1 / 20

Dick Bond

Dick Bond. Constraining Inflation Trajectories, now & then. Inflation Then  k  =(1+q)(a) = - dlnH / dlna ~r(k)/16 0<  <1 = multi-parameter mode expansion in ( ln Ha ~ ln k ) ~ 10 good e-folds in a (k~10 -4 Mpc -1 to ~ 1 Mpc -1 LSS)

lorant
Télécharger la présentation

Dick Bond

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dick Bond Constraining Inflation Trajectories, now&then Inflation Thenk=(1+q)(a) = -dlnH/dlna ~r(k)/16 0<  <1 = multi-parameter mode expansion in (lnHa ~ lnk) ~ 10 good e-folds in a (k~10-4Mpc-1 to ~ 1 Mpc-1 LSS) ~ 10+ parameters? Bond, Contaldi, Huang, Kofman, Vaudrevange 08 H(f),V(f)  ~0 to 2 to 3/2 to ~.4 now, on its way to 0? Inflation Now1+w(a) goes to2(1+q)/3 ~1 good e-fold. only ~2params es= (dlnV/dy)2/4 @ pivot pt all 1+w <2/3 trajectories give an allowed potential & kinetic energy but … Huang, Bond & Kofman 08

  2. COSMIC PARAMETERS NOW & THEN

  3. Standard Parameters of Cosmic Structure Formation r < 0.47 or < 0.2895% CL New Parameters of Cosmic Structure Formation

  4. TheParameters of Cosmic Structure Formation Cosmic Numerology: aph/0801.1491 – our Acbar paper on the basic 7+; bchkv07 WMAP3modified+B03+CBIcombined+Acbar08+LSS (SDSS+2dF) + DASI (incl polarization and CMB weak lensing and tSZ) ns = .962 +- .014(+-.005 Planck1) .93 +- .03 @0.05/Mpcrun&tensor r=At / As < 0.47cmb95% CL (+-.03 P1) <.55 CMB+LSS eprior 5-pivot B-spline < .22 CMB+LSS lneprior 5-pivot B-spline dns /dln k=-.04 +- .02 (+-.005 P1) CMB+LSS run&tensorprior change?<#(1-ns) As = 22 +- 2 x 10-10 1+w = 0.02 +/- 0.05 ‘phantom DE’ allowed?! +-.07 then Wbh2 = .0226 +- .0006 Wch2= .116 +- .005 WL = .72 +.02- .03 h = .704 +- .022 Wm= .27 + .03 -.02 zreh =11.7 +2.1- 2.4 fNL=87+-60?! (+- 5-10 P1)

  5. TheParameters of Cosmic Structure Formation Cosmic Numerology: wmap5+acbar08 wmap5 ns = .964 +- .014(+-.005 Planck1) r=At / As< 0.54cmb95% CL (+-.03 P1) < < dns /dln k=-.048 +- .027*(+-.005 P1) WMAP5+ACBAR08 run&tensor As = 24 +- 1.1 x 10-10 Wbh2 = .0227 +- .0006 Wch2= .110 +- .005 WL = .74 +.03- .03 h = .72 +- .027 Wm= .26 + .03 -.03 zreh =11.0 +1.5- 1.4 -9< fNL <111 (+- 5-10 P1)

  6. INFLATION PARAMETERS THEN ns(+-.005 Planck1) r (+-.03 P1, +-.02 Spider +P2, +-.001? a Bpol > 100 Planck ) dns /dln k (+-.005 P1) cf. .04 +- .02 Blind scalar & tensor power spectrum analyses then more parameters Blind primoridial non-Gaussian analyses then fNL (+- 5-10 P1) cf. +-30wmap5

  7. INFLATION THEN WHAT IS ALLOWED? radically broken scale invariance by variable braking as acceleration approaches deceleration, preheating & the end of inflation k=(1+q)(a) =r(k)/16 Blind power spectrum analysis cf. data, then & now expand k in localized mode functions e.g. Chebyshev/B-spline coefficients b what a priori measures on b : choice for “theory prior” = informed priors?

  8. lne(nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in nodal bandpowers reconstructed from 2007 CMB+LSS+Lya data using cubic B-spline nodal point expansion & MCMC: shows prior dependence with current data self consistency: 5 node ln(e +0.1) ~uniform prior r(.002) <0.55 (0.11 best) eself consistency: 5 node ln(e +0.0001) ~ log prior r(.002) <0.43 (.06 best)

  9. CL TT lne(nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in nodal bandpowers reconstructed from 2007 CMB+LSS data using cubic B-splinenodal point expansion & MCMC: shows prior dependence with current data ~ log prior ~ uniform prior

  10. CL BB forlne(nodal 5) + 4 paramsinflation trajectories reconstructed from 2007 CMB+LSS data using cubic B-spline nodal point expansion & MCMC Planck satellite 2008.9 Spider balloon 2009.9 ~ uniform prior ~ log prior Spider+Planck broad-band error good shot at 0.02 95% CL with BB polarization (+- .02 PL2.5+Spider), .01 target; Bpol .001 BUT foregrounds/systematics? But r(k), low Energy inflation

  11. lne(nodal 5,11) + 4 params. Uniform in e*(.02 pivot) & ln(eb/ e*) bandpowers using cubic B-spline nodal point expansion & MCMC on 2007 CMB+LSS+Lya data 1-ns~2e+dlne/dlnk captures nearly uniform acceleration and e~0 low energy inflation 5 node B-spline e* & ln(eb/ e*) uniform r(.002) <0.30 (.054 best) 11 node B-spline e* & ln(eb/ e*) uniform r(.002) <0.73 (.17 best)

  12. lne(nodal 5,11) + 4 params. Uniform in e*(.02 pivot) & ln(eb/ e*) bandpowers using cubic B-splinenodal point expansion & MCMC on 2007 CMB+LSS+Lya data 1-ns~2e+dlne/dlnk captures nearly uniform acceleration and e~0 low energy inflation 5 node e* & ln(eb/ e*) uniform r(.002) <0.30 (.054 best) 11 node e* & ln(eb/ e*) uniform r(.002) <0.73 (.17 best)

  13. CL TT lne(nodal 5,11)+4 params. Uniform in e*(.02 pivot) & ln(eb/ e*) bandpowers using cubic B-spline nodal point expansion & MCMC on 2007 CMB+LSS+Lya data 5 node B-spline e* & ln(eb/ e*) uniform 11 node B-spline e* & ln(eb/ e*) uniform

  14. CL TT lne(nodal 5,11)+4 params. Uniform in e*(.02 pivot) & ln(eb/ e*) bandpowers using cubic B-spline nodal point expansion & MCMC on 2007 CMB+LSS+Lya data 5 node B-spline e* & ln(eb/ e*) uniform 11 node B-spline e* & ln(eb/ e*) uniform Planck satellite 2008.9 Spider balloon 2009.9 Spider+Planck broad-band error good shot at 0.02 95% CL with BB polarization (+- .02 PL2.5+Spider), .01 target; Bpol .001 BUT foregrounds/systematics? But r(k), low Energy inflation

  15. Planck1 simulation:input LCDM (Acbar)+run+uniform tensor order 5 Chebyshev expansions recover input r to r ~0.05 PsPtreconstructed cf. input of LCDM with scalar running & r=0.1 esorder 5 uniform prior esorder 5 log prior lnPslnPt(nodal 5 and 5) B-pol simulation:~10K detectors > 100x Planck stringent test of the e-trajectory method: input recovered to r <0.001

  16. INFLATION THEN WHAT IS PREDICTED? Smoothly broken scale invariance by nearly uniform braking (standard of 80s/90s/00s) r~0.03-0.5 or highly variable braking r tiny (stringy cosmology) r<10-10

  17. Old view: Theory prior = delta function of THE correct one and only theory Old Inflation 1980 -inflation Chaotic inflation New Inflation Power-law inflation SUGRA inflation Double Inflation Radical BSI inflation variable MP inflation Extended inflation 1990 Natural pNGB inflation Hybrid inflation Assisted inflation SUSY F-term inflation SUSY D-term inflation Brane inflation Super-natural Inflation 2000 SUSY P-term inflation K-flation N-flation DBI inflation inflation Warped Brane inflation Tachyon inflation Racetrack inflation Roulette inflation Kahler moduli/axion

  18. lnV~y = Uniform acceleration, ns= .97, r = 0.26 (ns= .95, r = 0.50) Power-law inflation V/MP4~y2, r=0.13, ns=.97, Dy ~10 ~ y4r = 0.26, ns= .95, Dy ~16 Chaotic inflation V~y2/3 , r ~ 0.044, ns ~.977 see EvaS & Westphal 08 Radical BSI inflation ), r(k), ns(k), e(k) V (f|| , fperp anything goes Natural pNGB inflation V/MP4 ~Lred4sin2(y/fred2-1/2 ), ns~ 1-fred-2 , to match ns=.96, r~0.032, fred~ 5, to match ns= .97, r ~0.048, fred~ 5.8, Dy ~13 • Old view: Theory prior = delta function of THE correct one and only theory Theory prior ~ probability of trajectories given potential parameters of “low-energy” collective coordinates(brane/antibrane separations, moduli fields such as complex hole sizes in 6D manifold) X probability of the potential parameters X probability of initial conditions

  19. stringy inflation 2003-08 General argument (Lyth96 bound): if the inflaton < the Planck mass, then Dy < 1 over DN ~ 50, since e = (dy /d ln a)2 & r = 16e hence r < .007 …N-flation? typical r < 10-10 D3-D7 brane inflation, a la KKLMMT03 Dy ~. 2/nbrane1/2 << 1 BM06 Roulette inflation Kahler moduli/axion r <~ 10-10 &Dy<.002 As & ns~0.97 OK but by statistical selection! running dns/dlnk exists, but small via smallobservable window

  20. Inflation then summary the basic 6 parameter model with or without GW fits all of the data OK uniform priors in (k) ~ r(k)/16: for current data, (k) goes up at low k & the scalar power downturns (if there is freedom in the mode expansion to do this). Enforces GW. ln (+ TINY) prior gives lower r. a B-pol with r<.001 breaks this prior dependence, even Planck+Spider r~.02 Prior probabilities on the inflation trajectories are crucial and cannot be decided at this time. Philosophy: be as wide open and least prejudiced as possible An ensemble of trajectories arises in many-moduli string models. Roulette inflation: complex hole sizes in `large 6D volume’TINY r~10-10& data-selected braking to get ns & Dy <<1 (general theorem: if the normalized inflatony < 1 over ~50 e-folds then r < .007). By contrast,for nearly uniform acceleration, (e.g. power law & PNGB inflaton potentials), r ~.03-.3 but Dy~10. Is this deadly??? Even with low energy inflation, the prospects are good with Spider and even Planck to either detect the GW-induced B-mode of polarization or set a powerful upper limit vs. nearly uniform acceleration, pointing to stringy or other exotic models. Both experiments have strong Cdn roles.Bpol is ~ 20xx

More Related