Fundamental Cosmology with EUCLID , The School of Athens, Rome Euclid Raphael, Luca Amendola University of Heidelberg andESTEC INAF/Roma 2009 The reconstruction of space-time geometry with Euclid

Dark matter and inflation with Euclid

Synergy of Euclid with Plank, LHC, Gaia, EELT

ESTEC 2009 Cosmic degeneracy

The background expansion background only probes H (z)

The matter clustering growth perturbations probes   (k, z)  H ' 3 ''(1 )     0 H 2 m

ESTEC 2009 What background hides perturbations reveal

The most general (linear, scalar) metric at first-order background ds2  a2[(1 2)dt 2  (1 2)(dx2  dy 2  dz 2 )]

Full metric reconstruction at first order requires 3 functions perturbations H (z) (k, z) (k, z)

ESTEC 2009 Two free functions ds2  a2[(1 2)dt 2  (1 2)(dx2  dy 2  dz 2 )]

At the linear perturbation level and sub-horizon scales

2 2  . modified Poisson’s equation k   4 Ga Q(k,a) m m    . non-zero anisotropic stress (k,a)  

ESTEC 2009 Modified Gravity at the linear level

Q(k,a) 1 . standard gravity (k,a)  0

G* 2(F  F'2 ) Boisseau et al. 2000 Q(a)  2 Acquaviva et al. 2004 . scalar-tensor models FGcav,0 2F  3F' Schimd et al. 2004 F'2 (a)  L.A., Kunz &Sapone 2007 F  F'2 k 2 k 2 * 1 4m 2 m 2 Bean et al. 2006 . f(R) G a R a R Q(a)  , (a)  Hu et al. 2006 FG k 2 k 2 cav,0 1 3m 1 2m Tsujikawa 2007 a2 R a2 R 1 Q(a) 1 ; 1 2Hrc wDE . DGP 3   Lue et al. 2004; 2 (a)  Koyama et al. 2006 3 1

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

ESTEC 2009 Reconstruction of the metric

ds2  a2[(1 2)dt 2  (1 2)(dx2  dy 2  dz 2 )]

massive particles respond to Ψ  H ' k 2 ''(1 )   H a2

massless particles respond to Φ-Ψ

   (  )dz  perp

ESTEC 2009 Reconstruction of the metric

Correlation of galaxy positions: galaxy clustering 2 2 2 2  Pgal (k, z, )  (1 ) b (k, z)   '   b 

Correlation of galaxy ellipticities: galaxy weak lensing

2 Pellipt (k, z)  (  )

ESTEC 2009 The Euclid theorem

Observables: Conservation equations:

b  P(k, z,transv)  ' 3'  ' Ha  P(k, z,rad) / P(k, z,transv) 1 b  k 2 '    z Ha P (k, z)  dz' K(z')(  )2 ellipt  0 5 unknown variables: b(k, z), (k, z), (k, z),(k, z),(k, z)

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

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

ESTEC 2009 The Euclid theorem

Observables: Conservation equations:

b  P(k, z,transv)  ' 3'  ' Ha  P(k, z,rad) / P(k, z,transv) 1 b  k 2 '    z Ha P (k, z)  dz' K(z')(  )2 ellipt  0 5 unknown variables: b(k, z), (k, z), (k, z),(k, z),(k, z)

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

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

ESTEC 2009 An example: DGP (Dvali, Gabadadze, Porrati 2000) S   d 5 x g (5) R (5)  L d 4 x  g R H 8G H 2    L 3

brane 5D Minkowski bulk: L = crossover scale: infinite volume 1 extra dimension r  L  V  r gravity 1 r  L  V  leakage r 2 • 5D gravity dominates at low energy/late times/large scales • 4D gravity recovered at high energy/early times/small scales ESTEC 2009  Modified Gravity predictions  H' 3 d log k ''(1 ) k ' Q(k,a)mk  0  H 2  m (a) d log a 1 m Q 1 3(1 w) 3    0.55 s 6w  5  1Q DGP   s (1 )  0.65 0.70 (1 w)(1 m )

 k 2a2 f(R)   (1 )  0.40 0.55 s M ( f )2  k 2a2

     (1 w)a3w clustered DE   1  s 2 2 2   k c sa  (1 w)13w    2    H 0m  ESTEC 2009 Euclid vs. gamma

current

DGP Euclid

LCDM

tomographic weak lensing galaxy power spectrum (redshift distortions)

ESTEC 2009 ancient questions for Euclid

whatwhat is the is the nature sky of darkmade matter of?

which are the inflationarywhere do we initialcome conditionsfrom?

ESTEC 2009 Euclid vs. dark matter

dark matter halos from weak lensing maps of clusters dark matter abundance from power spectrum shape dark matter clustering from cluster abundance neutrino mass from power spectrum shape

ESTEC 2009 Euclid cosmological bounty

error m  0.03 eV Neutrino mass error N  0.3

error n  0.005 Inflationary spectrum s error   0.05

Primordial non gaussianity error f NL  5

ESTEC 2009 Euro-Synergy

Planck 2009 LHC 2009 Gaia 2011 EELT 2020

ESTEC 2009 LHC (beyond the Higgs)

Standard model is complete but.....

no unification of forces and particles no consistent inclusion of gravity

Answer: supersymmetry Answer: string theory

Consequence for cosmology: Consequence for cosmology: the lightest the gravity leakage supersymmetric particle is a into the extra-dimensions required by perfect cold dark matter candidate strings could explain acceleration

ESTEC 2009 EELT

ESTEC 2009 EELT

2010today...... ten years later

a(t  t ) a(t ) z  0 0  0 a(ts  ts ) a(ts ) Sandage effect H (z) z  H 0t0 (1 z  ) H 0 cz v  | 1cm / sec 1 z 1yr ESTEC 2009 CODEX at EELT

• large colleting area • high resolution spetrographs • stable, low-peculiar motion 1/ 2 1.8 targets: Lyman-alpha lines  2350  30   5    2   cm / s       S / N  NQSO  1 z  Liske et al. 2008 ESTEC 2009 Euclid range

Balbi & Quercellini 2007 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 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 2-colour (B and V) Low-res. spectra to V = 20 Radial velocity None 15 km/s to V = 16-17 Observing Pre-selected Complete and unbiased

ESTEC 2009 The cosmic reference frame

a(t)

 Bianchi I 2  1

b(t)

c(t)

ESTEC 2009 Anisotropic dark energy

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

DE

H C. Quercellini, P. Cabella, L.A., R  104 , at any z M. Quartin, A. Balbi 2009 H ESTEC 2009 A European Dream Team

Euclid • The combination of weak lensing and clustering allows the full recostruction of the space-time geometry • In addition, Euclid will provide unique new constraints on dark matter and initial conditions LHC • Togther with Planck, LHC, Gaia, EELT, Euclid will draw a new 3D atlas of the universe

EELT

ESTEC 2009 Gaia Cosmic Degeneracy 3

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

Garcia-Bellido & Haugbolle 2008 void model

ESTEC 2009 One null cone

time H H 0 0 comoving dist. now

z0

H (z) a  1 z

z1

ESTEC 2009 One null cone One null cone time

H H out in com. dist. now

z0

H (z,r) a  1 z

z1 VOID

ESTEC 2009 Two null cones are better than one! time

t  t H now H out in com. dist. now

z0

H (z,r) a  1 z

z1 H (z) VOID

Mashhoon & Partovi 1985 ESTEC 2009 Uzan, Clarkson & Ellis 2007 Quartin, Quercellini, L.A. 2009 Cosmology and modified gravity in laboratory very limited time/space/energy scales; } only baryons in the solar system

complicated by non-linear/non- at astrophysical scales gravitational effects

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

ESTEC 2009 H (z1) H (z2 )

v  1cm / sec/ year

a(t  t ) a(t ) z  0 0  0 a(ts  ts ) a(ts ) H (z) z  H 0t0 (1 z  ) H 0 cz v  | 1cm / sec 1 z 1yr

9 H 0t 10 (10yrs) 109 c  30cm / sec

a(t  t ) a(t ) z  0 0  0 a(ts  ts ) a(ts ) H (z) z  H 0t0 (1 z  ) H 0 cz v  | 1cm / sec 1 z 1yr

Corasaniti, Huterer, Melchiorri 2007 Balbi & Quercellini 2007

CODEX at EELT

2010today...... ten years later

ESTEC 2009 CODEX at EELT

• large colleting area • high resolution spetrographs • stable, low-peculiar motion 1/ 2 1.8 targets: Lyman-alpha lines  2350  30   5    2   cm / s       S / N  NQSO  1 z  Liske et al. 2008 ESTEC 2009 Two null cones are better than one! time

t  t H now H out in com. dist. now

z0

z1 VOID

ESTEC 2009 M. Quartin & L. A. 2009 Evolution

Rest of the Universe Rest of the Universe

Us Us

Ptolemaic system, I century ESTEC 2009 LTB void model, XXI century Cosmic Parallax

9 H 0t 10 109 rad  200as astrometric satellites GAIA, SIM, Jasmine etc: 1-100 µas

LTB void model Quercellini, Quartin & LA, Phys. Rev. Lett. 2009 arXiv 0809.3675 ESTEC 2009 ESTEC 2009 LTB models

Garcia-Bellido & Haugbolle 2008

LTB void model

ESTEC 2009 ESTEC 2009 Garcia-Bellido & Haugbolle 2008

Quercellini, Quartin & LA, arXiv 0809.3675

ESTEC 2009 Cosmic Parallax

Quercellini, Quartin & LA, arXiv 0809.3675

ESTEC 2009 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 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 2-colour (B and V) Low-res. spectra to V = 20 Radial velocity None 15 km/s to V = 16-17 Observing Pre-selected Complete and unbiased

ESTEC 2009 Garcia-Bellido & Haugbolle 2008

Quercellini, Quartin & LA, arXiv 0809.3675

ESTEC 2009 Garcia-Bellido & Haugbolle 2008

Quercellini, Quartin & LA, arXiv 0809.3675

ESTEC 2009 Not only LTB

a(t)

 Bianchi I 2  1

b(t)

c(t)

ESTEC 2009 Current limits on anisotropy

H 4 R  10 at z = 1000 H

H 8 10 at z = 0 in a ΛCDM universe H

H  ? at z = 0 in anisotropic dark energy H

ESTEC 2009 Anisotropic dark energy

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

DE

H C. Quercellini, P. Cabella, L.A., R  104 , at any z M. Quartin, A. Balbi 2009 H ESTEC 2009 NG DARK ENERGY BU ER W theory and observations

L. A. and S. Tsujikawa Cambridge University Press mid 2010

ESTEC 2009 Breaking the degeneracies

• The task of understanding the nature of Dark energy is plagued by several cosmic degeneracies Euclid • We need to combine weak lensing and clustering to reconstruct the metric at first order • We need to use real-time observables to distinguish between real and apparent acceleration • Together with the Cosmic Parallax we can reconstruct the EELT full 3D picture of cosmic kinematics !

Gaia ESTEC 2009 radial transverse global Sandage Cosmic effect parallax local Peculiar Proper acceleration acceleration Real-time Cosmology

radial transverse global Expansion anisotropy rate local Gravity at galactic scales: eg Newton vs Modif. Grav.

ESTEC 2009 ToDo

figura redshiftdrift void figura cover book

ESTEC 2009 Peculiar Acceleration a

GM (r) a  sin  pec r 2

The PA is a direct probe of the gravitational potential: it does not assume virialization or hydrostatic equilibrium.

ESTEC 2009 Peculiar Acceleration

c c  NFW (r)  2 , rs  rv / c r  r  1  rs  rs    r  2  log(1 )   cm  t M  r  r 1 s( )  v  2 sin  v  s  C s   sec 10yr 1014 M  0.5Mpc   (r / r )2 r r       s (1 )    rs rs  rRc / cos

Mass rs

Andromeda 1011 20 kpc Virgo 1.21015 0.55 Mpc Coma 1.21015 0.29 Mpc

ESTEC 2009 Peculiar Acceleration   r  2  log(1 )   cm  T M  r  r 1 s( )  v  2 sin  v  s  C s   14    2 r r   sec  10yr 10 M   0.5Mpc  (r / rs )  (1 )   rs rs 

different lines of sight

L.A., A. Balbi, C. Quercellini, astro-ph arXiv/0708.1132 Phys.Lett.B660:81,2008 ESTEC 2009 PA versus Sandage effect

1015

14 Cluster 10 Mass LCDM

ESTEC 2009 Peculiar acceleration in the Galaxy

• Can we use the peculiar acceleration to discriminate among competing gravity theories? • Steps: – model the galaxy as a disc+CDM halo and derive the peculiar acceleration signal – model the galaxy as a disc in modified gravity (MOND) – analyse the different morphology of the signal in the Milky way

ESTEC 2009 Spiral galaxy: Newton

test particle outside the disc, where the presence/absence of a CDM halo is more influent. • Disc: Kuzmin potential, MG MG   a  K 1/2 K 2 2 R2  | z | h 2 R  | z | h • CDM halo: logarithmic

 2  1 2 2 2 z L  vo logRc  R   2  q2  • The total line of sight acceleration: tan2  MG 2 v0 Rg 1 2 as,K  2 sin   q    a  sin C. Quercellini, L.A., A. Balbi 2008 2 2 h  s,L  tan2   Rg 1 | tan |   2 2 2  R   Rc  Rg 1 2  arXiv:0807.3237   g   q  

v  as,K  as,L t ESTEC 2009 Spiral galaxy: MOND

• Beckenstein-Milgrom modified Poisson equation  |  |    4G   a0   • peculiar acceleration in MOND:

1/2  2   2  2    4a0 4 4 h  MG1 1 2 2 Rg 1 | tan |    M G   R      g     as,M   sin     h  2 2  2Rg 1 | tan |     Rg  

ESTEC 2009 Most accelerated globular clusters

v 1.5cm / sec/ yr

ESTEC 2009 Newton vs. MOND

ESTEC 2009 Memo for the future

• The Sandage-Loeb effect is a direct measure of the expansion/acceleration of the Universe • The Cosmic Parallax is a direct test of anisotropy • The Peculiar/Proper Acceleration is a direct measure of the gravitational potential • Full 3D picture of cosmic and local kinematics ! • A sensitivity of 1 cm/sec could be achieved with the next generation of ELTs • A sensitivity of 1-10 mu arcsec will be achieved by planned astrometric missions like GAIA, SIM, Jasmine • New observables for DE, cosmology and gravity theories !

ESTEC 2009