Observations are converging…
62
ISAPP 2011 Observations are converging… …to an unexpected universe
description
Observations are converging…. …to an unexpected universe. Classifying the unknown, 1. Cosmological constant Dark energy w=const Dark energy w=w(z) quintessence scalar-tensor models coupled quintessence mass varying neutrinos k-essence Chaplygin gas Cardassian quartessence - PowerPoint PPT Presentation
Transcript of 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
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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
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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)
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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
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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
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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
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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
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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
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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
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One null cone
0H
1z
0znow
time
comoving dist.0H
z
zHa
1
)(
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One null cone
inH
1z
0znow
VOID
time
com. dist.outH
One null cone
z
rzHa
1
),(
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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
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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
),(
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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
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EELT
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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
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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
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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
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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
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Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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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
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Quercellini, Quartin & LA, arXiv 0809.3675
Cosmic Parallax
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Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Quercellini, Quartin & LA, arXiv 0809.3675
Garcia-Bellido & Haugbolle 2008
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Bianchi I
Not only LTB
a(t)
b(t)
c(t)
12
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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
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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
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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
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Peculiar Acceleration
a
2
)(sin
r
rGMapec
The PA is a direct probe of thegravitational potential: itdoes not assume virialization orhydrostatic equilibrium.
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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
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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
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local versus global
ClusterMass
LCDM
1410
1510
redshift drift
pec. acc.
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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
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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
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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
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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
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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
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Cambridge UP
ISAPP 2011
!!! COMING SOON !!!New full Professorship in Heidelberg
in theoretical astroparticle physics
for inquiries, write to [email protected]
