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Measuring local-type might not rule out single-field inflation.

based on arXiv : 1104.0244. Measuring local-type might not rule out single-field inflation. Jonathan Ganc Physics Dept., Univ. of Texas July 6, 2011 PASCOS 2011, Univ. of Cambridge. Overview of presentation.

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Measuring local-type might not rule out single-field inflation.

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  1. based on arXiv: 1104.0244 Measuring local-type might not rule out single-field inflation. Jonathan Ganc Physics Dept., Univ. of Texas July 6, 2011 PASCOS 2011, Univ. of Cambridge

  2. Overview of presentation • I will demonstrate that single-field, slow-roll, canonical kinetic-term inflation with a non Bunch-Davies (BD) initial state has an enhanced local-limit bispectrum • I will discuss the observed from this scenario in the CMB and whether it could affect the interpretation of a Planck detection of . Local non-Gaussianity, Jonathan Ganc

  3. Conventional wisdom • Single field inflation produces ≈ (5/12) (1 – ns)≈0.01, regardless of potential, kinetic term, or initial vacuum stateCreminelli & Zaldarriaga, 2004 Local non-Gaussianity, Jonathan Ganc

  4. What is… ? • … the bispectrum? the Fourier transform of the three-point function of the curvature perturbation ζ ζ(x1) ζ(x2) ζ(x3) • … the squeezed or local limit? when one of the wavenumbers is much smaller than the other two, e.g. k3≪k1≈k2. k1 k3 k2 • … local-type or ? the best-fit parameter to a target bispectrum by the family of local bispectra, i.e. those generated from a Gaussian field by .

  5. Consider slow-roll inflation • Canonical action: • Assume slow-roll , • Write action in terms of (Maldacena 2003): Local non-Gaussianity, Jonathan Ganc

  6. To quantize ζ… • … we promote it to an operator :The mode functions , are independent solutions of the classical equation of motion for ζ. • The vacuum, slow-roll mode function is • We can represent a non-vacuum state by performing a Bogoliubov transformation:new state has occupation number . vacuum or Bunch-Davies state ⇒, Local non-Gaussianity, Jonathan Ganc

  7. To calculate the bispectrum… • … we use the in-in formalism: • We find Local non-Gaussianity, Jonathan Ganc

  8. Bunch-Davies vs. non-Bunch-Davies Bunch-Davies (, ) non-Bunch-Davies in the squeezed limit ( enhancement of in squeezed limit vs. BD! This effect noticed only recently (Agullo & Parker 2011). Why was it missed earlier? People expected signal only in folded limit.

  9. What is the observable signal in the CMB from this enhancement? • is calculated from the CMB by fitting the observed angular bispectrum (using transfer functions and projecting onto a sphere) to that predicted by the local bispectrum • The angular bispectrum must be calculated numerically. Local non-Gaussianity, Jonathan Ganc

  10. What we find • If we suppose that across the wavenumbers visible today, Thus, , even for very large . • Such a signal is not distinguishable in the CMB. • However, it’s larger than predicted by the consistency relation (c.f. ). Local non-Gaussianity, Jonathan Ganc

  11. But… • … we’ve glossed over , the phase angle between the Bogoliubov parameters and . • Why is this usually OK? • Expect to set , at early time by matching mode functions to some non-slow-roll equations. • Relative phase will be dominated by exponential factors in mode functions . • Thus, we expect . is very large, so oscillates quickly and averages out. Local non-Gaussianity, Jonathan Ganc

  12. What happens if ? • Depending on choice of , we can get large positive or negative : Can achieve for Local non-Gaussianity, Jonathan Ganc

  13. What about the consistency relation? • The consistency relation predicts for single-field models. • Here we can have .Is this a counterexample? Local non-Gaussianity, Jonathan Ganc

  14. Is this a counterexample to the consistency relation? • Initial conditions are set at some time , when is inside the horizon, i.e. . • Non-BD terms are multiplied by. On average, the rapidly oscillating term so the above expression ; thus, we get contributions from non-BD terms. • In exact local limit, , and we get zero contribution from non-BD terms. Consistency relation does hold in exact local limit

  15. The takeaway • Slow-roll single-field inflation with an excited initial state can produce an larger than expected. • In the more probable case, and still not detectable in the CMB. • If we allow the phase angle to be constant, we can get large, detectable . The consistency relation is a useful guideline but it holds precisely only in the exact squeezed limit. (A similar conclusion is reached in Ganc & Komatsu 2010). Local non-Gaussianity, Jonathan Ganc

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