnetically charged BH:
No sign of this in EFT
In D=5:
So that:
requires
It seems that inflationary models with detectable GWs cannot be embedded in string theory
N-flation
Dimopoulos, Kachru, McGreevy, Wacker, hep-th/0507205
If we cannot get parametrically
gain if we a large number of fields N?
for a single field, can we
E.g, we can have a large number of axions:
Pythagoras saves the day. Effective displacement:
Problem: to have a large N you would need a large compactification space,
cannot take N large keeping MP fixed
Hard to make a parametric separation, but on some compactification one can get observable GWs
Bottom line: GWs are surely not generic. If observed they would force to look at very
specific corners of the landscape
Non-Gaussianity: any correlation among modes?
Slow-roll = weak coupling
V
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
•
Any modification enhances NG
– Modify inflaton Lagrangian. Higher derivative terms, ghost inflation, DBI
inflation…
– Additional light fields during inflation. Curvaton, variable decay width…
•
Potential wealth of information
Translation invariance:
Scale invariance:
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
Change inflaton dynamics and thus density perturbations
P.C. JCAP 0310:003,2003
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:
DBI inflation
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.
AdS
The dual description of this limit is
encoded in h.d. operators. DBI action:
Geometrically there is a speed limit
Conformal
invariance
The scalar is moving towards the origin of the moduli space. H.d. operators come
integrating out states becoming massless at the origin.
• It helps inflation slowing down the scalar (potential?)
• Generic in any warped brane model of inflation (reconstruct the shape of the throat?)
(see e.g. S. Kecskemeti etal, hep-th/0605189)
• 3pf can be as large as you like
• Generic 3pf for any model with:
S. Kachru etal. hep-th/0605045
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
• Curvaton
• Variable inflaton decay
• 2 field inflation
• Perturbation of parameters
relevant for cosmo evolution
with L.Boubekeur, hep-ph/0602052
•
Parallel Universes:
The RHN goes out of equilibrium and
decay in ≠ way in ≠ regions of the Universe
•
NG is generated by inefficiency: RHN neutrinos will not be completely dominant.
To match 10-5 we need larger fluctuations and thus larger NGs
•
In general: NG > 10-5, but model dependent. Possible isocurvature contributions.
The shape of non-Gaussianities
Babich, P.C., Zaldarriaga, JCAP 0408:009,2004
• LOCAL DISTRIBUTION
Typical for NG produced outside the horizon. 2 field models, curvaton, variable decay…
• EQUILATERAL DISTRIBUTIONS
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
Shape comparison
The NG signal is concentrated on different
configurations.
• They can be easily distinguished (once NG is detected!)
• They need a dedicated analysis
Analysis of WMAP 3yr data
P.C., Senatore, Zaldarriaga, Tegmark, astro-ph/0610600
WMAP alone gives almost all we know about NG. Large data sample + simple.
Not completely straightforward!
It scales like Npixels5/2 ~ 1016 for WMAP!!! Too much…
But if F is “factorizable” the computation time scales as Npixels3/2 ~ 109. Doable!
Use a fact. shape with equilateral properties
New: tilt in the 3yr analysis!
No detection
WMAP data (after foreground template corrections) are compatible with Gaussianity
We have the best limits on NG for the two shapes
-36 < fNLlocal < 100 at 95% C.L.
-256 < fNLequil. < 332 at 95% C.L.
• Reduction of noise + change in cosmo. parameters (e.g. optical depth)
• Slight (20%) improvement wrt to WMAP3 analysis for the local shape.
• Limits on equil. shape are not weaker: different normalization.
In models:
cs > 0.028 at 95% C.L.
Conclusions
•
Cosmology is converging to its own Standard Model
•
Compelling but not particularly constraining for fundamental physics
•
There is some room for future data to change the simplest picture
1.
Gravitational waves:
2.
Non-Gaussianities: non-minimal models ruled out
3.
Something more exotic. Who thought
?