Dick Bond

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• Dick Bond

Constraining Inflation Trajectories, now then
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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 !
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SBB89 multi-field, the hybrid inflation
prototype, with curvature isocurvature Ps(k)
with any shape possible Pt(k) almost any shape
(mountains valleys of power), gorges, moguls,
waterfalls, m2eff lt 0, i.e., tachyonic,
non-Gaussian, baroqueness, radically broken by
variable braking e(k) SB90,91 Hamilton-Jacobi
formalism to do non-G ( Bardeen pix of non-G)
e(k) - H(f) cf. gentle break by smooth brake in
the slow roll limit.
Radical BSI inflation
1987
f fperp
2003
2003
Blind power spectrum analysis cf. data, then
now measures matter theory prior informed
priors?
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• Dick Bond

Constraining Inflation Trajectories, now then

• Inflation Then ??k?(1q)(a) r(k)/16 0lt???
• multi-parameter expansion in (lnHa lnk)
• 10 good e-folds in a (k10-4Mpc-1 to 1 Mpc-1
  LSS)
• 10 parameters? Bond, Contaldi, Kofman,
  Vaudrevange 0508 H(f), V(f)

Cosmic Probes now then CMBpol (TE,B modes of
polarization), LSS
? 0 to 2 to 3/2 to .4 now, on its way to 0?
Inflation Now1w(a) goes to 2(1q)/3 1 good
e-fold. only 2params
V(f)_at_ pivot pt
Zhiqi Huang, Bond Kofman 07
Cosmic Probes Now CFHTLS SN(192),WL(Apr07),CMB,BAO
,LSS,Lya
Cosmic Probes Then JDEM-SN DUNE-WL Planck
ACT/SPT
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Standard Parameters of Cosmic Structure Formation
r lt 0.6 or lt 0.28 95 CL
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The Parameters of Cosmic Structure Formation
Cosmic Numerology aph/0611198 our Acbar paper
on the basic 7 bckv07 WMAP3modifiedB03CBIcomb
inedAcbar06LSS (SDSS2dF) DASI (incl
polarization and CMB weak lensing and tSZ)
ns .958 - .015 (-.005 Planck1) .93 - .03
_at_0.05/Mpc runtensor rAt / As lt 0.28 95 CL
(-.03 P1) lt.36 CMBLSS runtensor lt .05 ln r
prior! dns /dln k-.038 - .024 (-.005 P1)
CMBLSS runtensor prior change? As 22 - 2 x
10-10 fNL (- 5-10 P1)
1w 0.02 /- 0.05 phantom DE allowed?!
Wbh2 .0226 - .0006 Wch2 .114 - .005 WL
.73 .02 - .03 h .707 - .021 Wm .27 .03
-.02 zreh 11.4 - 2.5
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New Parameters of Cosmic Structure Formation
Hubble parameter at inflation at a pivot pt
1q, the deceleration parameter history order
N Chebyshev expansion, N-1 parameters (e.g. nodal
point values)
Fluctuations are from stochastic kicks H/2p
superposed on the downward drift at Dlnk1.
Potential trajectory from HJ (SB 90,91)
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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(trajecto
rydata, th) P(lnHp,ekdata, th) P(data
lnHp,ek ) P(lnHp,ek th) /
P(datath) Likelihood theory prior
/ evidence
Data CMBall (WMAP3,B03,CBI, ACBAR, DASI,VSA,MAXI
MA) LSS (2dF, SDSS, s8lens)
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 ek (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 )
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Old view Theory prior delta function of THE
correct one and only theory
Old Inflation
1980
-inflation
Chaotic inflation
New Inflation
Power-law inflation
SUGRA inflation
Double Inflation
Radical BSI inflation
Extended inflation
variable MP inflation
1990
Hybrid inflation
Natural pNGB inflation
Assisted inflation
SUSY F-term inflation
SUSY D-term inflation
Brane inflation
Super-natural Inflation
2000
SUSY P-term inflation
K-flation
N-flation
DBI inflation
inflation
Warped Brane inflation
Tachyon inflation
Racetrack inflation
Roulette inflation Kahler moduli/axion
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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 (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
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lnes (nodal 5) 4 params. Uniform in exp(nodal
bandpowers) cf. uniform in nodal bandpowers
reconstructed from April07 CMBLSS data using
Chebyshev nodal point expansion MCMC shows
prior dependence with current data
es self consistency order 5 log prior r lt0.34
.lt03 at 1s!
es self consistency order 5 uniform prior r
lt0.64
lnPs lnPt no consistency order 5 log prior
rlt0.08
lnPs lnPt no consistency order 5 uniform prior
rlt0.42
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lnes (nodal 5) 4 params. Uniform in exp(nodal
bandpowers) cf. uniform in nodal bandpowers
reconstructed from April07 CMBLSS data using
Chebyshev nodal point expansion MCMC shows
prior dependence with current data
logarithmic prior r lt 0.33, but .03 1-sigma
uniform prior r lt 0.64
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CL BB for lnes (nodal 5) 4 params inflation
trajectories reconstructed from CMBLSS data
using Chebyshev nodal point expansion MCMC
Planck satellite 2008.6
Spider balloon 2009.9
uniform prior
SpiderPlanck broad-band error
log prior
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Quiet2
Bicep _at_SP
CBI pol to Apr05 _at_Chile
(1000 HEMTs) _at_Chile
CBI2 to early08
QUaD _at_SP
Acbar to Jan06, 07f _at_SP
Quiet1
SCUBA2
Spider
(12000 bolometers)
2312 bolometer _at_LDB
APEX
SZA
JCMT _at_Hawaii
(400 bolometers) _at_Chile
(Interferometer) _at_Cal
ACT
Clover _at_Chile
(3000 bolometers) _at_Chile
Boom03_at_LDB
EBEX_at_LDB
2017
2004
2006
2008
LMT_at_Mexico
2005
2007
2009
SPT
Bpol_at_L2
LHC
WMAP _at_L2 to 2009-2013?
(1000 bolometers) _at_South Pole
ALMA
DASI _at_SP
(Interferometer) _at_Chile
Polarbear
(300 bolometers)_at_Cal
CAPMAP
Planck08.8
AMI
(84 bolometers) HEMTs _at_L2
GBT
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WMAP3 sees 3rd pk, B03 sees 4th

• Shallow scan, 75 hours, fsky3.0, large scale
  TT
• deep scan, 125 hours, fsky0.28 115sq deg,
  Planck2yr

B03B98 final soon
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Current state October 06 Polarization a Frontier
CBI E
CBI B
Current state October 06 You are seeing this
before people in the field
CBI 2,5 yr EE, best so far, QuaD
WMAP3 V band
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Does TT Predict EE ( TE)? (YES, incl wmap3 TT)
Inflation OK EE ( TE) excellent agreement with
prediction from TT
pattern shift parameter 0.998 - 0.003
WMAP3CBItDASIB03 TT/TE/EE pattern shift
parameter 1.002 - 0.0043 WMAP1CBIDASIB03
TT/TE/EE Evolution Jan00 11 Jan02 1.2 Jan03
0.9 Mar03 0.4 EE 0.973 - 0.033, phase
check of CBI EE cf. TT pk/dip locales amp EETE
0.997 - 0.018 CBIB03DASI (amp0.93-0.09)
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Current high L frontier state Nov 07
WMAP3 sees 3rd pk, B03 sees 4th
CBI5yr sees 4th 5th pk
CBI5yr excess 07, marginalization critical to get
ns dns /dlnk
Jan08_at_AAS CBI5yr full ACBAR data 4X includes
2005 observations
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Planck1yr simulation input LCDM
(Acbar)rununiform tensor
r (.002 /Mpc) reconstructed cf. rin
es order 5 log prior
es order 5 uniform prior
GW/scalar curvature current from CMBLSS r lt
0.6 or lt 0.25 (.28) 95 good shot at 0.02 95
CL with BB polarization (- .02 PL2.5Spider),
.01 target BUT foregrounds/systematics?? But
r-spectrum. But low energy inflation
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Planck1 simulation input LCDM (Acbar)rununiform
tensor
Ps Pt reconstructed cf. input of LCDM with
scalar running r0.1
es order 5 uniform prior
es order 5 log prior
lnPs lnPt (nodal 5 and 5)
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SPIDER Tensor Signal

• Simulation of large scale polarization signal

No Tensor
Tensor
http//www.astro.caltech.edu/lgg/spider_front.htm
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forecast Planck2.5 100143 Spider10d 95150
Synchrotron poln Dust poln are higher in
B Foreground Template removals from
multi-frequency data is crucial
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B-pol simulation 10K detectors gt 100x Planck
input LCDM (Acbar)rununiform tensor
r (.002 /Mpc) reconstructed cf. rin
es order 5 log prior
es order 5 uniform prior
a very stringent test of the e-trajectory
methods A also input trajectory is recovered
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Uniform acceleration, exp V r 0.26, ns .97,
(r 0.50, ns .95)
Power-law inflation
V/MP4 y2, r0.13, ns.97, Dy 10 y4 r
0.26, ns .95, Dy 16
Chaotic inflation
), e(k) but isoc feed, r(k), ns(k)
V (f , fperp
Radical BSI inflation
V/MP4 Lred4 sin2(y/fred 2-1/2 ), ns 1-fred-2
, to match ns .96, fred 5, r0.032 to match
ns .97, fred 5.8, r 0.048 , Dy 13
Natural pNGB inflation
typical r lt 10-10
D3-D7 brane inflation, a la KKLMMT03
Dy . 2/nbrane1/2 ltlt 1 BM06
General argument (Lyth96 bound) if the inflaton
lt the Planck mass, then Dy lt 1 over DN 50,
since e (dy /d ln a)2 r 16e hence r lt
.007 N-flation?
Roulette inflation Kahler moduli/axion
r lt 10-10 Dylt.002 As ns0.97 OK but by
statistical selection! running dns /dlnk exists,
but small via small observable window
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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
VMP4 Ps r (1-e/3) 3/2 (1016 Gev)4 r/0.1
(1-e/3) (few x1013 Gev)4 ns - dln e /dlnk
/(1-e) i.e., a finely-tuned potential shape
Roulette inflation Kahler moduli/axion
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INFLATION NOW
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Inflation Now1w(a) esf(a/a?eqas/a?eqzs) to
?(a)x3/2 3(1q)/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,Lya

• es (dlnV/dy)2/4
  late-inflaton (potential gradient)2
• 0.0-0.25 now
• weak as lt 0.3 (zs gt2.3) now
• es to -0.07 then Planck1JDEM SNDUNE WL,
  weak as lt0.21 then, (zs gt3.7)
• 3rd param zs (des /dlna) ill-determined now
  then
• cannot reconstruct the quintessence potential,
  just the slope es hubble drag info
• (late-inflaton mass is lt Planck mass, but not by
  a lot)

Cosmic Probes Then JDEM-SN DUNE-WL Planck1
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Measuring the 3 parameters with current data

• Use 3-parameter formula over 0ltzlt4 w(zgt4)wh
  (irrelevant parameter unless large).

as lt0.3 data (zs gt2.3)
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45 low-z SN ESSENCE SN SNLS 1st year SN
Riess high-z SN, 192 goldSN all fit with MLCS
illustrates the near-degeneracies of the contour
plot
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Forecast JDEM-SN (2500 hi-z 500 low-z)
DUNE-WL (50 sky, gals _at_z 0.1-1.1, 35/min2 )
Planck1yr
Beyond Einstein panel LISAJDEM
aslt0.21 (95CL) (zs gt3.7)
ESA (NASA/CSA)
es0.020.07-0.06
zs (des /dlna) ill-determined
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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 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
PlanckSpider 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 lt 1 over 50
e-folds then r lt .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. Bpol2050
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PRIMARY END _at_ 2012?
CMB 2009 Planck1WMAP8SPT/ACT/QuietBicep/QuAD/
Quiet SpiderClover
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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.
  Parameter eigenmodes show what is probed
• 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
  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, es) WQ to describe
  w to a few for the not-too-baroque
  w-trajectories.
• as is lt 0.3 current data (zs gt2.3)
  to lt0.21 (zs gt3.7) in Planck1yr-CMBJDEM-SNDUNE
  -WL future
• 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.
• a 3rd param zs, (des /dlna) is ill-determined
  now in a Planck1yr-CMBJDEM-SNDUNE-WL future
• To use given V, compute trajectories, do
  a-averaged es test (or simpler es -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 es0.0-0.25
• in Planck1yr-CMBJDEM-SNDUNE-WL future es to
  -0.07
• but cannot reconstruct the quintessence
  potential, just the slope es hubble drag info
• late-inflaton mass is lt 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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End