Dick Bond Constraining Inflation Trajectories now then INFLATION

Dick Bond Constraining Inflation Trajectories, now & then

INFLATION 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. PS, Chibisov & Mukhanov 81: ‘phonon’ appendix as exercise for Advanced GR class at Stanford then !

1987 SBB 89: multi-field, the hybrid inflation prototype, with Radical BSI inflation curvature & isocurvature & P (k) with any shape s possible & Pt(k) almost any shape (mountains & valleys of power), gorges, moguls, waterfalls, m 2 eff < 0, i. e. , tachyonic, non-Gaussian, baroqueness, f|| 2003 fperp radically broken by variable braking (k); SB 90, 91 Hamilton-Jacobi formalism to do non-G (& Bardeen pix of non-G) (k) - H(f) cf. gentle break by smooth brake in the slow roll limit. Blind power spectrum analysis cf. data, then & now measures matter “theory prior” informed priors?

Dick Bond Constraining Inflation Trajectories, now & then 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) Cosmic Probes now & then CMBpol (T+E, B modes of polarization), LSS ~ 10+ parameters? Bond, Contaldi, Kofman, Vaudrevange 05… 08 H(f), V(f)~0 to 2 to 3/2 to ~. 4 now, on its way to 0? Inflation Now 1+w(a) goes to 2(1+q)/3 & Kofman ~1 good e-fold. only ~2 params. Zhiqi Huang, Bond 07 Cosmic Probes Now CFHTLS V’(f)@ pivot pt SN(192), WL(Apr 07), CMB, BAO, LSS, Lya Cosmic Probes Then JDEM-SN + DUNE-WL + Planck +ACT/SPT…

Standard Parameters of Cosmic Structure Formation r < 0. 6 or < 0. 28 95% CL

The Parameters of Cosmic Structure Formation Cosmic Numerology: aph/0611198 – our Acbar paper on the basic 7+; bckv 07 WMAP 3 modified+B 03+CBIcombined+Acbar 06+LSS (SDSS+2 d. F) + DASI (incl polarization and CMB weak lensing and t. SZ) 1+w = 0. 02 +/- 0. 05 ns =. 958 +-. 015 (+-. 005 Planck 1). 93 +-. 03 @0. 05/Mpc run&tensor r=At / As < 0. 28 95% CL (+-. 03 P 1) <. 36 CMB+LSS run&tensor; <. 05 ln r prior! dns /dln k=-. 038 +-. 024 (+-. 005 P 1) CMB+LSS run&tensor prior change? As = 22 +- 2 x 10 -10 ‘phantom DE’ allowed? ! Wbh 2 =. 0226 +-. 0006 Wch 2 =. 114 +-. 005 WL =. 73 +. 02 -. 03 h =. 707 +-. 021 Wm =. 27 +. 03 -. 02 f. NL = (+- 5 -10 P 1) z reh = 11. 4 +- 2. 5

New Parameters of Cosmic Structure Formation Hubble parameter at inflation at a pivot pt =1+q, the deceleration parameter history order N Chebyshev expansion, N-1 parameters (e. g. nodal point values) Fluctuations are from stochastic kicks ~ H/2 p superposed on the downward drift at Dlnk=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 modefunction 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(ln. Hp, k|data, th) ~ P(data| ln. Hp, k ) P(ln. Hp, k | th) Likelihood Data: theory prior / P(data|th) / evidence Theory prior CMBall The theory prior matters a lot for current (WMAP 3, B 03, CBI, ACBAR, data. Not so much for a Bpol future. DASI, VSA, MAXIMA) We have tried many theory priors + LSS (2 d. F, SDSS, 8[lens]) 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 …)

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

Old view: Theory prior = delta function of THE correct one and only theory 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 (6 D) manifold approaching stabilization moving brane & antibrane separations (D 3, D 7) 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 April 07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data es self consistency: order 5 uniform prior r = <0. 64 log prior r <0. 34; . <03 at 1 s! ln. Ps ln. Pt no consistency: order 5 uniform prior r<0. 42 ln. Ps ln. Pt 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 April 07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data uniform prior logarithmic prior r < 0. 64 r < 0. 33, but. 03 1 -sigma

CL BB for ln s (nodal 5) + 4 params inflation trajectories reconstructed from CMB+LSS data using Chebyshev nodal point expansion & MCMC Planck satellite 2008. 6 Spider balloon 2009. 9 uniform prior log prior Spider+Planck broad-band error

CBI pol to Apr’ 05 @Chile Bicep @SP Acbar to Jan’ 06, 07 f @SP QUa. D @SP Quiet 2 CBI 2 to early’ 08 (1000 HEMTs) Quiet 1 SCUBA 2 SZA (Interferometer) @Cal Spider (12000 bolometers) APEX JCMT @Hawaii (~400 bolometers) @Chile (3000 bolometers) 2312 bolometer ACT @LDB Clover @Chile EBEX@LDB @Chile Boom 03@LDB 2004 2006 2005 2008 2007 WMAP @L 2 to 2009 -2013? DASI @SP SPT LMT@Mexico 2009 LHC (1000 bolometers) @South Pole 2017 Bpol@L 2 ALMA Polarbear (300 bolometers)@Cal CAPMAP @Chile (Interferometer) @Chile Planck 08. 8 AMI GBT (84 bolometers) HEMTs @L 2

WMAP 3 sees 3 rd pk, B 03 sees 4 th ‘Shallow’ scan, 75 hours, fsky=3. 0%, large scale TT ‘deep’ scan, 125 hours, fsky=0. 28% 115 sq deg, ~ Planck 2 yr n n B 03+B 98 final soon

Current state October 06 Polarization a Frontier Current state CBI E October 06 You are seeing this before people in the field CBI 2, 5 yr EE, ~ best so far, ~Qua. D WMAP 3 V band CBI B

Does TT Predict EE (& TE)? (YES, incl wmap 3 TT) Inflation OK: EE (& TE) excellent agreement with prediction from TT pattern shift parameter 0. 998 +- 0. 003 WMAP 3+CBIt+DASI+B 03+ TT/TE/EE pattern shift parameter 1. 002 +- 0. 0043 WMAP 1+CBI+DASI+B 03 TT/TE/EE Evolution: Jan 00 11% Jan 02 1. 2% Jan 03 0. 9% Mar 03 0. 4% EE: 0. 973 +- 0. 033, phase check of CBI EE cf. TT pk/dip locales & amp EE+TE 0. 997 +- 0. 018 CBI+B 03+DASI (amp=0. 93+-0. 09)

Current high L frontier state Nov 07 WMAP 3 sees 3 rd pk, B 03 sees 4 th CBI 5 yr sees 4 th 5 th pk CBI 5 yr excess 07, marginalization critical to get ns & dns /dlnk Jan 08@AAS: CBI 5 yr+ full ACBAR data ~ 4 X includes 2005 observations

Planck 1 yr simulation: input LCDM (Acbar)+run+uniform tensor r (. 002 /Mpc) reconstructed cf. rin es order 5 log prior es order 5 uniform prior GW/scalar curvature: current from CMB+LSS: r < 0. 6 or < 0. 25 (. 28) 95%; good shot at 0. 02 95% CL with BB polarization (+-. 02 PL 2. 5+Spider), . 01 target BUT foregrounds/systematics? ? But r-spectrum. But low energy inflation

Planck 1 simulation: input LCDM (Acbar)+run+uniform tensor reconstructed cf. input of LCDM with scalar running & r=0. 1 Ps Pt es order 5 uniform prior es order 5 log prior ln. Ps ln. Pt (nodal 5 and 5)

SPIDER Tensor Signal • Simulation of large scale polarization signal No Tensor http: //www. astro. caltech. edu/~lgg/spider_front. htm

forecast Planck 2. 5 100&143 Spider 10 d 95&150 Synchrotron pol’n Dust pol’n are higher in B Foreground Template removals from multifrequency data is crucial

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

Uniform acceleration, exp V: r = 0. 26, ns=. 97, (r = 0. 50, ns=. 95) Power-law inflation Chaotic inflation V/MP Radical BSI inflation Natural p. NGB inflation 4 2 ~y , r=0. 3, ns=. 97, Dy ~ 0 ~ y 4 r = 0. 26, ns=. 95, Dy ~ 6 V (f|| , fperp ), (k) but isoc feed, r(k), ns(k) V/MP 4 ~Lred 4 sin 2 y/fred 2 -1/2 , ns~ -fred-2 , to match ns=. 96, fred ~ 5, r~0. 032 to match ns=. 97, fred ~ 5. 8, r ~0. 048 , Dy ~ 3 D 3 -D 7 brane inflation, a la KKLMMT 03 r < 10 -10 Dy ~. 2/nbrane 1/2 << 1 BM 06 typical General argument (Lyth 96 bound) : if the inflaton < the Planck mass, then Dy over DN ~ 50, since = (dy /d ln a)2 & r = 6 Roulette inflation Kahler moduli/axion hence r <. 007 …N-flation? r <~ 10 -10 & Dy. 002 As & ns~0. 97 OK but by statistical selection! running dns /dlnk exists, but small via small observable window

Roulette: which minimum for the rolling ball depends upon the throw; but which roulette wheel we play is chance too. 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 BKPV 06 The ‘house’ does not just play dice with the world. V~MP 4 Ps r (1 - /3) 3/2 ~ (1016 Gev)4 r/0. 1 (1 - /3) ~(few x 1013 Gev)4 ns ~ - dln /dlnk /(1 - i. e. , a finely-tuned potential shape Roulette inflation Kahler moduli/axion

INFLATION NOW

Inflation Now 1+w(a)= sf(a/a eq; as/a eq; zs) to a x 3/2 = 3(1+q)/2 ~1 good e-fold. only ~2 eigenparams Zhiqi Huang, Bond & Kofman 07: 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(Apr 07), CMB, BAO, LSS, Lya s= (dln. V/dy)2/4 = late-inflaton (potential gradient)2 =0. 0+-0. 25 now; weak as < 0. 3 (z >2. 3) now Cosmic Probes Then JDEM-SN s to s + DUNE-WL + Planck 1 +-0. 07 then Planck 1+JDEM SN+DUNE WL, weak (zs >3. 7) as <0. 21 then, 3 rd param zs (~d s /dlna) ill-determined now & then cannot reconstruct the quintessence potential, just the slope & hubble drag

Measuring the 3 parameters with current data • Use 3 -parameter formula over 0<z<4 & w(z>4)=wh (irrelevant parameter unless large). as <0. 3 data (zs >2. 3)

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

Beyond Einstein panel: LISA+JDEM Forecast: JDEM-SN (2500 hi-z + 500 low-z) + DUNE-WL (50% sky, gals @z = 0. 1 -1. 1, 35/min 2 ) + Planck 1 yr ESA (+NASA/CSA) as<0. 21 (95%CL) (zs >3. 7) s=0. 02+0. 07 -0. 06 zs (~d s /dlna) illdetermined

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 CL 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 ~ 10 -10 if the normalized inflaton y < 1 over ~50 e-folds then r <. 007 Dy ~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. Bpol 2050

PRIMARY END @ 2012? CMB ~2009+ Planck 1+WMAP 8+SPT/ACT/Quiet+Bicep/Qu. AD/Quiet +Spider+Clover

Inflation now summary • 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+wa(1 -a) phenomenology requires baroque potentials • Philosophy of HBK 07: 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 WQ (a) at z_dec and z_bbn • For general slow-to-moderate rolling one needs 2 “dynamical parameters” (as, s) & WQ to describe w to a few % for the not-too-baroque w-trajectories. • as is < 0. 3 current data (zs >2. 3) SN+DUNE-WL future to <0. 21 (zs >3. 7) in Planck 1 yr-CMB+JDEM- In the early-exit scenario, the information stored in as is erased by Hubble friction over the observable range & w can be described by a single parameter s. • • • a 3 rd param zs, (~d s /dlna) is ill-determined now & in a Planck 1 yr-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 s=0. 0+-0. 25 • current observations are well-centered around the cosmological constant • • in Planck 1 yr-CMB+JDEM-SN+DUNE-WL future s to +-0. 07 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 •

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