SAIT 2008

Luca Amendola

INAF/Osservatorio Astronomico di Roma

The dark side ofgravity

SAIT 2008

Why DE is interesting

How to observe it

g

SAIT 2008

Observations are converging…

…to an unexpected universe

SAIT 2008

GTRgR 82

1

gravity matter

1tot 3.0cluster

Solution: modify either the Matter sector

or the Gravity sector

)( gF )(8 GT

DE

MG

The dark energy problem

SAIT 2008

Can we detect traces of modified gravity atbackground linear level ?non-linear

{ }

Modified gravityModified gravity

SAIT 2008

What is gravity ?

A universal force in 4D mediated by a massless tensor field

What is modified gravity ?

What is modified gravity ?

A non-universal force in nD mediated by (possibly massive) tensor, vector and scalar fields

What is modified gravity?

SAIT 2008

Cosmology and modified gravity

in laboratory

in the solar system

at astrophysical scales

at cosmological scales

} very limited time/space/energy scales;only baryons

complicated by non-linear/non-gravitational effects

unlimited scales; mostly linear processes;baryons, dark matter, dark energy !

Cosmology and modified gravity

SAIT 2008

L = crossover scale:

• 5D gravity dominates at low energy/late times/large scales

• 4D gravity recovered at high energy/early times/small scales

5D Minkowski bulk:

infinite volume extra dimension

gravity leakage

2

1

1

rVLr

rVLr

brane

RgxdLRgxdS 4)5()5(5

(Dvali, Gabadadze, Porrati 2000)(Dvali, Gabadadze, Porrati 2000)

3

82 G

L

HH

Simplest MG (I) : DGP

SAIT 2008

f(R) models are simple and self-contained (no need of potentials) easy to produce acceleration (first inflationary model) high-energy corrections to gravity likely to introduce higher-order terms particular case of scalar-tensor and extra-dimensional theory

matterL+Rfgxd 4eg higher order corrections ...324 RR+Rgxd

The simplest modification of Einstein’s gravity: f(R)

Simplest MG (II): f(R)Simplest MG (II): f(R)

SAIT 2008

Is this already ruled out by local gravity?

''

1

'

4'

''

1

)1()3

41(

22

/2*

ff

fRf

fm

eGeGG rrm

(on a local minimum)

α

λ

Is MG already ruled out by local gravity ?

Yukawa correction to Newton’s potential

SAIT 2008

From dark energy to dark forceFrom dark energy to dark force

rad mat

field

rad mat

fieldMDE

toda

y

9/1=Ωφ

2/1=β

a= t 1/2

)( 3

8

2

33

2

3)'(3

2

m

mmm

m

H

H

VH

2/3t=ainstead of !!

In Jordan frame:

From Dark Energy to Dark Force

L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302, astro-ph/0603173

SAIT 2008

A recipe to modify gravity

Can we find f(R) models that work?

A recipe for modified gravity

SAIT 2008

The m,r plane

The dynamics becomes 1-dimensional !

The qualitative behavior of any f(R) model can beunderstood by looking at the geometrical properties of the

m,r plot

m(r) curve

crit. line

acceleration

matter era

deSitter

L.A., D. Polarski, S. Tsujikawa, PRD, astro-ph/0612180

f

Rfr

f

Rfrm

'

'

'')(

The m,r plane

SAIT 2008

The power of the m(r) method

REJECTED

REJECTED

REJECTED

REJECTED

1/0)( ReRRf

REJECTED

SAIT 2008

The triangle of viable trajectories

There exist only two kinds of cosmologically viable trajectories

baRRf )()(

pp

p

RRRf 1

1

1 )()(naRRRf )(

SAIT 2008

A theorem on phantom crossing

Theorem: for all viable f(R) models

there is a phantom crossing of there is a singularity of both occur typically at low z when 1m

DEwDEw

phantom DE

standard DE

baRRf )()(

L.A., S. Tsujikawa, 2007

SAIT 2008

What do we need to test DE?

1) observations at z~1

2) observations involving background and perturbations

3) independent, complementary probes

DE observations checklist

SAIT 2008

Why z~1

probes at z=0 and z=1000

SAIT 2008

Why background+perturbations

The background expansion only probes H(z)

The (linear) perturbations probe first-order quantities

Full metric reconstruction at first order

)])(21()21[( 222222 dzdydxdtads

),(),()( zkzkzH

SAIT 2008

Why independent probes

a) systematics: because we need to test systematics like evolutionary effects in SN Ia, biasing effects in the baryon acoustic oscillations, intrinsic alignments in lensing, etc.b) theory: because in all generality we need to measure two free functions at pert. level (in addition to H(z) at background level)

SAIT 2008

Two free functions

At the linear perturbation level and sub-horizon scales, a modified gravity model will

mmakQGak ),(4 22 modify Poisson’s equation

induce an anisotropic stress

)])(21()21[( 222222 dzdydxdtads

),( ak

SAIT 2008

MG at the linear level

scalar-tensor models

2

2

2

2

0,

*

'

')(

'32

)'(2)(

FF

Fa

FF

FF

FG

GaQ

cav

0),(

1),(

ak

akQ

standard gravity

DGP

13

2)(

21;3

11)(

a

wHraQ DEc

f(R)

Ra

km

Ra

km

a

Ra

km

Ra

km

FG

GaQ

cav2

2

2

2

2

2

2

2

0,

*

21

)(,

31

41)(

Lue et al. 2004; Koyama et al. 2006

Bean et al. 2006Hu et al. 2006Tsujikawa 2007

coupled Gauss-Bonnet see L. A., C. Charmousis, S. Davis 2006...)(

...)(

a

aQ

Boisseau et al. 2000Acquaviva et al. 2004Schimd et al. 2004L.A., Kunz &Sapone 2007

SAIT 2008

Growth of fluctuationsas a measure of modified gravity

we parametrizeInstead of

LCDMDE

DGPST

is an indication of modified gravity

0),(4')'

1('' kkk akGQH

H good fit Peebles 1980Lahav et al. 1991Wang et al. 1999Bernardeau 2002L.A. 2004Linder 2006

Di Porto & L.A. 2007

SAIT 2008

Present constraints on gamma

Viel et al. 2004,2006; McDonald et al. 2004; Tegmark et al. 2004

s≡ d lo g δ /d lo g a

Present constraints on gamma

SAIT 2008

Present constraints on gamma

C. Di Porto & L.A. Phys.Rev. 2007

DGP

LCDM

SAIT 2008

Observables

222 ),(),( bzkPbzkP mattgal

2)(),( zkPellipt

Correlation of galaxy positions:galaxy clustering

Correlation of galaxy ellipticities:galaxy weak lensing

Correlation of galaxy velocities:galaxy peculiar field

2.. )

'(),(

bzkP velpec

SAIT 2008

Peculiar velocities

xH

xvrz

0

rz PP )1( 2

b

'

Correlation of galaxy velocities:galaxy peculiar field

Guzzo et al. 2008

redshift distortion parameter

rz PP )1( 2

SAIT 2008

The EUCLID theorem

2.. )

'(),(

bzkP velpec

),( zkPellipt

reconstructing in k,z requires

An imaging tomographic surveyand a spectroscopic survey:

Ψ ,Φ ,b

THE EUCLID THEOREM:

222 ),(),( bzkPbzkP mattgal

2)(),( zkPellipt

Correlation of galaxy positions:galaxy clustering

Correlation of galaxy ellipticities:galaxy weak lensing

Correlation of galaxy velocities:galaxy peculiar field

),(),,( .. zkPzkP velpecgal

SAIT 2008

DUNE x SPACE = EUCLID

- a satellite mission that merges DUNE and SPACE proposals- one of 4 mission selected by ESA Cosmic Vision in 2007- final selection 2011- launch 2015-2020, 5 years duration, half-sky- an imaging mission in several bands optical+NIR (>1 billion galaxies)- a spectroscopic survey: 500.000.000 galaxy redshifts- a pan-european collaboration

30CPS Review CNES Paris

Requirements for Weak LensingStatistical Requirements:• a 20,000 deg2 survey at high galactic latitude (|b|>30 deg) • sample of at least 35 galaxies/amin2 usable for weak lensing (SNR[Sext]>7,

FWHM>1.2FWHM[PSF]) with a median z~1 and an rms shear error per galaxy of

=0.35 (or equivalent combination)• a PSF FWHM smaller than 0.23’’ to be competitive with ground based surveys• photometric redshifts to derive 3 redshift bins over the survey area (from ground

based observations)

Systematics Requirements:• Survey scanned in compact regions <20 on a side, with 10% overlap between

adjacent stripes• a precision in the measurement of the shear after deconvolution of the PSF better

than about 0.1%. This can be achieved with a PSF with a FWHM of 0.23’’, an

ellipticity |e|<6% with an uncertainty after calibration of |e|<0.1%.• good image quality: low cosmic ray levels, reduced stray light, linear and stable

CCDs, achromatic optics

• Photometric redshifts with precision ∆z<0.1 in a subset of the survey to place limits

on the intrinsic correlations of galaxy shapes (from ground based observations)

31CPS Review CNES Paris

Science from DUNE/EUCLID

• Primary goal: Cosmology with WL and SNe

– Measurement of the evolution of the dark energy equation of state (w,w’) from z=0 to ~1

– Statistics of the dark matter distribution (power spectrum, high order correlation functions)

– Reconstruction of the primordial power spectrum (constraints on inflation)

• Cross-correlation with CMB (Planck)

– Search for correlations of Galaxy shear with ISW effect, SZ effect, CMB lensing

– Search for DE spatial fluctuations on large scales

• Study of Dark Matter Haloes:

– Mass-selected halo catalogues (about 80,000 haloes) with multi- follow-up (X-ray, SZ,

optical) halo mass calibration

– Strong lensing: probe the inner profiles of haloes

• Galaxy formation:

– Galaxy bias with galaxy-galaxy and shear-galaxy correlation functions

– Galaxy clustering with high resolution morphology

• Core Collapse supernovae:

– constraints on the history of star formation up to z~1

• Fundamental tests:

– Test of gravitational instability paradigm

– Dark Energy clustering

– Distinguish dark energy from modification of gravity

32CPS Review CNES Paris

Weak Lensing Power Spectrum Tomography

DUNE baseline: 20,000 deg2, 35 galaxies/amin2, ground-based photometry for photo-z’s, 3 year WL survey

z>1

z<1

Redshift bins from photo-z’sWL power spectrum for each z-bin

The power of WL

SAIT 2008

The power of WL

SAIT 2008

Probing gravity with weak lensing

In General Relativity, lensing is causedby the “lensing potential”

and this is related to the matter perturbationsvia Poisson’s equation. Therefore the lensing signal depends on two modified gravity functions

and in the growth function

in the WL power spectrum

{

SAIT 2008

Forecasts for Weak Lensing

L.A., M. Kunz, D. Sapone JCAP 2007

Marginalization over the modified gravity parameters

does not spoil errors on standard parameters

)1/()( 0 zzwwzw a

SAIT 2008

Weak lensing measures Dark Gravity

DGP Phenomenological DE

Weak lensing tomography over half sky

LCDM

DGP

L.A., M. Kunz, D. Sapone arXiv:0704.2421

Σ0

SAIT 2008

Non-linearity in WL

Weak lensing tomography over half sky

ell_max=1000,3000,10000

SAIT 2008

Non-linearity in BAO

Matarrese & Pietroni 2007

SAIT 2008

Clustering measures Dark Gravity

Galaxy clustering at 0<z<2 over half sky ....if you know the bias to 1%

SAIT 2008

Combining P(k) with WL

Weak lensing/ BAO over half sky

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Conclusions

Two solutions to the DE mismatch: either add “dark energy” or “dark gravity” The high precision data of present and near-future allow to test for dark energy/gravity It is crucial to combine background and perturbations A full reconstruction to first order requires imaging and spectroscopy Let EUCLID fly...