Can Trans-Planckian Physics be Seen in the CMB? 1.

Can Trans-Planckian Physics be Seen in the

CMB?

Can Trans-Planckian Physics be Seen in the

CMB?

1

OutlineOutline

• Trans-Planckia: Some basic issues

• Inflation and Decoupling: Can we calculate?

• Effective Theory of Initial Conditions in Inflation

Conclusions

Trans-PlanckiaTrans-Planckia

Inflation and Trans-Planckian Physics

Inflation and Trans-Planckian Physics

• WMAP data are consistent with inflationary paradigm: metric perturbations start as quantum fluctuations which decohere into classical fluctuations.

Higher resolution probes should give us even better evidence (for or against) inflation as the source of CMB fluctuations.

NASA/WMAP

Inflation and Structure Formation

Inflation and Structure Formation

H–1(t)

rhor(t)

space

tim

e

inflation ends

homogeneous part of inflaton

quantum fluctuations of inflaton

quantum fluctuations start with

wavelengths get stretched during inflation

fluctuations freeze once

this translates into curvature perturbations

after inflation ends, fluct’s re-enter the Hubble radius and generate CMB

anistropies

H–1(t)

rhor(t)

space

tim

e

inflation ends

MPl

The Trans-Planckian “Problem”

What was the physical size of the fluctuations that contribute to large-scale structure, during

inflation?

That depends on how much inflation occurs. 60-70 e-folds

solve all the problems, but most models typically have

MUCH more

In fact, in most models (except for very finely-tuned ones) these fluctuations will have

started at lengths smaller than

Does the Physics stretch as well?

From Martin and Ringeval: arXiv:astro-ph/0310382

Possible Effects of TP Physics on the CMB

Possible Effects of TP Physics on the CMB

This is both a problem and an opportunity

- On the other hand, if TP physics is infiltrating long-distance observables like the CMB, will we have to know everything to calculate anything?

- On the one hand, we might be able to use the CMB to see physics beyond the Planck scale!

Either way, we need to learn how to calculate these potential corrections reliably.

Two approaches:

- Look at specific models (minimal lengths, NC

geometry...)- Try to make generic statements using only

symmetries etc.

How big could TP Effects be?How big could TP Effects be?

Unless p=1,2, these effects will be too small to be observed

Shenker et al: EFT says no bigger than

Model builders: Effects are LARGER!

TP corrections should come into the power spectrum as

From O. Dore, Chalonge School July 2005

Inflation and Decoupling

Inflation and Decoupling

with C.P. Burgess, J. Cline and F.Lemieuxhep-th/0210233, 0306079

with C.P. Burgess, J. Cline and F.Lemieuxhep-th/0210233, 0306079

• How can the influence of TP physics be reconciled with decoupling?

• Our claim: Inflationary physics is like other physics:

• Some kinds of HE physics need not decouple, yet can retain predictive power,

• Some effects can be bigger than even if decoupling occurs.

Loophole 1: Non-Adiabatic PhysicsLoophole 1: Non-Adiabatic Physics

Suppose background fields are varying at high frequency; then massive modes can be repopulated and cannot be integrated out.

Model: Hybrid inflation with bi-quadratic

couplings

- Standard hybrid inflation: inflaton rolls along ridge until

-Variant: Start with oscillating about the bottom of the trough

Mass is large so oscillations are non-

adiabatic Can’t integrate out

What happens to the CMB power spectrum?

Can have 10 e-folds of oscillations without dominating energy density during inflation

Get oscillatory effects +low k suppresion

Loophole 2: When effective Lagrangians make sense

Loophole 2: When effective Lagrangians make sense

• Most inflaton effective interactions are suppressed by powers of

• Some are NOT. Most of these can be renormalized, BUT...

• It can happen that the inflaton potential is dominated by M-dependent loop effects.

Model: Supersymmetric hybrid inflation

(Copeland et al, Linde, Riotto)

Log potential due entirely to integrating out heavy

field along trough.

No-scale SUGRA models have a similar property

Upshot: Shenker et al. analysis TOO generic; lots of interesting situations

where HE effects are NOT as suppressed as they thought!

Effective Theory of Initial Conditions in Inflation

Effective Theory of Initial Conditions in Inflation

with Hael Collins, hep-th/0501158,0507081with Hael Collins, hep-th/0501158,0507081

How do we calculate the power spectrum?

1. Solve the massless, minimally coupled KG equation for the modes in a de Sitter background:

2. Pick linear combination that matchesto the flat space vacuum at short distancesThis gives the Bunch-Davies (Euclidean) vacuum

How do we know KG eqn. is still valid in this limit?

More reasonable: At energy scales higher than M, effective theory described by KG equation breaks down.

More general IC:

(initial state structure function)

Redshifting of scales means that effective theory can be valid only for times later than

with

What about propagators?

Forward propagation only for initial state information

Structure function contains: --IR aspects, which are real observable excitations

-- UV virtual effects encoding the mistake made by extrapolating free theory states to arbitrarily high energy.

RenormalizationRenormalizationBulk:

+ + · · ·

barepropagator

radiativecorrections

finite

Boundary:

t = t0

tim

e

F

k

c.t.

boundarycounterterm

loop at t0

finite

Initial time hypesurface splits spacetime into bulk+boundary.

Bulk divergences should be able to be absorbed by bulk counterterms only

Need to show that new divergences due to short-distance structure of initial stateare indeed localized to boundary.

Renormalization condition: Set time-dependent tadpole of inflaton flucutations to zero:

Need to use Schwinger-Keldysh formalism here.

Boundary Renormalization

IR piece: Divergences can be cancelled by renormalizable boundary counterterms

UV piece: Need non-renormalizable boundary counterterms

Example: theory

IR: Marginal or relevant operators

UV: irrelevant operators

ConclusionsConclusions

• Effective theory of initial states allows us to compute TP corrections in a robust fashion.

• We can now use this to compute corrections to the power spectrum,

and to look at the issues of backreaction

€

Pinfl(k)=H2

4π 2 1+O H M( )[ ]

10–2 observable now,10–6 observable eventually

Easther, Kinney & Peiris; Greene, Schalm, Shiu, & van der Schaar; Collins & Holman (in progress)

Nitti, Porrati & Rombouts v. Greene, Schalm, Shiu, & van der Schaar; Collins & Holman (in progress)