Dick Bond Constraining Inflation Trajectories, now & then

Bad Timing: I arrived at Cambridge in summer 82 from Stanford for a year, sadly just after Nuffield VEU. armed with Hot, warm, cold dark matter, classified by the degree of collisionless damping Transparencies of the time: fluctuation spectra were breathed out of the mouth of the great dragon, quantum gravity Linear then non-linear amplifier Primordial spectrum as variable n, could be variable anything. Plots used HZP argument that scale invariant avoids nonlinearities at large or small scales. Gaussian because of central limit theorem & simplicity. Bad Timing: I arrived at Cambridge in summer 82 from Stanford for a year, sadly just after Nuffield VEU. armed with Hot, warm, cold dark matter, classified by the degree of collisionless damping Transparencies of the time: fluctuation spectra were breathed out of the mouth of the great dragon, quantum gravity Linear then non-linear amplifier Primordial spectrum as variable n, could be variable anything. Plots used HZP argument that scale invariant avoids nonlinearities at large or small scales. Gaussian because of central limit theorem & simplicity. PS, Chibisov & Mukhanov 81: ‘phonon’ appendix as exercise for Advanced GR class at Stanford then ! INFLATION THEN

Radical BSI inflation SBB89: multi-field, the hybrid inflation prototype, with curvature & isocurvature & P s (k) with any shape possible & P t (k) almost any shape (mountains & valleys of power), gorges, moguls, waterfalls, m 2 eff < 0, i.e., tachyonic, non-Gaussian, baroqueness, radically broken by variable braking  (k); SB90,91 Hamilton-Jacobi formalism to do non-G (& Bardeen pix of non-G)  (k) - H(  ) cf. gentle break by smooth brake in the slow roll limit. f || f perp 2003 Blind power spectrum analysis cf. data, then & now measures matter “theory prior” informed priors?

Dick Bond Inflation Then  k  =(1+q)(a) ~r(k)/16 0<   = multi-parameter expansion in ( ln Ha ~ lnk) ~ 10 good e-folds in a (k~10 -4 Mpc -1 to ~ 1 Mpc -1 LSS) ~ 10+ parameters? Bond, Contaldi, Kofman, Vaudrevange 05…08 H(  ), V(  ) Cosmic Probes now & then CMBpol (T+E,B modes of polarization), LSS Inflation Now 1+ w (a) goes to 2 (1+q)/3 ~1 good e-fold. only ~2params Zhiqi Huang, Bond & Kofman 07 Cosmic Probes Now CFHTLS SN(192),WL(Apr07),CMB,BAO,LSS,Ly  Cosmic Probes Then JDEM-SN + DUNE-WL + Planck +ACT/SPT… V’(  pivot pt  ~0 to 2 to 3/2 to ~.4 now, on its way to 0? Constraining Inflation Trajectories, now & then

Standard Parameters of Cosmic Structure Formation r < 0.6 or < % CL

n s = ( Planck1).93 run&tensor r=A t / A s < % CL (+-.03 P1) <.36 CMB+LSS run&tensor; <.05 ln r prior! dn s /dln k= ( P1) CMB+LSS run&tensor prior change? A s = x f NL = ( P1) The Parameters of Cosmic Structure Formation Cosmic Numerology: aph/ – our Acbar paper on the basic 7+; bckv07 WMAP3modified+B03+CBIcombined+Acbar06+LSS (SDSS+2dF) + DASI (incl polarization and CMB weak lensing and tSZ)  b h 2 =  c h 2 =   = h =  m  = z reh = w = / ‘phantom DE’ allowed?!

New Parameters of Cosmic Structure Formation =1+q, the deceleration parameter history order N Chebyshev expansion, N-1 parameters (e.g. nodal point values) Hubble parameter at inflation at a pivot pt Fluctuations are from stochastic kicks ~ H/2  superposed on the downward drift at  lnk=1. Potential trajectory from HJ (SB 90,91):

Constraining Inflaton Acceleration Trajectories Bond, Contaldi, Kofman & Vaudrevange 07 “path integral” over probability landscape of theory and data, with mode- function expansions of the paths truncated by an imposed smoothness criterion [e.g., a Chebyshev-filter: data cannot constrain high ln k frequencies] P(trajectory|data, th) ~ P(lnH p,  k |data, th) ~ P(data| lnH p,  k ) P(lnH p,  k | th) / P(data|th) Likelihood theory prior / evidence “path integral” over probability landscape of theory and data, with mode- function expansions of the paths truncated by an imposed smoothness criterion [e.g., a Chebyshev-filter: data cannot constrain high ln k frequencies] P(trajectory|data, th) ~ P(lnH p,  k |data, th) ~ P(data| lnH p,  k ) P(lnH p,  k | th) / P(data|th) Likelihood theory prior / evidence Data: CMBall (WMAP3,B03,CBI, ACBAR, DASI,VSA,MAXIMA) + LSS (2dF, SDSS,  8[lens]) Data: CMBall (WMAP3,B03,CBI, ACBAR, DASI,VSA,MAXIMA) + LSS (2dF, SDSS,  8[lens]) Theory prior The theory prior matters a lot for current data. Not so much for a Bpol future. We have tried many theory priors e.g. uniform/log/ monotonic in  k (philosophy of equal a-prior probability hypothesis, but in what variables) linear combinations of grouped Chebyshev nodal points & adaptive lnk-space cf. straight Chebyshev coefficients (running of running …) Theory prior The theory prior matters a lot for current data. Not so much for a Bpol future. We have tried many theory priors e.g. uniform/log/ monotonic in  k (philosophy of equal a-prior probability hypothesis, but in what variables) linear combinations of grouped Chebyshev nodal points & adaptive lnk-space cf. straight Chebyshev coefficients (running of running …)

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

Old view: Theory prior = delta function of THE correct one and only theory are New view: Theory prior = probability distribution on an energy landscape whose features are at best only glimpsed, huge number of potential minima, inflation the late stage flow in the low energy structure toward these minima. Critical role of collective coordinates in the low energy landscape: moduli fields, sizes and shapes of geometrical structures such as holes in a dynamical extra-dimensional (6D) manifold approaching stabilization moving brane & antibrane separations (D3,D7) are New view: Theory prior = probability distribution on an energy landscape whose features are at best only glimpsed, huge number of potential minima, inflation the late stage flow in the low energy structure toward these minima. Critical role of collective coordinates in the low energy landscape: moduli fields, sizes and shapes of geometrical structures such as holes in a dynamical extra-dimensional (6D) manifold approaching stabilization moving brane & antibrane separations (D3,D7) Theory prior ~ probability of trajectories given potential parameters of the collective coordinates X probability of the potential parameters X probability of initial conditions

ln  s (nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in nodal bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data  s self consistency: order 5 log prior r <0.34;.<03 at 1  !  s self consistency: order 5 uniform prior r = <0.64 ln P s ln P t no consistency: order 5 uniform prior r<0.42 ln P s ln P t no consistency: order 5 log prior r<0.08

ln  s (nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in nodal bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data logarithmic prior r < 0.33, but.03 1-sigma uniform prior r < 0.64

C L BB for ln  s (nodal 5) + 4 params inflation trajectories reconstructed from CMB+LSS data using Chebyshev nodal point expansion & MCMC Planck satellite Spider balloon uniform prior log prior Spider+Planck broad-band error

Polarbear (300 SZA APEX (~400 SPT (1000 Pole ACT (3000 Planck 08.8 (84 bolometers) ALMA (12000 bolometers) SCUBA2 Quiet1 Quiet2 CBI pol to Acbar to Jan’06, to ? 2017 (1000 Spider CAPMAP AMI GBT CBI2 to early’08 LHC

WMAP3 sees 3 rd pk, B03 sees 4 th ‘Shallow’ scan, 75 hours, f sky =3.0%, large scale TT ‘Shallow’ scan, 75 hours, f sky =3.0%, large scale TT ‘deep’ scan, 125 hours, fsky=0.28% 115sq deg, ~ Planck2yr ‘deep’ scan, 125 hours, fsky=0.28% 115sq deg, ~ Planck2yr B03+B98 final soon

Current state October 06 You are seeing this before people in the field Current state October 06 You are seeing this before people in the field Current state October 06 Polarization a Frontier Current state October 06 Polarization a Frontier WMAP3 V band CBI ECBI B CBI 2,5 yr EE, ~ best so far, ~QuaD

Does TT Predict EE (& TE)? (YES, incl wmap3 TT) Inflation OK: EE (& TE) excellent agreement with prediction from TT pattern shift parameter WMAP3+CBIt+DASI+B03+ TT/TE/EE pattern shift parameter WMAP1+CBI+DASI+B03 TT/TE/EE Evolution: Jan00 11% Jan02 1.2% Jan03 0.9% Mar03 0.4% EE: , phase check of CBI EE cf. TT pk/dip locales & amp EE+TE CBI+B03+DASI (amp= )

Current high L frontier state Nov 07 CBI5yr sees 4 th 5 th pk CBI5yr excess 07, marginalization critical to get n s & dn s /dlnk WMAP3 sees 3 rd pk, B03 sees 4 th CBI5yr+ full ACBAR data ~ 4X includes 2005 observations

Planck1yr simulation: input LCDM (Acbar)+run+uniform tensor r (.002 /Mpc) reconstructed cf. r in  s order 5 uniform prior  s order 5 log prior GW/scalar curvature: current from CMB+LSS : r < 0.6 or < 0.25 (.28) 95%; good shot at % CL with BB polarization (+-.02 PL2.5+Spider),.01 target BUT foregrounds/systematics?? But r-spectrum. But low energy inflation

Planck1 simulation : input LCDM (Acbar)+run+uniform tensor P s P t reconstructed cf. input of LCDM with scalar running & r=0.1  s order 5 uniform prior  s order 5 log prior lnP s lnP t (nodal 5 and 5)

No Tensor SPIDER Tensor Signal Tensor Simulation of large scale polarization signal

forecast Planck &143 Spider10d 95&150 Synchrotron pol’n Dust pol’n are higher in B Foreground Template removals from multi- frequency data is crucial

B-pol simulation: ~10K detectors > 100x Planck input LCDM (Acbar)+run+uniform tensor r (.002 /Mpc) reconstructed cf. r in  s order 5 uniform prior  s order 5 log prior a very stringent test of the  -trajectory methods: A+ also input trajectory is recovered

Chaotic inflation Power-law inflation Roulette inflation Kahler moduli/axion Natural pNGB inflation Radical BSI inflation Uniform acceleration, exp V: r  n s   r  n s  Uniform acceleration, exp V: r  n s   r  n s  V/M P 4 ~  2  r   n s    4 r  n s  V/M P 4 ~  2  r   n s    4 r  n s  V ( f ||, f perp   (k) but isoc feed, r(k), n s (k) V/M P 4 ~  red 4  sin 2  f red  -1/2  n s  f red -2  to match n s .96, f red  ~ 5, r~0.032 to match n s .97, f red  ~ 5.8, r ~0.048,  V/M P 4 ~  red 4  sin 2  f red  -1/2  n s  f red -2  to match n s .96, f red  ~ 5, r~0.032 to match n s .97, f red  ~ 5.8, r ~0.048,  D3-D7 brane inflation, a la KKLMMT03 typical r < . 2/n brane 1/2 << 1 BM06 General argument (Lyth96 bound)  : if the inflaton < the Planck mass, then  over  since  = (d  d ln a) 2 & r  hence r <.007 …N-flation? r <~    A s & n s ~0.97 OK but by statistical selection! running d n s /dlnk exists, but small via small observable window r <~    A s & n s ~0.97 OK but by statistical selection! running d n s /dlnk exists, but small via small observable window

Roulette inflation Kahler moduli/axion Roulette: which minimum for the rolling ball depends upon the throw; but which roulette wheel we play is chance too. The ‘house’ does not just play dice with the world. focus on “4-cycle Kahler moduli in large volume limit of IIB flux compactifications” Balasubramanian, Berglund 2004, + Conlon, Quevedo 2005, + Suruliz 2005 Real & imaginary parts are both important BKPV06 V~M P 4 P s r (1-  3) 3/2 ~ (10 16 Gev) 4 r/0.1 (1-  3) ~(few x10 13 Gev) 4 ~ - dln  dlnk /(1-  n s ~ - dln  dlnk /(1-  i.e., a finely-tuned potential shape V~M P 4 P s r (1-  3) 3/2 ~ (10 16 Gev) 4 r/0.1 (1-  3) ~(few x10 13 Gev) 4 ~ - dln  dlnk /(1-  n s ~ - dln  dlnk /(1-  i.e., a finely-tuned potential shape

INFLATION NOW

Inflation Now 1+ w (a)=  s f(a/a  eq ;a s /a  eq ;  s ) to  a  x3/2 = 3 (1+q)/2 ~1 good e-fold. only ~2 eigenparams Zhiqi Huang, Bond & Kofman07: 3-param formula accurately fits slow-to-moderate roll & even wild rising baroque late-inflaton trajectories, as well as thawing & freezing trajectories Cosmic Probes Now CFHTLS SN(192),WL(Apr07),CMB,BAO,LSS,Ly   s = (dlnV/d  ) 2 /4 = late-inflaton (potential gradient) 2  = now; weak a s 2.3) now  s to then Planck1+JDEM SN+DUNE WL, weak a s 3.7) 3 rd param  s (~d  s /dlna) ill-determined now & then cannot reconstruct the quintessence potential, just the slope  s & hubble drag info (late-inflaton mass is < Planck mass, but not by a lot) Cosmic Probes Then JDEM-SN + DUNE-WL + Planck1

Measuring the 3 parameters with current data Use 3-parameter formula over 0 4)=w h (irrelevant parameter unless large). a s 2.3)

w(a)=w 0 +w a (1-a) models 45 low-z SN + ESSENCE SN + SNLS 1st year SN + Riess high-z SN, 192 “gold”SN all fit with MLCS illustrates the near-degeneracies of the contour plot

Forecast: JDEM-SN (2500 hi-z low-z) + DUNE-WL (50% sky, = , 35/min 2 ) + Planck1yr  s = a s <0.21 (95%CL) (z s >3.7) Beyond Einstein panel: LISA+JDEM ESA (+NASA/CSA)  s (~d  s /dlna) ill-determined

Inflation then summary the basic 6 parameter model with no GW allowed fits all of the data OK Usual GW limits come from adding r with a fixed GW spectrum and no consistency criterion (7 params). Adding minimal consistency does not make that much difference (7 params) r (<.28 95%) limit comes from relating high k region of  8 to low k region of GW C L Uniform priors in  (k) ~ r(k): with current data, the scalar power downturns (  (k) goes up) at low k if there is freedom in the mode expansion to do this. Adds GW to compensate, breaks old r limit. T/S (k) can cross unity. But log prior in  drives to low r. a B-pol r~.001? breaks this prior dependence, maybe Planck+Spider r~.02 Complexity of trajectories arises in many-moduli string models. Roulette example: 4-cycle complex Kahler moduli in large compact volume Type IIB string theory TINY r ~ if the normalized inflaton  < 1 over ~50 e-folds then r <.007  ~10 for power law & PNGB inflaton potentials. Is this deadly??? 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 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. Both have strong Cdn roles. Bpol2050

PRIMARY 2012? CMB ~2009+ Planck1+WMAP8+SPT/ACT/Quiet+Bicep/QuAD/Quiet +Spider+Clover

the data cannot determine more than 2 w-parameters (+ csound?). general higher order Chebyshev expansion in 1+w as for “inflation-then”  =(1+q) is not that useful. Parameter eigenmodes show what is probed The w(a)=w 0 +w a (1-a) phenomenology requires baroque potentials Philosophy of HBK07: backtrack from now (z=0) all w-trajectories arising from quintessence (  s >0) and the phantom equivalent (  s <0) ; use a 3-parameter model to well-approximate even rather baroque w-trajectories. We ignore constraints on Q-density from photon-decoupling and BBN because further trajectory extrapolation is needed. Can include via a prior on  Q (a) at z_dec and z_bbn For general slow-to-moderate rolling one needs 2 “dynamical parameters” ( a s,  s ) &  Q to describe w to a few % for the not-too-baroque w-trajectories. a s is 2.3) to 3.7) in Planck1yr-CMB+JDEM-SN+DUNE-WL future In the early-exit scenario, the information stored in a s is erased by Hubble friction over the observable range & w can be described by a single parameter  s. a 3 rd param  s, (~d  s /dlna) is ill-determined now & in a Planck1yr-CMB+JDEM-SN+DUNE-WL future To use: given V, compute trajectories, do a-averaged  s & test (or simpler  s -estimate) for each given Q-potential, velocity, amp, shape parameters are needed to define a w-trajectory current observations are well-centered around the cosmological constant  s = in Planck1yr-CMB+JDEM-SN+DUNE-WL future  s to but cannot reconstruct the quintessence potential, just the slope  s & hubble drag info late-inflaton mass is < Planck mass, but not by a lot Aside: detailed results depend upon the SN data set used. Best available used here (192 SN), soon CFHT SNLS ~300 SN + ~100 non-CFHTLS. will put all on the same analysis/calibration footing – very important. Newest CFHTLS Lensing data is important to narrow the range over just CMB and SN Inflation now summary

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