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