Looking for Trans-Planckia in the CMB Hael Collins (U. Mass, Amherst) and R.H. (CMU) Miami2006 Physics Conference arXiV: hep-th/ , , ,

Outline Trans-Planckian issues in Inflation. Nothing is Everything: the role of the inflaton vacuum. Effective Field Theory of Initial Conditions for the inflaton. Naturalness, backreaction and all that; how to calculate. Conclusions and outlook.

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) r hor (t) time 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) r hor (t) time inflation ends M Pl

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/

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 no larger than Models can give What about decoupling? This potential infiltration of high energy physics into low energy observables represents either a great opportunity or a great disaster! Need to learn how to calculate these effects reliably DESPITE 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 Text 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 in flat 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.

Renormalization Bulk: ++ · · · bare propagator radiative corrections finite Boundary: t = t 0 time FkFk c.t. boundary counterterm loop at t 0 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 state are 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)