ISAPP 2011

Observations are converging…

…to an unexpected universe

ISAPP 2011

Classifying the unknown, 11. Cosmological constant2. Dark energy w=const3. Dark energy w=w(z)4. quintessence5. scalar-tensor models6. coupled quintessence7. mass varying neutrinos8. k-essence9. Chaplygin gas10. Cardassian11. quartessence12. quiessence13. phantoms14. f(R)15. Gauss-Bonnet16. anisotropic dark energy17. brane dark energy18. backreaction19. void models20. degravitation21. TeVeS22. oops....did I forget your model?

ISAPP 2011

Classifying the unknown, 3

a) change the equations i.e. add new matter field (DE) or modify gravity (MG)

b) change the symmetriesi.e. inhomogeneous non-linear effects, void models, etc

Standard cosmology:GR gravitational equations + symmetries

ISAPP 2011

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 G

L

HH

ISAPP 2011

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)

ISAPP 2011

Faces of the same Faces of the same physicsphysics

matterL+Rφ,fgxd 4

Extra-dim. degrees of freedom

Higher order gravity

Coupled scalar field

Scalar-tensor gravity

Faces of the same physics

ISAPP 2011

Is this already ruled out by

local gravity? matterL+Rfgxd )(4

is a scalar-tensor theory with Brans-Dickeparameter ω=0 or

a coupled dark energy model with coupling β=1/2

* 2 2 /

2

(1 ) (1 )

1

''

m r rG G e G e

mf

β

λAdelberger et al. 2005

ISAPP 2011

The fourfold way out of local

constraints

* 2(1 )m rG G e

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

ISAPP 2011

The simplest caseThe simplest case

matterL+

R

μRgxd

44

2/1=β

03

0)'(3

mm H

VH

In Einstein Frame

2

33

2

3)'(3

mmm

m

H

VH

Turner, Carroll, Capozzielloetc. 2003

)'(g 2 gf

'log

'

')'(

2

f

f

ffRV

…a particular case ofcoupled dark energy

ISAPP 2011

R-1/R model :R-1/R model : the the φφMDEMDE

rad mat

field

rad mat

fieldMDE

toda

y

9/1=Ωφ

2/1=β

a= t 1/2Caution:Plots in theEinstein frame!

)( 3

8

2

33

2

3)'(3

2

m

mmm

m

H

H

VH

2/3t=ainstead of !!

In Jordan frame:

ISAPP 2011

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

dec

dec

z

z

s

zH

dz

zH

dzc

0 )(/

)(

2/1ta

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

matterL+

R

μRgxd

44

in the Matter Era !

ISAPP 2011

A recipe to modify gravity

Can we find f(R) models that work?

ISAPP 2011

cLGC+Cosmology

Take for instance the ΛCDM clone

baRRf )()( Applying the criteria of LGC and background cosmology

2 31 01 ba

i.e. ΛCDM to an incredible precision

ISAPP 2011

Space-time geometry

The most general (linear, scalar) metric at first-order

Full metric reconstruction at first order requires 3 functions

2 2 2 2 2 2[(1 2 ) (1 2 )( )]ds a dt dx dy dz

( ) ( , ) ( , )H z k z k z

background

perturbations

ISAPP 2011

Two free functions

At linear order we can write:

2 24 m mGa Poisson equation

zero anisotropic stress

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

ISAPP 2011

Two free functions

2 2 ( ,4 ) m mQ aa kG modified Poisson equation

non-zero anisotropic stress

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

( , )k a

At linear order we can write:

' 3'' (1 ) ' [1 ( , )] 0

2 m

HQ k z

H

ISAPP 2011

Modified Gravity 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)

Rak

m

Rak

ma

Rak

m

Rak

m

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

ISAPP 2011

Reconstruction of the metric

v Hv

dzperp )(

massive particles respond to Ψ

massless particles respond to Φ-Ψ

2 2 2 2 2 2[(1 2 ) (1 2 )( )]ds a dt dx dy dz

ISAPP 2011

Reality check

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

),( zkPmatter

),(),(2 zkPzkb matter

),(),()cos),(1( 222 zkPzkbzk matter

Matter power spectrum

Galaxy power spectrum

Galaxy power spectrumin redshift space

Density fluctuation in space ),(2 zkPk 0

0

( )x

θ

ISAPP 2011

Peculiar velocities

.

r = v/H0

ISAPP 2011

Peculiar velocities

'

b

redshift distortion parameter

2 2(1 )z rP P

Kaiser 1987

ISAPP 2011

Observer

Dark matter halos

Background sources

Radial distances depend on

geometry of Universe

Weak lensing

Foreground mass distribution depends on growth/distribution of structure

ISAPP 2011

The Euclid theorem

( )

( )'1

( )

transv

radial

transv

b P k

P k

b P k

2

0

( , ) ' ( ')( )z

ellipt k kP k z dz K z

We can measure 3 combinations and we have 1 theoretical relation…

( , ), ( , ), ( , ), ( , )b k z k z k z k z

Observables: Conservation equations:

Theorem: lensing+galaxy clustering allows to measure all (total matter) perturbation variables at first order

without assuming any specific gravity theory

4 unknown functions:

' 3'' (1 ) ' [1 ( , )] 0

2 m

HQ k z

H

ISAPP 2011

The Euclid theorem

From these we can derive the deviations from Einstein’s gravity:

2

2

4( , )

Ga

kQ k a

( , )k a

( , ), ( , ), ( , ), ( , )b k z k z k z k z

Euclid Surveys

‣ Simultaneous (i) visible imaging (ii) NIR photometry (iii) NIR spectroscopy

‣ 20,000 square degrees

‣ 100 million redshifts, 2 billion images

‣ Median redshift z = 1

‣ PSF FWHM ~0.18’’

‣ Final ESA selection (launch 2017)

‣ 500 peoples, 10 countries

Euclid in a nutshell

Euclid satellite

Bertinoro 2011

Real-time cosmology

ISAPP 2011

One null cone

0H

1z

0znow

time

comoving dist.0H

z

zHa

1

)(

ISAPP 2011

One null cone

inH

1z

0znow

VOID

time

com. dist.outH

One null cone

z

rzHa

1

),(

ISAPP 2011

Cosmic Degeneracy 3

void model

Garcia-Bellido & Haugbolle 2008

Tomita 2001Celerier 2001Alnes & Amarzguioi 2006,07Bassett et al. 07 Clifton et al. 08Notari et al. 2005-08Marra et al. 08Garcia-Bellido & Haugbolle 2008

ISAPP 2011

Two null cones are better than one!

)(zH1z

0znow

VOID

time

com. dist.ttnow

inHoutH

Mashhoon & Partovi 1985Uzan, Clarkson & Ellis 2007Quartin, Quercellini, L.A. 2009

z

rzHa

1

),(

ISAPP 2011

Sandage 1962

yearcmv sec//1

)( 1zH )( 2zH

ISAPP 2011

Loeb 1998

ISAPP 2011

The Sandage effect

sec/1|1

))(

1(

)(

)(

)(

)(

1

000

000

cmz

zcv

H

zHztHz

ta

ta

tta

ttaz

yr

sss

Corasaniti, Huterer, Melchiorri 2007Balbi & Quercellini 2007

sec/3010

)10(109

90

cmc

yrstH

ISAPP 2011

EELT

ISAPP 2011

2010

CODEX at EELT

today......ten years later

ISAPP 2011

CODEX at EELT

Liske et al. 2008

scmzNNS QSO

/1

530

/

23502

8.12/1

• large colleting area• high resolution spetrographs• stable, low-peculiar motion targets: Lyman-alpha lines

ISAPP 2011

Two null cones are better than one!

1z

0z

now

VOID

time

com. dist.ttnow

inHoutH

Two null cones are better than one!

M. Quartin & L. A. 2009

5yrs

10yrs

15yrs

ISAPP 2011 LTB void model, XXI century

Evolution

Us

Rest of the Universe

Ptolemaic system, I century

Us

Rest of the Universe

ISAPP 2011

Quercellini, Quartin & LA, Phys. Rev. Lett. 2009arXiv 0809.3675

LTB void model

Cosmic Parallax

asrad

tH

20010

109

90

astrometric satellitesGAIA, SIM, Jasmine etc: 1-100 µas

ISAPP 2011

Lemaitre-Tolman-Bondi models

2222

22 ),()(1

)],('[

drtRdr

r

rtRdtds

2)(sinh

2)1(cosh),(

t

trR

Exact solution in matter-dominated universe:

Garcia-Bellido & Haugbolle 2008

ISAPP 2011

Quercellini, Quartin & LA, arXiv 0809.3675

Garcia-Bellido & Haugbolle 2008

ISAPP 2011

Gaia: Complete, Faint, Accurate

Hipparcos Gaia

Magnitude limit 12 20 mag Completeness 7.3 – 9.0 20 mag Bright limit 0 6 mag Number of objects 120 000 26 million to V = 15 250 million to V = 18 1000 million to V = 20 Effective distance limit

1 kpc 50 kpc Quasars None 5 x 105

Galaxies None 106 – 107 Accuracy 1 milliarcsec 7 µarcsec at V = 10 10-25 µarcsec at V = 15 300 µarcsec at V = 20 Photometry photometry

2-colour (B and V) Low-res. spectra to V = 20 Radial velocity None 15 km/s to V = 16-17 Observing programme

Pre-selected Complete and unbiased

ISAPP 2011

Quercellini, Quartin & LA, arXiv 0809.3675

Cosmic Parallax

ISAPP 2011

Quercellini, Quartin & LA, arXiv 0809.3675

Garcia-Bellido & Haugbolle 2008

ISAPP 2011

Quercellini, Quartin & LA, arXiv 0809.3675

Garcia-Bellido & Haugbolle 2008

ISAPP 2011

Bianchi I

Not only LTB

a(t)

b(t)

c(t)

12

ISAPP 2011

Current limits on anisotropy

410

H

HR at z = 1000

810H

Hat z = 0 in a ΛCDM universe

?H

Hat z = 0 in anisotropic dark energy

ISAPP 2011

Anisotropic dark energy

DE

zanyatH

HR ,10 4

Mota & Koivisto 2008, Barrow, Saha, Bruni, Rodrigues and many others..

C. Quercellini, P. Cabella, L.A., M. Quartin, A. Balbi 2009

ISAPP 2011

Future of Dark Energy research

•Move from background to perturbations•Test for gravity/new physics at large scales•New full sky surveys at redshift beyond unity•Find new observables: eg real-time cosmology

ISAPP 2011

Peculiar Acceleration

a

2

)(sin

r

rGMapec

The PA is a direct probe of thegravitational potential: itdoes not assume virialization orhydrostatic equilibrium.

ISAPP 2011

Peculiar Accelerationcrr

rr

rr

r vs

ss

ccNFW /,

1

)( 2

cos/

2

2

14

)1(

1

)/(

)1log(

11010sin

sec44.0)(

cRrss

s

ssv

r

r

r

rrr

r

r

CMpc

r

M

M

yr

Tcmvs

Mass

Andromeda 20 kpc

Virgo 0.55 Mpc

Coma 0.29 Mpc15102.1

15102.1

1110

sr

ISAPP 2011

Peculiar Acceleration

)1(

1

)/(

)1log(

11010sin

sec44.0)(

2

2

14

ss

s

ssv

rr

rrrr

rr

CMpc

r

M

M

yr

Tcmvs

L.A., A. Balbi, C. Quercellini, astro-ph arXiv/0708.1132Phys.Lett.B660:81,2008

differentlines of sight

ISAPP 2011

local versus global

ClusterMass

LCDM

1410

1510

redshift drift

pec. acc.

ISAPP 2011

Peculiar acceleration in the Galaxy

• Can we use the peculiar acceleration to discriminate among competing gravity theories ?

• Steps:– We model the galaxy as a disc+CDM halo and

derive the peculiar acceleration signal– We model the galaxy as a disc in modified

gravity (MOND)– We analyse the different morphology of the

signal in the Milky way

ISAPP 2011

spiral galaxy: Newton

• Disc: Kuzmin potential,

• CDM halo: logarithmic

• The total line of sight

acceleration:

aK MG

R2 | z |h 2

test particle outside the disc, where the presence/absence of a CDM halo is more influent.

L 1

2vo

2 log Rc2 R2

z2

q2

as,K MG

Rg2 2 1 | tan | h

Rg

2

sin

as,L v0

2Rg 1tan2

q2

Rc2 Rg

2 2 1 tan2 q2

sin

v as,K as,L t

C. Quercellini, L.A., A. Balbi 2008

arXiv:0807.3237

ISAPP 2011

spiral galaxy: MOND

• Beckenstein-Milgrom modified Poisson equation

• For configurations with spherical, cylindrical or plane symmetry

• Assuming and solving for

| |

a0

4G

| |

a0

N

(x)x

1 x 2

a M

aM aK

1 1 4a02

| aK |2

1/ 2

2

ISAPP 2011

spiral galaxy: MOND

• peculiar acceleration in MOND:

as,M

MG 1 14a0

2

M 2G2 Rg4 4 1 | tan |

h

Rg

2

2

1/ 2

2Rg2 2 1 | tan |

h

Rg

sin

ISAPP 2011

Most accelerated globular clusters

yrcmv sec//5.1

ISAPP 2011

Newton vs. MOND

ISAPP 2011

Proper Acceleration

a

2

)(cos

r

rGMapec

The PropAcc could be seen by averagingover many stars in open and globularclusters

ISAPP 2011

Cambridge UP

ISAPP 2011

!!! COMING SOON !!!New full Professorship in Heidelberg

in theoretical astroparticle physics

for inquiries, write to l.amendola@thphys.uni-heidelberg.de

t.plehn@thphys.uni-heidelberg.de