Dick Bond

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• Dick Bond

Dynamical Trajectories for Inflation now then
Inflation Now1w(a) esf(a/a?eq as/a?eq) goes to
?(a)x3/2 3(1q)/2 1 good e-fold. only
2params
Zhiqi Huang, Bond Kofman 07 es0.0-0.25
, weak as
Cosmic Probes Now CFHTLS SNe (192), WL (Apr07),
CMB, BAO, LSS

• Inflation Then ??k?(1q)(a) r/16 0lt???
• multi-parameter expansion in (lnHa lnk)
• Dynamics Resolution 10 good e-folds
  (10-4Mpc-1 to 1 Mpc-1 LSS) 10 parameters?
• r(kp) i.e. ??k? is very prior dependent. Large
  (uniform ?), Small (uniform ?). Tiny (roulette
  inflation of moduli almost all string-inspired
  models).

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w-trajectories for V(f)
For a given quintessence potential V(f), we set
the initial conditions at z0 and evolve
backward in time. w-trajectories for Om (z0)
0.27 and (V/V)2/(16pG) (z0) 0.25, the 1-sigma
limit, varying the initial kinetic energy w0
w(z0) Dashed lines are our 2-param
approximation using an a-averaged es
(V/V)2/(16pG) and ?2 -fitted as.
Wild rise solutions
S-M-roll solutions
Complicated scenarios roll-up then roll-down
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Approximating Quintessence for Phenomenology
Zhiqi Huang, Bond Kofman 07
Friedmann Equations DMB
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slow-to-moderate roll conditions
1wlt 0.3 (for 0ltzlt10) gives a 2-parameter model
(as and es)
Early-Exit Scenario scaling regime info is lost
by Hubble damping, i.e.small as
1wlt 0.2 (for 0ltzlt10) and gives a 1-parameter
model (asltlt1)
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w-trajectories for V(f) varying V
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w-trajectories for V(f) varying es
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w-trajectories for pNGB potentials
pNGB potentials (Sorbos talk Jun7/07) are also
covered by our 2-param approximation Dashed lines
are using a-averaged es (V/V)2/(16pG) and ?2
fitted as.
Wild rise solutions
S-M-roll solutions
Complicated scenarios roll-up then roll-down
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w-trajectories for pNGB V(f) varying f, f(z0)
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Higher Chebyshev expansion is not useful data
cannot determine gt2 EOS parameters. e.g.,
Crittenden etal.06 Parameter eigenmodes

• Some Models
• Cosmological Constant (w-1)
• Quintessence
• (-1w1)
• Phantom field (w-1)
• Tachyon fields (-1 w 0)
• K-essence
• (no prior on w)

• Uses latest April07
• SNe, BAO, WL, LSS, CMB, Lya data

effective constraint eq.
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cf. SNLSHSTESSENCE 192 "Gold" SN illustrates
the near-degeneracies of the contour plot
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Measuring constant w (SNeCMBWLLSS)
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Include a wlt-1 phantom field, via a negative
kinetic energy term

• f -gt if ? es - (V/V)2/(16pG) lt 0

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45 low-z SN ESSENCE SN SNLS 1st year SN
Riess high-z SN, all fit with MLCS
SNLSHST 182 "Gold" SN
SNLSHSTESSENCE 192 "Gold" SN
SNLS1 117 SN (50  are low-z)
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Measuring es and as(SNeCMBWLLSSLya)
Well determined es 0.0 - 0.25 ill-determined as
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estrajectories cf. the 1-parameter model
Dynamical es (1w)(a)/f(a) cf. shape es (V/V)2
(a) /(16pG)
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Measuring es (SNeCMBWLLSSLya)
Modified CosmoMC with Weak Lensing and
time-varying w models
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Measuring es (SNeCMBWLLSSLya)
Marginalizing over the ill-determined as (2-param
model) or setting as 0 (1-param model) has
little effect on prob(es , Wm)
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Inflation now summary

• The data cannot determine more than 2
  w-parameters ( csound?). general higher order
  Chebyshev expansion in 1w as for
  inflation-then ?(1q) is not that useful
• The w(a)w0wa(1-a) phenomenology requires
  baroque potentials
• Philosophy of HBK07 backtrack from now (z0) all
  w-trajectories arising from quintessence (es gt0)
  and the phantom equivalent (es lt0) 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 (as, es) WQ 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)
• as is not well-determined by the current data
• 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 es.
• phantom (es lt0), cosmological constant (es 0),
  and quintessence (es gt0) are all allowed with
  current observations which are well-centered
  around the cosmological constant es0.0-0.25
• To use given V, compute trajectories, do
  a-averaged es test (or simpler es -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

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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
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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 (lt.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 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 10-10 a
general argument that the normalized inflaton
cannot change by more than unity over 50 e-folds
gives r lt 10-3 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