dick bond inflation then k =(1+q)(a) ~r/16 0< = multi-parameter expansion in ( ln ha ~ lnk) ~...
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Dick Bond
Inflation Then k=(1+q)(a) ~r/16 0< = multi-parameter expansion in (lnHa ~ lnk)
~ 10 good e-folds in a (k~10-4Mpc-1 to ~ 1 Mpc-1 LSS)
~ 10+ parameters? Bond, Contaldi, Kofman, Vaudrevange 07 V() Cosmic Probes now & then CMBpol (T+E,B modes of polarization), LSS
Inflation Histories & their Cosmic Probes, now & then
Inflation Now1+w(a) goes to 2(1+q)/3
~1 good e-fold. only ~2params Zhiqi Huang, Bond & Kofman 07
Cosmic Probes Now CFHTLS SN(192),WL(Apr07),CMB,BAO,LSS,Ly
Cosmic Probes Then JDEM-SN + DUNE-WL + Planck +ACT/SPT…
V()?
~0 to 2 to 3/2 to ~.4 now, on its way to 0?
CMBology
ForegroundsCBI, Planck
ForegroundsCBI, Planck
SecondaryAnisotropies (CBI,ACT)
(tSZ, kSZ, reion)
SecondaryAnisotropies (CBI,ACT)
(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
wide open braking
approach to preheating
roulette inflation potential T=+i
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
CMB/LSS Phenomenology CITA/CIfAR here
• Bond
• Contaldi
• Lewis
• Sievers
• Pen
• McDonald
• Majumdar
• Nolta
• Iliev
• Kofman
• Vaudrevange
• Huang
UofT here
• Netterfield
• Crill
• 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
WMAP3 sees 3rd pk, B03 sees 4th ‘‘Shallow’ scan, 75 hours, fShallow’ scan, 75 hours, fskysky=3.0%, large scale TT=3.0%, large scale TT
‘‘deep’ scan, 125 hours, fsky=0.28% 115sq deg, ~ Planck2yrdeep’ scan, 125 hours, fsky=0.28% 115sq deg, ~ Planck2yr
B03+B98 final soon
CBIpol 2.5 yrs EE, ~ best so far, ~QuaD
TEBB
TT
CBI excess 04, 2.5 yrs cf. CBI excess Dec07,
5 yrs
Jan08: Full ACBAR data ~ 4X includes 2005 observations
Current high L state
November 07
Current high L state
November 07
CBI sees 4th 5th pk
CBI excess 07
WMAP3 sees 3rd pk, B03 sees 4th
ACT@5170m
CBI2@5040m
why Atacama? driest desert in the world. thus: cbi, toco, apex,
asti, act, alma, quiet, clover
forecast Planck2.5
100&143
Spider10d
95&150
Synchrotron pol’n
Dust pol’n
are higher in B
Foreground Template removals
from multi-frequency data
is crucial
PRIMARY END @ 2012? PRIMARY END @ 2012?
CMB ~2009+ Planck1+WMAP8+SPT/ACT/Quiet+Bicep/QuAD/Quiet +Spider+Clover
INFLATION THEN
INFLATION THEN
Standard Parameters of Cosmic Structure Formation
Òk
What is the average curvature of the universe (we can see)?
Òbh2 ÒË nsÒdmh2
Density of Baryonic Matter
Density of non-interacting Dark
Matter
Cosmological Constant
Spectral index of primordial scalar
(curvature) perturbations
nt
Spectral index of
primordial tensor
(Gravity Wave)
perturbations
lnAs
Scalar Amplitude
r = A t=As
Tensor Amplitude
Period of inflationary expansion, quantum noise metric perturbations
üc
Compton Depth to Last
Scattering Surface
When did stars reionize the universe?
òø `à1s
r < 0.6 or
< 0.28 95% CLø lnû2
8 nçs
ns = .958 +- .015 (+-.005 Planck1)
.93 +- .03 @0.05/Mpc run&tensor
r=At / As < 0.28 95% CL (+-.03)
<.36 CMB+LSS run&tensor
< .05 ln r prior!
dns /dln k =-.038 +- .024 (+-.005)
CMB+LSS run&tensor prior change?
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
1+w = 0.02 +/- 0.05 ‘phantom DE’ allowed?!
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)
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)2or dual ln P s(k);P t(k)
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
(Chebyshev-filter) criterion [data cannot constrain high ln k frequencies]
P(trajectory|data, th) ~ P(lnHp,k|data, th)
~ P(data| lnHp,k ) P(lnHp,k | th) / P(data|th)
Likelihood theory prior / evidence
“path integral” over probability landscape of theory and data, with mode-function expansions of the paths truncated by an imposed smoothness
(Chebyshev-filter) criterion [data cannot constrain high ln k frequencies]
P(trajectory|data, th) ~ P(lnHp,k|data, th)
~ P(data| lnHp,k ) P(lnHp,k | th) / P(data|th)
Likelihood theory prior / evidenceData:
CMBall
(WMAP3,B03,CBI, ACBAR,
DASI,VSA,MAXIMA)
+
LSS (2dF, SDSS, 8[lens])
Data:
CMBall
(WMAP3,B03,CBI, ACBAR,
DASI,VSA,MAXIMA)
+
LSS (2dF, SDSS, 8[lens])
Theory prior
uniform in lnHp,k
(equal a-prior probability hypothesis)
Nodal points cf. Chebyshev coefficients (linear
combinations)
uniform in / log in / monotonic in k
The theory prior matters a lot for current data.
Not quite as much for a Bpol future.
We have tried many theory priors
Theory prior
uniform in lnHp,k
(equal a-prior probability hypothesis)
Nodal points cf. Chebyshev coefficients (linear
combinations)
uniform in / log in / monotonic in k
The theory prior matters a lot for current data.
Not quite as much for a Bpol future.
We have tried many theory priors
1980
2000
1990
-inflation Old Inflation
New InflationChaotic inflation
Double Inflation
Extended 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 pNGB inflation
Old view: Theory prior = delta function of THE correct one and only theoryOld view: Theory prior = delta function of THE correct one and only theory
Radical BSI inflation variable MP inflation
1980
2000
1990
Chaotic inflation
Double Inflation
Extended inflation
Power-law inflation
Roulette inflation Kahler moduli/axion
Natural pNGB inflation
Radical BSI inflation variable MP inflation
1980
2000
1990
Power-law inflation
Uniform acceleration
V/MP4 ~ exp MP
-
1/2
1-nsnt rrns
rns
Uniform acceleration
V/MP4 ~ exp MP
-
1/2
1-nsnt rrns
rnsMP
-2= 8G
1980
2000
1990
Chaotic inflation
V/MP4 ~ 2 MP
-1/2
(k) NI(k) +/3
ns-1+1NI(k) -/6ntNI(k) -/6
forNI =1, rnsnt
=2, rnsnt
V/MP4 ~ 2 MP
-1/2
(k) NI(k) +/3
ns-1+1NI(k) -/6ntNI(k) -/6
forNI =1, rnsnt
=2, rnsnt
1980
2000
1992 Natural pNGB inflation
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 ,
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 ,
abffo92
Old view: Theory prior = delta function of THE correct one and only theoryOld view: Theory prior = delta function of THE correct one and only theory
New view: Theory prior = probability distribution on an energy landscape
whose features areare 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)
New view: Theory prior = probability distribution on an energy landscape
whose features areare 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
1980
2006
1990
Roulette inflation Kahler moduli/axion
typical r ~ 10-10
As & ns~0.97 OK
but by statistical selection!
running dns /dlnk exists, but small
because small observable window
typical r ~ 10-10
As & ns~0.97 OK
but by statistical selection!
running dns /dlnk exists, but small
because small observable window
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 BKVP06
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
Planck1yr simulation: input LCDM (Acbar)+run+uniform tensor
r (.002 /Mpc) reconstructed cf. rin
s order 5 uniform prior s order 5 log prior
GW/scalar curvature: current from CMB+LSS: r < 0.6 or < 0.25 (.28) 95%; good shot at 0.02 95% CL with BB polarization (+- .02 PL2.5+Spider), .01 target
BUT foregrounds/systematics?? But r-spectrum. But low energy inflation
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)
http://www.astro.caltech.edu/~lgg/spider_front.htmhttp://www.astro.caltech.edu/~lgg/spider_front.htm
No Tensor
SPIDER Tensor Signal
Tensor
• Simulation of large scale polarization signal
B-pol simulation: ~10K detectors > 100x Planck
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+
also input trajectory is recovered
INFLATION NOW
Inflation Now1+w(a)= sf(a/aeq;as/aeq;s) to ax3/2 = 3(1+q)/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 trajectoriesCosmic Probes Now CFHTLS SN(192),WL(Apr07),CMB,BAO,LSS,Ly
s= (dlnV/d)2/4 = late-inflaton (potential
gradient)2
=0.0+-0.25 now;
weak as < 0.3 (zs >2.3) now
s to +-0.07 then Planck1+JDEM SN+DUNE WL, weak as <0.21 then, (zs >3.7)
3rd param s (~ds /dlna) ill-determined now & then
cannot reconstruct the quintessence potential, just the slope s & hubble drag info
(late-inflaton mass is < Planck mass, but not by a lot)
Cosmic Probes Then JDEM-SN + DUNE-WL + Planck1
w(a)=w0+wa(1-a) models
45 low-z SN + ESSENCE SN + SNLS 1st year SN+ Riess high-z SN, 192 “gold”SN all fit with MLCS
illustrates the near-degeneracies of the contour plotillustrates the near-degeneracies of the contour plot
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
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
End End
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