cmb lensing and cosmic acceleration viviana acquaviva sissa, trieste
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CMB lensingCMB lensingand cosmic accelerationand cosmic acceleration
Viviana Acquaviva Viviana Acquaviva
SISSA, TriesteSISSA, Trieste
OutlineOutline
Physics of lensingPhysics of lensing
From CMB to dark energyFrom CMB to dark energy
Results and forecastsResults and forecasts
small deflection angles small deflection angles WEAK LENSING WEAK LENSING
sourcesource
lenslens
lenslensplaneplane
αα
unlensedunlensedimageimage
lensedlensedimageimage
deflectiondeflectionangleangle
gRRTG2
18
dλ
dr
dλ
drggg
dλ
rd νμ
μν,ββν,μαβ
α
2
12
2
Einstein equationsEinstein equations
geodesic equationgeodesic equation
why lensing for dark energy?why lensing for dark energy?C
MB
lig
ht
from
LS
S
usus
z1000 ~ 1 0
r/H0-1
~ 2 ~ 1 0
DE
lensing selection effect
OVERLAPPING OVERLAPPING
CMB lensing phenomenologyCMB lensing phenomenology
observed imageobserved image source emissionsource emissionre-mappingre-mapping
)()ˆ()ˆ()ˆ()ˆ( 2αnαnαnn ii
ilensed OXXXX
iBEiBEX ,, αilensing is quadratic in the lensing is quadratic in the
cosmological perturbations !cosmological perturbations !
hard life if we arehard life if we aredominated bydominated by
primary anisotropiesprimary anisotropies
lensing generates UNBIASEDlensing generates UNBIASEDB-modes at l > 100 !B-modes at l > 100 !
there is a CMB observationthere is a CMB observationin the DE-related in the DE-related redshift windowredshift window
B polarization modes power spectrumB polarization modes power spectrum
reionizationreionization primordial GWprimordial GW lensinglensing
B polarization modes power spectrumB polarization modes power spectrum
unbiased observable, tracking DE at lensing epochunbiased observable, tracking DE at lensing epoch
plan of our workplan of our work
1.1.Formal extension of lensing frameworkFormal extension of lensing framework to generalized theories of gravityto generalized theories of gravity
fluid;
;4 )()(2
1),(
2
1LVRfgxdS
2. Study of lensed B signal in different models2. Study of lensed B signal in different models
fluid
4
16L
G
RgxdS
VA, Baccigalupi and Perrotta 2004
RP: V(RP: V() = M) = M4+4+// (aka IPL) (aka IPL) Ratra & Peebles 2000
SUGRA: V(SUGRA: V() = M) = M4+4+// e e44((/Mpl)/Mpl)2 2 Brax & Martin 2000
VA & Baccigalupi 2005
)(1),(),(16)( 0
0
2
0
320
kJWkPdkdkLS
LS
technicalities technicalities lensed correlation functions are obtained
by a convolution with a gaussian of arguments:
background expansionbackground expansionW = (W = (χχLS LS – – χχ)/)/χχLSLS
evolution of evolution of gravitational potentialgravitational potential
PPψψ (k,(k,χχ) ≠ T) ≠ T22(k,0) g(k,0) g22((χχ))
no analytical fit is availableno analytical fit is available
Zaldarriaga & Seljak 1998
ΨΨ generalized gauge-invariant variable generalized gauge-invariant variable accounting for all the fluctuating accounting for all the fluctuating componentscomponents
lensing of the spectra performed in the mainlensing of the spectra performed in the main integration routine (all k,z needed!)integration routine (all k,z needed!)
RESULTS FOR THE QUINTESSENCE MODELSRESULTS FOR THE QUINTESSENCE MODELS
no anisotropic stressbasically geometry effects
tracking behaviour main dependence is on α
ww00 = - 0.9 = - 0.9
tuned to get
Geff = G0
SAME PRIMORDIALSAME PRIMORDIALNORMALIZATIONNORMALIZATION
SUGRAIPL
SUGRAIPL
Lensing kernelLensing kernel
PerturbationPerturbationgrowth factorgrowth factor
different amountdifferent amountof dark energyof dark energy
at z at z ~ 1 ~ 1 significant deviationsignificant deviation
SUGRAIPL
SUGRAIPL
)(1]/)[(16)( 0
0
2
0
3
kJdkdkLS
LSLS
SUGRAIPL
rad3104
11.0 Mpck
TTTTpowerpower
spectrumspectrum
EEEEpowerpower
spectrumspectrum
only slight projection effectonly slight projection effect
SUGRAIPL
SUGRAIPL
SUGRA
IPL
COMPARISON OF B-MODES SPECTRA COMPARISON OF B-MODES SPECTRA
effect is due to B-modes sensitivity effect is due to B-modes sensitivity to DE equation of state DERIVATIVE!to DE equation of state DERIVATIVE!
30% difference in amplitude at peak30% difference in amplitude at peak
GETTING MORE QUANTITATIVE:GETTING MORE QUANTITATIVE:A FISHER MATRIX ANALYSISA FISHER MATRIX ANALYSIS
set of parameters αi
ESTIMATOR OF ACHIEVABLE PRECISIONESTIMATOR OF ACHIEVABLE PRECISION
j
l
i
l
l lij
CC
CF
2)(
1 j
Yl
XYll XY i
Xl
ij
CCF
1
single spectrum four spectra
FF-1-1ijij gives marginalized 1- gives marginalized 1-σσ error on parameters error on parameters
iii F ][)( 12
LS
z
z
z
zwdz
m
LS
zz
dzHd
0 '1
)'(1'33
10
0)1()1(
dark energy parametrization:dark energy parametrization:
)1)(()( 00 awwwaw
fixing primordial normalization one hasfixing primordial normalization one hasonly projection effects on TT,TE,EE spectra only projection effects on TT,TE,EE spectra
B spectrum B spectrum amplitude changes! amplitude changes!
(sensitivity to dynamics at lower redshifts)(sensitivity to dynamics at lower redshifts)
Chevallier & Polarski 2001, Linder & Huterer 2005
PARAMETERSPARAMETERS
1.1. ww0 0 = -1= -1
2.2. ww∞∞= -1= -1
3.3. nns s = 0.96= 0.96
4.4. hh00 = 0.72 = 0.72
5.5. ττ = 0.11 = 0.11
6.6. ΩΩbbhh22 = 0.022= 0.022
7.7. ΩΩmm h h2 2 = 0.11= 0.11
8.8. A = 1A = 1
1.1. ww0 0 = -0.9= -0.9
2.2. ww∞∞= -0.4= -0.4
3.3. nns s = 0.96= 0.96
4.4. hh00 = 0.72 = 0.72
5.5. ττ = 0.11 = 0.11
6.6. ΩΩbbhh22 = 0.023= 0.023
7.7. ΩΩmm h h22= 0.12= 0.12
8.8. A = 1A = 1
SUGRASUGRAΛΛCDMCDM
EBEX-like experimentEBEX-like experiment
ΛΛCDM RESULTS
CDM RESULTS
SUGRA RESULTS
SUGRA RESULTS
0.1
few ·10-2
3·10-3
6·10-2
3·10-3
8·10-5
7·10-4
3·10-3
5 ·10-2
few·10-2
2·10-3
2·10-2
3·10-3
7·10-5
5·10-4
5.0·10-3
ww00
w’w’
nnss hh00
ττΩΩbbhh22
ΩΩmmhh22
AA
√(F-1)ii
√(F-1)ii
CONCLUSIONS AND FURTHER THOUGHTSCONCLUSIONS AND FURTHER THOUGHTS
We can extract valuable information from the lensed CMB spectra The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models We have a computational machine allowing us to predict the lensed spectra of a wide range of models We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)
CONCLUSIONS AND FURTHER THOUGHTSCONCLUSIONS AND FURTHER THOUGHTS
We can extract valuable information from the lensed CMB spectra The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models We have a computational machine allowing us to predict the lensed spectra of a wide range of models We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)
CONCLUSIONS AND FURTHER THOUGHTSCONCLUSIONS AND FURTHER THOUGHTS
We can extract valuable information from the lensed CMB spectra The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models We have a computational machine allowing us to predict the lensed spectra of a wide range of models We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)
CONCLUSIONS AND FURTHER THOUGHTSCONCLUSIONS AND FURTHER THOUGHTS
We can extract valuable information from the lensed CMB spectra The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models We have a computational machine allowing us to predict the lensed spectra of a wide range of models We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)
CONCLUSIONS AND FURTHER THOUGHTSCONCLUSIONS AND FURTHER THOUGHTS
We can extract valuable information from the lensed CMB spectra The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models We have a computational machine allowing us to predict the lensed spectra of a wide range of models We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)
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