Munich 2008Luca Amendola

INAF/Osservatorio Astronomico di Roma

The dark side ofgravity

Munich 2008

Why DE/MG is interesting

How to observe it

g

Munich 2008

Observations are converging…

…to an unexpected universe

Munich 2008

Classifying the unknown

a) change the equations i.e. add new matter field (DE) or modify gravity (MG)b) change the metrici.e. inhomogeneous non-linear effects, void models, etc

Standard cosmology:GR gravitational equations + FRW metric

Munich 2008

Which are the effects of modified gravity atbackground linear level ?non-linear

{ }

Modified gravity

Munich 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 !

Munich 2008

How to hide modified gravity (in the solar system)

L.A., C. Charmousis, S. Davis, PRD 2008, arXiv 0801.4339

Generalized Brans-Dicke-Gauss-Bonnet Lagrangian

Solution in static spherical symmetry in a linearizedPPN metric with

1/U

Conclusion: there are solutions which look “Einsteinian” but are not…

Munich 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

Simplest MG (I): DGP

RgxdLRgxdS 4)5()5(5

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

3

82 GLHH

Munich 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 MG in 4D: f(R)

Simplest MG (II): f(R)

Munich 2008

Is this already ruled out by local gravity?

matterL+Rfgxd )(4is a scalar-tensor theory with Brans-Dicke

parameter ω=0 or a coupled dark energy model with coupling β=1/2

''1

)1()341(

2

/2*

fm

eGeGG rrm

α

λAdelberger et al. 2005

Munich 2008

The fourfold way out of local gravity

)341( 2* rmeGG

,m { depend on timedepend on spacedepend on local densitydepend on species

Munich 2008

Sound horizon in R+R Sound horizon in R+R - - nn model model

dec

dec

z

z

s

zHdz

zHdzc

0 )(/

)(

2/1ta

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

matterL+RμRgxd

44

Turner, Carroll, Capozziello etc. 2003

in the Matter Era !

Munich 2008

A recipe to modify gravity

Can we find f(R) models that work?

Munich 2008

MG in the background (JF)

321

23

22

1

16

'6

''

xxx=ΩHRx

Hffx

Hffx

m

An autonomous dynamical system

fRfr

fRfrm

'''')(

)2(2]/[

'

)42(]/[

'

31'

3332

313

13232

312

312

1231

xxxxm

xxx

xxxxxm

xxx

xxxxxx

characteristic function

rprrmeRRf

rrnrmRRRf

nmRRf

mRRf

qRp

n

n

)()(

1)()(

1)(

0)(

Munich 2008

MG in the background

ΩKΩP

Ωγ

Munich 2008

Classification of f(R) solutions

,...)21

)1(2(

,...)13(

)0,5,4()0,0,1(

)0,0,1()2,1,0(

6

5

4

3

2

1

mmP

mmP

PPPP

deSitter acceleration, w = -1

General acceleration, any w0

)1(2)107(1

0020

2

m

m

m

m

m

m

mmm

For all f(R) theories:

wrong matter era (t1/2)

good matter era (t2/3) for m≥0

Munich 2008

The power of the m(r) method

REJECTED

REJECTED

REJECTED

REJECTED

1/0)( ReRRf

REJECTED

Munich 2008

The triangle of viable trajectoriescosmologically viable trajectories

baRRf )()(

ppp

RRRf 11

1 )()(naRRRf )(

Notice that in the triangle m>0L.A., D. Polarski, S. Tsujikawa 2007 PRD astro-ph/0612180

fRfrfRfrm

/''/'')(

Munich 2008

Local Gravity Constraints are very tight

Depending on the local field configuration

623 1010'

'')( s

sss f

fRRm

depending on the experiment: laboratory, solar system, galaxy

see eg. Nojiri & Odintsov 2003; Brookfield et al. 2006Navarro & Van Acoyelen 2006; Faraoni 2006; Bean et al. 2006;Chiba et al. 2006; Hu, Sawicky 2007; Mota et al. 2006;....

Munich 2008

cLGC+Cosmology

Take for instance the ΛCDM clone

baRRf )()(

Applying the criteria of LGC and background cosmology

23101 ba

i.e. ΛCDM to an incredible precision

Munich 2008

What background hidesperturbations reveal

The background expansion only probes H(z)

The (linear) perturbations probe first-order quantities

Full metric reconstruction at first order requires 3 functions

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

),(),()( zkzkzH

Munich 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

(most of what follows in collaboration with M. Kunz, D. Sapone)

Munich 2008

MG at the linear level

scalar-tensor models

2

2

2

2

0,

*

'')(

'32)'(2)(

FFFa

FFFF

FGGaQcav

0),(1),(

akakQ

standard gravity

DGP

132)(

21;311)(

a

wHraQ DEc

f(R)

Rakm

Rakm

a

Rakm

Rakm

FGGaQcav

2

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...)(

...)(

aaQ

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

Munich 2008

Reconstruction of the metric

b

zkbzkPgal

'

),()1(),,( 2222

2)(),( zkPellipt

Correlation of galaxy positions:galaxy clustering

Correlation of galaxy ellipticities:galaxy weak lensing

Munich 2008

Peculiar velocities

xHxv

rz

0

rz PP )1( 2

b '

Correlation of galaxy velocities:galaxy peculiar field

Guzzo et al. 2008

redshift distortion parameter

rz PP )1( 2

=0.70±0.2

Munich 2008

The Euclid theorem

1),,(/),,('),,(

transvzkPradzkPb

transvzkPb

2

0

)()'('),( z

ellipt zKdzzkP

We can measure 3 combinations and we have 2 theoretical relations…

),(),,(),,(),,(),,( zkzkzkzkzkb

Observables: Conservation equations:

HakHa

2

'

'3'

Theorem: lensing+galaxy clustering allows to measure all (total matter) perturbation variables at first order without

assuming any particular gravity theory

5 unknown variables:

Munich 2008

The Euclid theorem

1),,(/),,('),,(

transvzkPradzkPb

transvzkPb

2

0

)()'('),( z

ellipt zKdzzkP

We can measure 3 combinations and we have 2 theoretical relations…

),(),,(),,(),,(),,( zkzkzkzkzkb

Observables: Conservation equations:

HakHa

2

'

'3'

Theorem: lensing+galaxy clustering allows to measure all (total matter) perturbation variables at first order without

assuming any particular gravity theory

5 unknown variables:

Munich 2008

The Euclid theorem

From these we can estimate deviations from Einstein’s gravity:

),(),,(),,(),,(),,( zkzkzkzkzkb

),(4 22 akQGak

),( ak

Munich 2008

EuclidA geometrical probe of the universe proposed for Cosmic Vision

= +

All-sky optical imaging for gravitational lensing

All-sky near-IR spectra to H=22 for BAO

Munich 2008

Weak lensing

Weak lensing tomography over half sky

LCDM

DGP

L.A., M. Kunz, D. Sapone arXiv:0704.2421DiPorto & L.A. 2007

add

loglog

Euclid forecast Present constraints

02.0

4.0

Munich 2008

Power spectrum

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

Munich 2008

Non-linearity in BAO

Matarrese & Pietroni 2007

Munich 2008

Poster advertisement

See poster by Miguel Quartin…

Quercellini, Quartin & LA, arXiv 0809.3675

yrst 10

as 11.0

LTB void model

Garcia-Bellido & Haugbolle 2008

Cosmic parallax

Munich 2008

Conclusions

Two solutions to the DE mismatch: either add “dark energy” or “dark gravity” High-precision next generation cosmological observations are the best tool to test for modifications of gravity It is crucial to combine background and perturbations A full reconstruction to first order requires imaging and spectroscopy: Euclid

Munich 2008

Luca AmendolaINAF/Osservatorio

Astronomico di Roma

The bright side ofMunich

Munich 2008

Weak lensing measures Dark Gravity

scalar-tensor model

Weak lensing tomography over half sky V. Acquaviva, L.A., C. Baccigalupi, in prep.

Munich 2008

Non-linearity in WL

Weak lensing tomography over half sky

=1000,3000,10000

log

max

Munich 2008

Non-linearity in BAO

Matarrese & Pietroni 2007

Munich 2008

Conclusions: the teachings of DE

Two solutions to the DE mismatch: either add “dark energy” or “dark gravity”The high precision data of present and near-future observations allow to test for dark energy/gravityNew MG parameters: γ,Σ A general reconstruction of the first order metric requires galaxy correlation and galaxy shear Let EUCLID fly...

Munich 2008

References

Basics: L.A. , Phys. Rev. D62, 043511, 2000; L.A. , Phys. Rev. D62, 043511, 2000;CMB: L.A. , Phys. Rev. Lett. 86,196,2001; L.A. , Phys. Rev. Lett. 86,196,2001;Bias: L.A. & D. Tocchini-Valentini, PRD66, 043528, L.A. & D. Tocchini-Valentini, PRD66, 043528,

20022002WMAP: astro-ph/0303228, Phys Rev 2003 astro-ph/0303228, Phys Rev 2003N-body: : A. Maccio’ et al. 2004A. Maccio’ et al. 2004Dilatonic dark energy: L.A., M. Gasperini, D. Tocchini-

Valentini, C. Ungarelli, Phys. Rev. D67, 043512, 2003

Munich 2008

Current Observational Status: CFHTLS

First resultsFrom CFHT Legacy Survey with Megacam

(w=constant and other priors assumed)

Weak Lensing

Type IaSuper-novae

Hoekstra et al. 2005Semboloni et al. 2005

Astier et al. 2005