Dick Bond

1

• Dick Bond

Inflation its Cosmic Probes, now then
Cosmic Probes CMB, CMBpol (E,B modes of
polarization) B from tensor Bicep, Planck,
Spider, Spud, Ebex, Quiet, Pappa, Clover, ,
Bpol CFHTLS SN(192),WL(Apr07), JDEM/DUNE
BAO,LSS,Lya
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?
Bond, Contaldi, Kofman, Vaudrevange
07 r(kp) i.e. ??k? is prior dependent now, not
then. Large (uniform ?), Small (uniform ln?).
Tiny (roulette inflation of moduli almost all
string-inspired models) KKLMMT etc, Quevedo
etal, Bond, Kofman, Prokushkin, Vaudrevange 07,
Kallosh and Linde 07 General argument if the
inflaton lt the Planck mass, then r lt .007
(Lyth96 bound)
2

• Dick Bond

Inflation its Cosmic Probes, now then
Inflation Now1w(a) esf(a/a?eqas/a?eqzs) goes
to ?(a)x3/2 3(1q)/2 1 good e-fold. only
2params
Zhiqi Huang, Bond Kofman 07 es0.0-0.25 now,
late-inflaton (potential gradient)2 to -0.07
then Planck1JDEM SNDUNE WL, weak as lt 0.3
now lt0.21 then (late-inflaton mass is lt
Planck mass, but not by a lot)
Cosmic Probes NowCFHTLS SN(192),WL(Apr07),CMB,BAO,
LSS,Lya
Cosmic Probes Then JDEM-SN DUNE-WL Planck1
3
NOW
4

• Dick Bond

Inflation its Cosmic Probes, now then
Inflation now Dynamical background
late-inflaton-field trajectories imprint
luminosity distance, angular diameter distance,
volume growth, growth rate of density
fluctuations Prior late-inflaton primordial
fluctuation information is largely lost because
tiny mass (field sound speedc?) late-inflaton
may have an imprint on other fields? New
late-inflaton fluctuating field power is tiny
5
w-trajectories for V(f) pNGB example e.g.sorbo
et07
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 first 2-param
approximation using an a-averaged es
(V/V)2/(16pG) and c2 -fitted as.
Wild rise solutions
Slow-to-medium-roll solutions
Complicated scenarios roll-up then roll-down
6
Approximating Quintessence for Phenomenology
Zhiqi Huang, Bond Kofman 07
Friedmann Equations DMB
Include a wlt-1 phantom field, via a negative
kinetic energy term
1w-2sinh2 ?
7
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
CMBSNLSSWLLya
1wlt 0.2 (for 0ltzlt10) and gives a 1-parameter
model (asltlt1)
8

• 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.
9
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
10
z-modes of w(z)
Higher Chebyshev expansion is not useful data
cannot determine gt2 EOS parameters 9 40 into
Parameter eigenmodes DETF Albrecht etal06,
Crittenden etal06, hbk07
piecewise parameterization 4,9,40
9
4
s10.12 s20.32 s30.63
40
Data used 07.04 CMBSNWL LSSLya
11
Measuring constant w (SNeCMBWLLSS)
1w 0.02 /- 0.05
12
Measuring es (SNeCMBWLLSSLya)
Modified CosmoMC with Weak Lensing and
time-varying w models
13
3-parameter parameterization
next order corrections Wm (a) (depends on es
redefines aeq) ev es (a) (adds new zs
parameter) enforce asymptotic kinetic-dominance
w1 (add as power suppression) perfect
moderate-to-slow roll fits ... even the baroque

correction on w only 0.01
14
fits the baroque wild-rising trajectories
15
Measuring the 3 parameters with current data

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

as lt0.3
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Comparing 1-2-3-parameter results
CMB SN WL LSS Lya
estrajectories are slowly varying why the fits
are good
Conclusion for current data, the multi-parameter
complications are largely irrelevant (as
lt0.3) we cannot reconstruct the quintessence
potential we can only measure the slope es
17
Thawing, freezing or non-monotonic?

• Thawing 1w monotonic up as z decreases
• Freezing 1w monotonic down to 0 as z decreases
• 15 thaw, 8 freeze, most non-monotonic with
  flat priors

With freezing prior
With thawing prior
18
the quintessence field is below the reduced
Planck mass
19
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
es0.020.07-0.06
ESA
aslt0.21 (95CL)
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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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THEN
22

• Dick Bond

Inflation its Cosmic Probes, now then
Inflation then Amplitude As, average slope
ltnsgt, slope fluctuations dns ns -lt ns gt
(running, running of running, ) for scalar (low
L to high L CMB ACT/SPT Epol Quad, SPTpol,
Quiet2, Planck) tensor At, ltntgt, dnt nt-lt nt
gt (low L lt100 Planck, Bicep, EBEX, Spider, SPUD,
Clover, Bpol) isocurvature Ais, ltnisgt, dnis
nis-lt nisgt power spectra (subdominant) Blind
search for structure (not really blind because of
prior probabilities/measures) Fluctuation field
power spectra related to dynamical background
field trajectories Defines a tensor/scalar
functional relation between both to Hubble
inflaton potential
23
Standard Parameters of Cosmic Structure Formation
Period of inflationary expansion, quantum noise ?
metric perturbations
r lt 0.6 or lt 0.28 95 CL
Scalar Amplitude
Density of Baryonic Matter
Spectral index of primordial scalar
(compressional) perturbations
Spectral index of primordial tensor (Gravity
Waves) perturbations
Density of non-interacting Dark Matter
Cosmological Constant
Optical Depth to Last Scattering Surface When did
stars reionize the universe?
Tensor Amplitude
What is the Background curvature of the
universe?
closed
flat
open
24
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 .93 - .03 _at_0.05/Mpc
runtensor rAt / As lt 0.28 95 CL lt.36 CMBLSS
runtensor dns /dln k -.060 - .022 -.038 -
.024 CMBLSS runtensor As 22 - 2 x 10-10
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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CMBology
Probing the linear nonlinear cosmic web
Inflation Histories (CMBallLSS)
Kahler modulus potential Ttiq
subdominant phenomena (isocurvature, BSI)
Secondary Anisotropies (CBI,ACT) (tSZ, kSZ, reion)
Foregrounds CBI, Planck
Polarization of the CMB, Gravity Waves (CBI,
Boom, Planck, Spider)
Non-Gaussianity (Boom, CBI, WMAP)
Dark Energy Histories ( CFHTLS-SNWL)
wide open braking approach to preheating
26
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
27
ACT_at_5170m
why Atacama? driest desert in the world. thus
cbi, toco, apex, asti, act, alma, quiet, clover
CBI2_at_5040m
28
WMAP3 sees 3rd pk, B03 sees 4th
29
Current high L state November 07
WMAP3 sees 3rd pk, B03 sees 4th
CBI sees 4th 5th pk
CBI excess 07
30
PRIMARY END _at_ 2012?
CMB 2009 Planck1WMAP8SPT/ACT/QuietBicep/QuAD/
Quiet SpiderClover
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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
32
forecast Planck2.5 100143 Spider10d 95150
Synchrotron poln Dust poln are higher in
B Foreground Template removals from
multi-frequency data is crucial
33
Very very difficult to get at with direct gravity
wave detectors even in our dreams (Big Bang
Observer 2030)
Latham Boyle 07
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
34
Inflation in the context of ever changing
fundamental theory
1980
-inflation
Old Inflation
New Inflation
Chaotic inflation
SUGRA inflation
Power-law inflation
Double Inflation
Extended inflation
1990
Hybrid inflation
Natural 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
35
Power law (chaotic) potentials V/MP4 l y2n ,
yf/MP 2-1/2 e(n/y)2 , e (n/2) /(NI(k)
n/3), ns-1 - (n1) / (NI(k) -n/6), nt - n/
(NI(k) -n/6), n1, NI 60, r 0.13, ns .967,
nt -.017 n2, NI 60, r 0.26, ns .950, nt
-.034
MP-2 8pG
36
PNGBV/MP4 Lred4 sin2(y/fred 2-1/2 ) ns
1-fred-2 , e (1-ns)/2 /(exp(1-ns) NI (k)
(1(1-ns)/ 6) -1), exponentially suppressed
higher r if lower NI 1-ns to match ns .96,
fred 5, r0.032 to match ns .97, fred 5.8,
r0.048 cf. n1, r 0.13, ns .967, nt -.017
ABFFO93
37
Moduli/brane distance limitation in stringy
inflation. Normalized canonical inflaton Dy lt 1
over DN 50, e.g. 2/nbrane1/2 BM06 e (dy /d
ln a)2 so r 16e lt .007, ltlt?
roulette inflation examples r 10-10 Dy lt .002
possible way out with many fields assisting
N-flation
ns .97, fred 5.8, r0.048, Dy 13 cf. n1, r
0.13, ns .967, Dy 10 cf. n2, r 0.26, ns
.95, Dy 16
38
energy scale of inflation r V/MP4 Ps r
(1-e/3) 3/2 V (1016 Gev)4 r/0.1 (1-e/3)
roulette inflation examples V (few x1013 Gev)4
H/MP 10-5 (r/.1)1/2
inflation energy scale cf. the gravitino mass
(Kallosh Linde 07) if a KKLT/largeVCY-like
generation mechanism 1013 Gev (r/.01)1/2 H lt
m3/2 cf. Tev
39
Hybrid D3/D7 Potential
String Theory Landscape Inflation
Phenomenology for CMBLSS

• D3/anti-D3 branes in a warped geometry
• D3/D7 branes
• axion/moduli fields ... shrinking holes

KKLT, KKLMMT
BB04, CQ05, S05, BKPV06
f fperp
large volume 6D cct Calabi Yau
40
Roulette Inflation Ensemble of Kahler
Moduli/Axion Inflations Bond, Kofman, Prokushkin
Vaudrevange 06
end
41
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.
quantum eternal inflation regime stochastic
kick gt classical drift
Very small rs may arise from string-inspired
low-energy inflation models
42
Ps (ln Ha) Kahler trajectories
observable range
But it is much easier to get models which do not
agree with observationsi.e. data selectsthe few
that work from the vast cases that do not
43
e (ln a)
H (ln a)
10-10
44
New Parameters of Cosmic Structure Formation
tensor (GW) spectrum use order M Chebyshev
expansion in ln k, M-1 parameters amplitude(1),
tilt(2), running(3),...
scalar spectrum use order N Chebyshev expansion
in ln k, N-1 parameters amplitude(1), tilt(2),
running(3), (or N-1 nodal point k-localized
values)
Dual Chebyshev expansion in ln k Standard 6 is
Cheb2 Standard 7 is Cheb2, Cheb1 Run is
Cheb3 Run tensor is Cheb3, Cheb1 Low order
N,M power law but high order Chebyshev is
Fourier-like
45
lnPs Pt (nodal 2 and 1) 4 params cf Ps Pt
(nodal 5 and 5) 4 params reconstructed from
CMBLSS data using Chebyshev nodal point
expansion MCMC
Power law scalar and constant tensor 4
params effective r-prior makes the limit
stringent r .082- .08 (lt.22)
no self consistency order 5 in scalar and tensor
power r .21- .17 (lt.53)
runtensor r .13- .10 (lt.33)
46
lnPs lnPt (nodal 5 and 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 0.075
uniform prior r lt 0.42
47
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)
48
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 uniform prior r
(lt0.64)
log prior r (lt0.34 .lt03 at 1-sigma!)
49
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
50
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
51
CL BB for lnPs lnPt (nodal 5 and 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
52
B-pol simulation 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
53
Planck1yr simulation input LCDM
(Acbar)rununiform tensor
r (.002 /Mpc) reconstructed cf. rin
es order 5 log prior
es order 5 uniform prior
54
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)
55
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 could
break this prior dependence, maybe
PlanckSpider. 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 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
56
End