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

TemperatureTemperaturepower spectrum power spectrum

- - - unlensed lensed

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)