Download - Observations are converging…
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
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The fourfold way out of local
constraints
* 2(1 )m rG G e
,m { depend on timedepend on spacedepend on local densitydepend on species
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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
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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:
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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 !
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A recipe to modify gravity
Can we find f(R) models that work?
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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
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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
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Two free functions
At linear order we can write:
2 24 m mGa Poisson equation
zero anisotropic stress
)])(21()21[( 222222 dzdydxdtads
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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
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Peculiar velocities
.
r = v/H0
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Peculiar velocities
'
b
redshift distortion parameter
2 2(1 )z rP P
Kaiser 1987
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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
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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
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Loeb 1998
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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
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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
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Newton vs. MOND
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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 [email protected]