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?
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.
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).