Dynamical Trajectories for Inflation now & then Dick Bond Inflation Now 1+ w (a)=  s f(a/a  eq ; a s /a  eq ) 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? r(k p ) i.e.  k  is very prior dependent. Large (uniform  ), Small (uniform  ). Tiny (roulette inflation of moduli; almost all string-inspired models). Cosmic Probes Now CFHTLS SNe (192), WL (Apr07), CMB, BAO, LSS Zhiqi Huang, Bond & Kofman 07  s = , weak a s

w-trajectories for V(  ) 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 2-param approximation using an a-averaged  s = (V’/V) 2 /(16πG) and  2 -fitted a s. Wild rise solutions S-M-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 ):

w-trajectories for V(  ): varying V

w-trajectories for V(  ): varying  s

pNGB potentials (Sorbo’s talk Jun7/07) are also covered by our 2-param approximation Dashed lines are using a-averaged  s = (V’/V) 2 /(16πG) and  2 fitted a s. Wild rise solutions S-M-roll solutions Complicated scenarios: roll-up then roll-down w-trajectories for pNGB potentials

w-trajectories for pNGB V(  ): varying f,  (z=0)

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

Measuring constant w (SNe+CMB+WL+LSS)

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

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

Measuring  s and a s (SNe+CMB+WL+LSS+Lya) Well determined  s ill-determined a s

 s trajectories cf. the 1-parameter model Dynamical  s = (1+w)(a)/f(a) cf. shape  s = (V’/V) 2 (a) /(16πG)

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

Measuring  s (SNe+CMB+WL+LSS+Lya) Marginalizing over the ill- determined a s (2- param model) or setting a s =0 (1-param model) has little effect on prob(  s,  m )

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 few-parameter model to well-approximate the not-too-baroque w-trajectories 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 (cf. 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 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 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 Ensemble of Kahler Moduli/Axion Inflations Bond, Kofman, Prokushkin & Vaudrevange 06

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 L 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 CMBpol could break this prior dependence. 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