Inflation & its Cosmic Probes, now & then Dick Bond Inflation Now 1+ w (a)=  s f(a/a  eq ;a s /a  eq ;  s ) goes to  a  x3/2 = 3 (1+q)/2 ~1 good e-fold. only ~2params Inflation Then  k  =(1+q)(a) ~r/16 0<   = multi-parameter expansion in ( ln Ha ~ lnk) Dynamics ~ Resolution ~ 10 good e-folds (~10 -4 Mpc -1 to ~ 1 Mpc -1 LSS) ~10+ parameters? Bond, Contaldi, Kofman, Vaudrevange 07 r(k p ) i.e.  k  is prior dependent now, not then. Large (uniform  ), Small (uniform ln  ). Tiny (roulette inflation of moduli; almost all string-inspired models ) Cosmic Probes Now CFHTLS SN(192),WL(Apr07),CMB,BAO,LSS,Ly  Zhiqi Huang, Bond & Kofman 07  s = now, to Planck+JDEM SN, weak a s

w-trajectories for V(  ): pNGB example e.g.sorbo et07 For a given quintessence potential V(  ), we set the “initial conditions” at z=0 and evolve backward in time. w-trajectories for Ω m (z=0) = 0.27 and (V’/V) 2 /(16πG) (z=0) = 0.25, the 1-sigma limit, varying the initial kinetic energy w 0 = w(z=0) Dashed lines are our first 2-param approximation using an a-averaged  s = (V’/V) 2 /(16πG) and  2 -fitted a s. Wild rise solutions Slow-to-medium-roll solutions Complicated scenarios: roll-up then roll-down

Approximating Quintessence for Phenomenology + Friedmann Equations + DM+B 1+w=2sin 2  Zhiqi Huang, Bond & Kofman 07

slow-to-moderate roll conditions 1+w< 0.2 (for 0<z<10) and gives a 1- parameter model (a s <<1): Early-Exit Scenario: scaling regime info is lost by Hubble damping, i.e. small a s 1+w< 0.3 (for 0<z<10) gives a 2- parameter model (a s and  s ): CMB+SN+LSS+WL+Lya

Higher Chebyshev expansion is not useful: data cannot determine >2 EOS parameters. e.g., Crittenden etal.06 Parameter eigenmodes w(a)=w 0 +w a (1-a) effective constraint eq. Some Models  Cosmological Constant (w=-1)  Quintessence (-1≤w≤1)  Phantom field (w≤-1)  Tachyon fields (-1 ≤ w ≤ 0)  K-essence (no prior on w) Uses latest April’07 SNe, BAO, WL, LSS, CMB, Lya data

cf. SNLS+HST+ESSENCE = 192 "Gold" SN illustrates the near-degeneracies of the contour plot cf. SNLS+HST+ESSENCE = 192 "Gold" SN illustrates the near-degeneracies of the contour plot w(a)=w 0 +w a (1-a) models

w(z) probes: redshiftwDE fractionPresent day probes 0<z<0.4w0w0 dominantCMB,SN,WL,Lya,LSS,BAO 0.4<z<2w1w1 subdominantCMB,SN,WL,Lya 2<z<4w2w2 tiny ?CMB,WL,Lya z>4w3w3 negligible ?CMB Piecewise w parameterization (4) Rich information at z 4

piecewise parameterization with prior –3<w 0,w 1,w 2,w 3 <1 CMB+SN+WL+LSS+Lya What we know about w

Measuring constant w (SNe+CMB+WL+LSS) 1+w = /- 0.05

Include a w<-1 phantom field, via a negative kinetic energy term φ -> i φ   s = - (V’/V) 2 /(16πG)  < 0  s >0  quintessence  s =0  cosmological constant  s <0  phantom field

Measuring  s (SNe+CMB+WL+LSS+Lya) Modified CosmoMC with Weak Lensing and time- varying w models

45 low-z SN + ESSENCE SN + SNLS 1st year SN + Riess high-z SN, all fit with MLCS SNLS1 = 117 SN (~50 are low-z) SNLS+HST = 182 "Gold" SN SNLS+HST+ESSENCE = 192 "Gold" SN

 s trajectories are slowly varying : why the fits are good Dynamical  w = (1+w)(a)/f(a) cf. shape  V = (V’/V) 2 (a) /(16πG)  s =  v  uniformly averaged over 0<z<2 in a.

3-parameter parameterization next order corrections:  m (a) (depends on  s redefines a eq )  v  s (a) ( adds new  s parameter ) enforce asymptotic kinetic-dominance w=1 (add a s power suppression) refine the fit to encompass even baroque trajectories. this choice is analytic. The correction on w is only ~ 0.01

3-parameter parameterization

3-parameter fitting  s and ζ s are all calculated from  trajectory (linear least square). Only a s is  2 fitted. Perfectly fits slow-roll.

fits wild rising trajectories

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

Comparing parameter results 1-parameter: use 1-param formula for all redshifts. 2-parameter: use 2-param formula for 0 2)=w(z=2). 3-parameter: use 3-param formula for 0 4)=w h (free constant). Conclusion: all the complications are irrelevant: we cannot reconstruct the quintessence potential we can only measure the slope  s CMB + SN + WL + LSS +Lya

Planck + JDEM-SN forecast

Planck + JDEM In progress: adding JDEM-WL

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 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. Here we ignore constraints on Q-density effect on photon-decoupling and BBN because further trajectory extrapolation is needed. 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 3 rd param  s, (~d  s /dlna) is ill-determined now and even with Planck1yr+JDEM (for a given Q-potential, velocity, amp, shape parameters are needed to define a w-trajectory) a s is not well-determined by the current data: to with Planck1yr+JDEM 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. phantom (  s 0) are all allowed with current observations which are well-centered around the cosmological constant  s = to with Planck1yr+JDEM To use: given V, compute trajectories, do a-averaged  s & test (or simpler  s -estimate) Aside: detailed results depend upon the SN data set used. Best available used here (192 SN), but this summer CFHT SNLS will deliver ~300 SN to add to the ~100 non-CFHTLS and 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

Inflation Then Trajectories & Primordial Power Spectrum Constraints Constraining Inflaton Acceleration Trajectories Bond, Contaldi, Kofman & Vaudrevange 07 Roulette Inflation of Kahler Moduli and their Axions Bond, Kofman, Prokushkin & Vaudrevange 06

Inflation in the context of ever changing fundamental theory inflationOld 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 inflation

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 (Chebyshev-filter) criterion [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 (Chebyshev-filter) criterion [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 uniform in lnH p,  k (equal a-prior probability hypothesis) Nodal points cf. Chebyshev coefficients (linear combinations) uniform in / log in / monotonic in  k The theory prior matters a lot for current data We have tried many theory priors Theory prior uniform in lnH p,  k (equal a-prior probability hypothesis) Nodal points cf. Chebyshev coefficients (linear combinations) uniform in / log in / monotonic in  k The theory prior matters a lot for current data We have tried many theory priors

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 geometrical coordinates (moduli fields) and of brane and antibrane “moduli” (D3,D7).

lnP s P t (nodal 2 and 1) + 4 params cf P s P t (nodal 5 and 5) + 4 params reconstructed from CMB+LSS data using Chebyshev nodal point expansion & MCMC no self consistency: order 5 in scalar and tensor power r = (<.53) Power law scalar and constant tensor + 4 params effective r-prior makes the limit stringent r = (<.22)

lnP s P t (nodal 2 and 1) + 4 params cf P s P t (nodal 5 and 5) + 4 params reconstructed from CMB+LSS data using Chebyshev nodal point expansion & MCMC no self consistency: order 5 in scalar and tensor power r = (<.53) Power law scalar and constant tensor + 4 params effective r-prior makes the limit stringent r = (<.22) run+tensor r = (<.33)

lnP s lnP t (nodal 5 and 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 log prior r <0.075 lnP s lnP t no self consistency: order 5 in scalar and tensor power uniform prior r = (<.42)

lnP s lnP t (nodal 5 and 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 < uniform prior r < 0.42

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

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 log prior r (<0.34;.<03 at 1-sigma!)  s self consistency: order 5 uniform prior r = (<0.64)

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

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

B-pol simulation: 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+

Planck1 simulation : input LCDM (Acbar)+run+uniform tensor r (.002 /Mpc) reconstructed cf. r in  s order 5 uniform prior  s order 5 log prior

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 r= r=

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)

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. even so, even smaller r’s may arise from string-inspired inflation models e.g., KKLMMT inflation, large compactified volume Kahler moduli inflation

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 could break this prior dependence, maybe Planck+Spider. Complexity of trajectories arises in many-moduli string models. Roulette example: 4-cycle complex Kahler moduli in Type IIB string theory TINY r ~ a general argument that the normalized inflaton cannot change by more than unity over ~50 e-folds gives r < 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 against nearly uniform acceleration. Both have strong Cdn roles. CMBpol

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