Dick Bond

Inflation Then k=(1+q)(a) ~r/16 0<= 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 < the Planck mass, then r < .007 (Lyth96 bound)

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,Ly

Inflation & its Cosmic Probes, now & then

Inflation & its Cosmic Probes, now & then

Dick Bond

Inflation Now1+w(a)= sf(a/aeq;as/aeq;s) goes to ax3/2 = 3(1+q)/2 ~1

good e-fold. only ~2params

Cosmic Probes NowCFHTLS SN(192),WL(Apr07),CMB,BAO,LSS,Ly

Zhiqi Huang, Bond & Kofman 07 s=0.0+-0.25 now, late-inflaton (potential gradient)2

to +-0.07 then Planck1+JDEM SN+DUNE WL, weak as < 0.3 now <0.21 then

(late-inflaton mass is < Planck mass, but not by a lot)

Cosmic Probes Then JDEM-SN + DUNE-WL + Planck1

CMB/LSS Phenomenology CITA/CIfAR here

• Bond

• Contaldi

• Lewis

• Sievers

• Pen

• McDonald

• Majumdar

• Nolta

• Iliev

• Kofman

• Vaudrevange

• Huang

UofT here

• Netterfield

• Carlberg

• Yee

& Exptal/Analysis/Phenomenology Teams here & there

• Boomerang03 (98)

• Cosmic Background Imager1/2

• Acbar07

• WMAP (Nolta, Dore)

• CFHTLS – WeakLens

• CFHTLS - Supernovae

• RCS2 (RCS1; Virmos-Descart)

CITA/CIfAR there

• Mivelle-Deschenes (IAS)

• Pogosyan (U of Alberta)

• Myers (NRAO)

• Holder (McGill)

• Hoekstra (UVictoria)

• van Waerbeke (UBC)

Parameter data now: CMBall_pol

SDSS P(k), BAO, 2dF P(k)

Weak lens (Virmos/RCS1, CFHTLS, RCS2) ~100sqdeg Benjamin etal.

aph/0703570v1

Lya forest (SDSS)

SN1a “gold”(192,15 z>1) CFHTLS

then: ACT (SZ), Spider, Planck, 21(1+z)cm GMRT,SKA

• Dalal

• Dore

• Kesden

• MacTavish

• Pfrommer

• Shirokov

• Dalal

• Dore

• Kesden

• MacTavish

• Pfrommer

• Shirokov

ProkushkinProkushkin

NOW

Inflation & its Cosmic Probes, now & then

–Dick Bond

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 speed=c?)

late-inflaton may have an imprint on other fields?

New late-inflaton fluctuating field power is tiny

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 Ωm (z=0) = 0.27 and (V’/V)2/(16πG) (z=0) = 0.25, the 1-sigma limit, varying the initial

kinetic energy w0 = w(z=0)

Dashed lines are our first 2-param approximation using an a-averaged

s= (V’/V)2/(16πG) and 2 -fitted as.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=2sin2

Zhiqi Huang, Bond & Kofman 07

1+w=-2sinh2

Include a w<-1 phantom field, via a negative kinetic energy term

slow-to-moderate roll conditions

1+w< 0.2 (for 0<z<10) and gives a 1-parameter model (as<<1):

Early-Exit Scenario: scaling regime info is lost by Hubble damping, i.e.small as

1+w< 0.3 (for 0<z<10) gives a 2-parameter model (as and s):

CMB+SN+LSS+WL+Lya

w(a)=w0+wa(1-a)

effective constraint eq.

Some ModelsCosmological 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)=w0+wa(1-a) models

piecewise parameterization 4,9,40

z-modes of w(z)

1=0.12 2=0.32 3=0.63

Higher Chebyshev expansion is not useful:

data cannot determine >2 EOS

parameters 9 & 40 into Parameter

eigenmodes DETF Albrecht etal06, Crittenden etal06,

hbk07

Data used 07.04:

CMB+SN+WL

+LSS+Lya

49

40

Measuring constant w (SNe+CMB+WL+LSS)1+w = 0.02 +/- 0.05

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

strajectories are slowly varying: why the fits

are goodDynamicalw= (1+w)(a)/f(a) cf. shape V= (V’/V)2 (a) /(16πG)

s= vuniformly averaged over 0<z<2 in a.

3-parameter parameterizationnext order corrections:

m (a) (depends on s redefines aeq)

vs (a) (adds new s parameter)

enforce asymptotic kinetic-dominance w=1 (add as 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 fittings & ζs calculated from trajectory (linear least square)

as is 2 -fit

• Perfectly fits slow-to-moderate roll

fits wild rising trajectories

Measuring the 3 parameters with current data• Use 3-parameter formula over 0<z<4 &

w(z>4)=wh (irrelevant parameter unless large).

as <0.3

Comparing 1-2-3-parameter results

Conclusion: for current data, the multi-parameter complications are largely irrelevant (as <0.3):

we cannot reconstruct the quintessence potential

we can only measure the slope s

CMB + SN + WL + LSS +Lya

Thawing, freezing or non-monotonic?

• Thawing: 1+w monotonic up as z decreases

• Freezing: 1+w monotonic down to 0 as z decreases• ~15% thaw, 8% freeze, most non-monotonic with flat priors

With freezing prior:

With thawing prior:

the quintessence field is below the reduced Planck mass

Forecast: JDEM-SN (2500 hi-z + 500 low-z)

+ DUNE-WL (50% sky, gals @z = 0.1-1.1, 35/min2 ) +

Planck1yr

s=0.02+0.07-0.06

as<0.21 (95%CL)

Beyond Einstein panel: LISA+JDEM

ESA

• 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. Parameter eigenmodes show what is probed

• The w(a)=w0+wa(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.

• We ignore constraints on Q-density from photon-decoupling and BBN because further trajectory extrapolation is needed. Can include via a prior on Q (a) at z_dec and z_bbn

• For general slow-to-moderate rolling one needs 2 “dynamical parameters” (as, s) & Q to describe w to a few % for the not-too-baroque w-trajectories.

• as is < 0.3 current data (zs >2.3) to <0.21 (zs >3.7) in Planck1yr-CMB+JDEM-SN+DUNE-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 s.

• a 3rd param s, (~ds /dlna) is ill-determined now & in a Planck1yr-CMB+JDEM-SN+DUNE-WL future

• To use: given V, compute trajectories, do a-averaged s & test (or simpler s -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 s=0.0+-0.25 • in Planck1yr-CMB+JDEM-SN+DUNE-WL future s to +-0.07• but cannot reconstruct the quintessence potential, just the slope s & hubble drag info• late-inflaton mass is < 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

Inflation now summary

THEN THEN

Inflation & its Cosmic Probes, now & then

Dick Bond

Inflation then

Amplitude As, average slope <ns>, slope fluctuations ns = ns -< ns > (running,

running of running, …)

for scalar (low L to high L CMB ACT/SPT; Epol Quad, SPTpol, Quiet2, Planck)

& tensor At, <nt>, nt = nt-< nt >

(low L <100 Planck, Bicep, EBEX, Spider, SPUD, Clover, Bpol)

& isocurvature Ais, <nis>, nis= nis-< nis> 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

Standard Parameters of Cosmic Structure Formation

Òk

What is the Background curvature of the universe?

Òk > 0Òk = 0Òk < 0

closed

flatopen

Òbh2 ÒË nsÒdmh2

Density of Baryonic Matter

Density of non-interacting Dark

Matter

Cosmological Constant

Spectral index of primordial scalar (compressional)

perturbations

PÐ(k) / knsà1

nt

Spectral index of primordial tensor (Gravity Waves)

perturbations

Ph(k) / knt

lnAs ø lnû8

Scalar Amplitude

r = A t=As

Tensor Amplitude

Period of inflationary expansion, quantum noise metric perturbations

üc

Optical Depth to Last Scattering

SurfaceWhen did stars

reionize the universe?

òø `à1s ; cf :ÒË r < 0.6 or < 0.28 95% CL

New Parameters of Cosmic Structure FormationÒk

Òbh2

lnP s(k)Òdmh2

scalar spectrumuse order N Chebyshev

expansion in ln k, N-1 parameters

amplitude(1), tilt(2), running(3), …

(or N-1 nodal point k-localized values)

òø `à1s ; cf :ÒË

tensor (GW) spectrumuse order M Chebyshev

expansion in ln k, M-1 parameters amplitude(1), tilt(2),

running(3),...Dual Chebyshev expansion in ln k:

Standard 6 is Cheb=2

Standard 7 is Cheb=2, Cheb=1

Run is Cheb=3

Run & tensor is Cheb=3, Cheb=1

Low order N,M power law but high order Chebyshev is Fourier-like

üc

lnP t(k)

New Parameters of Cosmic Structure FormationÒk

Òbh2lnH(kp)

ï (k); k ù HaÒdmh2

=1+q, the deceleration parameter history

order N Chebyshev expansion, N-1 parameters (e.g. nodal point values) (adaptive Chebyshev groups)

P s(k) / H 2=ï ;P t(k) / H 2

òø `à1s ; cf :ÒË

Hubble parameter at inflation at a pivot pt

Fluctuations are from stochastic kicks ~ H/2 superposed on the downward drift at lnk=1.

Potential trajectory from HJ (SB 90,91):

üc

à ï = d lnH =d lna

1à ïà ï = d lnk

d lnH

d lnkd inf = 1à ï

æ ïp

V / H 2(1à 3ï );

ï = (d lnH =d inf)2

H(kp)

ns = .958 +- .015

.93 +- .03 @0.05/Mpc run&tensor

r=At / As < 0.28 95% CL

<.36 CMB+LSS run&tensor

dns /dln k = -.060 +- .022

-.038 +- .024 CMB+LSS run&tensor

As = 22 +- 2 x 10-10

The Parameters of Cosmic Structure FormationThe Parameters of Cosmic Structure FormationCosmic Numerology: aph/0611198 – our Acbar paper on the basic 7+; bckv07

WMAP3modified+B03+CBIcombined+Acbar06+LSS (SDSS+2dF) + DASI (incl polarization and CMB weak lensing and tSZ)

bh2 = .0226 +- .0006

ch2 = .114 +- .005

= .73 +.02 - .03

h = .707 +- .021

m= .27 + .03 -.02

zreh = 11.4 +- 2.5

CMBology

ForegroundsCBI, Planck

ForegroundsCBI, Planck

SecondaryAnisotropies

(tSZ, kSZ, reion)

SecondaryAnisotropies

(tSZ, kSZ, reion)

Non-Gaussianity(Boom, CBI, WMAP)

Non-Gaussianity(Boom, CBI, WMAP)

Polarization ofthe CMB, Gravity Waves

(CBI, Boom, Planck, Spider)

Polarization ofthe CMB, Gravity Waves

(CBI, Boom, Planck, Spider)

Dark Energy Histories(& CFHTLS-SN+WL)

Dark Energy Histories(& CFHTLS-SN+WL)

subdominant phenomena

(isocurvature, BSI)

subdominant phenomena

(isocurvature, BSI)

Inflation Histories(CMBall+LSS)

Inflation Histories(CMBall+LSS)

Probing the linear & nonlinear cosmic web

Probing the linear & nonlinear cosmic web

2004

2005

2006

2007

2008

2009

Polarbear(300 bolometers)@Cal

SZA(Interferometer) @Cal

APEX(~400 bolometers) @Chile

SPT(1000 bolometers) @South Pole

ACT(3000 bolometers) @Chile

Planck08.8

(84 bolometers)

HEMTs @L2

Bpol@L2

ALMA(Interferometer) @Chile

(12000 bolometers)SCUBA2

Quiet1

Quiet2Bicep @SP

QUaD @SP

CBI pol to Apr’05 @Chile

Acbar to Jan’06, 07f @SP

WMAP @L2 to 2009-2013?

2017

(1000 HEMTs) @Chile

Spider

Clover @Chile

Boom03@LDB

DASI @SP

CAPMAP

AMI

GBT

2312 bolometer @LDB

JCMT @Hawaii

CBI2 to early’08

EBEX@LDB

LMT@Mexico

LHC

Inflation in the context of ever changing fundamental theory

1980

2000

1990

-inflation Old Inflation

New Inflation Chaotic inflation

Double InflationExtended 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-flationN-flation

Warped Brane inflation

inflation

Power-law inflation

Tachyon inflationRacetrack inflation

Assisted inflation

Roulette inflation Kahler moduli/axion

Natural inflation

Power law (chaotic) potentials

V/MP4 ~ 2 MP

-1/2

NI(k) +/3

ns-1+1NI(k) -/6

ntNI(k) -/6

=1, NI

rnsnt

=2, NI

rnsnt

Power law (chaotic) potentials

V/MP4 ~ 2 MP

-1/2

NI(k) +/3

ns-1+1NI(k) -/6

ntNI(k) -/6

=1, NI

rnsnt

=2, NI

rnsnt

MP-2= 8G

PNGB:V/MP4 ~red

4sin2fred -1/2

nsfred-2

1-nsexp[1-nsNI (k)] (1+1-ns -1

exponentially suppressed; higher r if lowerNI & 1-ns

to match ns.96, fred~ 5, r~0.032

to match ns.97, fred~ 5.8, r~0.048

cf. =1, rnsnt

PNGB:V/MP4 ~red

4sin2fred -1/2

nsfred-2

1-nsexp[1-nsNI (k)] (1+1-ns -1

exponentially suppressed; higher r if lowerNI & 1-ns

to match ns.96, fred~ 5, r~0.032

to match ns.97, fred~ 5.8, r~0.048

cf. =1, rnsnt

ABFFO93ABFFO93

Moduli/brane distance limitation in stringy inflation. Normalized canonical inflaton

over e.g. 2/nbrane1/2

BM06

= (dd ln a)2 so r < .007, <<?

ns.97, fred~ 5.8, r~0.048,

cf. =1, rns

cf. =2, rns

ns.97, fred~ 5.8, r~0.048,

cf. =1, rns

cf. =2, rns

roulette inflation examples r ~ 10-10 roulette inflation examples r ~ 10-10 possible way out with many fields assisting: N-flationpossible way out with many fields assisting: N-flation

energy scale of inflation & r

V/MP4 ~ Ps r (1-3) 3/2

V~ (1016 Gev)4 r/0.1 (1-3)

energy scale of inflation & r

V/MP4 ~ Ps r (1-3) 3/2

V~ (1016 Gev)4 r/0.1 (1-3)

roulette inflation examples V~ (few x1013

Gev)4

roulette inflation examples V~ (few x1013

Gev)4

H/MP ~ 10-5 (r/.1)1/2 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 < m3/2 cf. ~Tev

String Theory Landscape & Inflation++ Phenomenology for CMB+LSS

Hybrid D3/D7 Potential

KKLT, KKLMMT

f||

fperp

•D3/anti-D3 branes in a warped geometry

•D3/D7 branes

•axion/moduli fields ... shrinking holesBB04, CQ05, S05, BKPV06

large volume 6D cct Calabi Yau

B-pol simulation: input LCDM (Acbar)+run+uniform tensor

r (.002 /Mpc) reconstructed cf. rin

s order 5 uniform prior s order 5 log prior

a very stringent test of the -trajectory methods: A+

Planck1yr simulation: input LCDM (Acbar)+run+uniform tensor

r (.002 /Mpc) reconstructed cf. rin

s order 5 uniform prior s order 5 log prior

Planck1 simulation: input LCDM (Acbar)+run+uniform tensor

Ps Pt reconstructed cf. input of LCDM with scalar running & r=0.1

s order 5 uniform prior s order 5 log prior

r=0.144 +- 0.032 r=0.096 +- 0.030

Planck1 simulation: input LCDM (Acbar)+run+uniform tensor

Ps Pt reconstructed cf. input of LCDM with scalar running & r=0.1

s order 5 uniform prior

s order 5 log prior

lnPs lnPt (nodal 5 and 5)

Inflation then summarythe 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 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 Planck+Spider.

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 < 1 over ~50 e-folds then r < .007

~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