Looking for Trans-Planckia in the CMB

Hael Collins (U. Mass, Amherst) and R.H. (CMU)Miami2006 Physics Conference

arXiV: hep-th/0507081, 0501158, 0605107, 0609002

Why we love Inflation

WMAP is consistent with the inflationary picture for the generation of metric perturbations.

Quantum fluctuations of the inflaton are inflated from micro to cosmological scales during inflation.

space

H–1(t)

rhor(t)

tim

e

inflation ends

The Trans-Planckian “Problem”(Brandenberger&Martin)

What was the physical size of cosmological scales contributing to the CMB today before inflation?

This depends on the number of e-folds of inflation. Most models give more than the minimum of 60’ish e-folds.

Generically, those scales begin at sizes less than the Planck scale! Certainly, we should expect these scales to encompass new physics thresholds.

Does new physics stretch as well?

space

H–1(t)

rhor(t)

tim

e

inflation ends

MPl

The Big Question(s)

Can Physics at scales larger than the inflationary scale imprint itself on the CMB?

If so, do different “UV Completions” of inflation exhibit different signatures?

How can we calculate these effects RELIABLY?

An Example of TP Effects on the CMB

From Martin and Ringeval, arXiV astro-ph/0310382

How big are these effects? Can we use these effects to observe

physics at scales well beyond the scale of inflation?

Shenker et al: Effects can be nolarger than

Models can give

What about decoupling?

This potential infiltrationof high energy physics into low energy observables

represents either a great opportunity or a great disaster!

Need to learn how to calculate these effects reliablyDESPITE our ignorance of the UV completion

of inflation.

O. Dore, Chalonge School 2005

An Effective Theory of Initial Conditions in Inflation

Q. How do we calculate the power spectrum?

A. Solve massless, minimally coupled Klein-Gordon mode equation in de Sitter

space

This is the Bunch-Davies vacuum.

Then choose linear combination that matches to the flat space vacuum state as

The rationale for this is that at short enough distances, observers

should not be able to tell that they are not inflat space.

Why pick this vacuum state?

On top of this, the BD state is de Sitter invariant.

How do we know that the KG equation is the correct description of inflaton physics to ARBITRARILY

short distances?

Suppose inflaton is a fermion composite with scale of

compositeness M. Near M, KG approx. breaks down.

Using the BD vacuum as the initial state is a RADICAL

assumption!

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.

RenormalizationBulk:

+ + · · ·

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

Stress Energy Tensor Renormalization

Can corrections to initial state back-react to even prevent inflation from occurring?

Effective field theory approach should eat up such divergences to leave a small backreaction

Stress Energy Tensor Renormalization (Cont’d)

The Procedure:

1.Expand metric about FRW,2.Construct interaction Hamiltonian linear in

fluctuations,3.Compute tadpole using S-K

formalism.

Stress-Energy and Backreaction

For TP corrections

Backreaction is under control!

Greene et al vs. Porrati et al.

Conclusions

To extract maximum information early Universe from the CMB we need to know how to reliably calculate all relevant effects.

There is a real possibility of using the CMB power spectra to get information about possible trans-Planckian physics effects.

We now have an effective initial state that allows for reliable, controllable calculations. We’ve shown that as expected, backreaction effects are small after renormalization of the effective theory.

Next Step: power spectrum as well as possible enhancements of the three point function (Maldacena, Weinberg).

Conclusions (Cont’d)