Transcript The nature of Dark Energy

Observations are converging…
…to an unexpected universe
ISAPP 2011
Classifying the unknown, 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
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21.
22.
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
quiessence
phantoms
f(R)
Gauss-Bonnet
anisotropic dark energy
brane dark energy
backreaction
void models
degravitation
TeVeS
oops....did I forget your model?
ISAPP 2011
Classifying the unknown, 3
Standard cosmology:
GR gravitational equations + symmetries
a) change the equations
i.e. add new matter field (DE) or modify gravity (MG)
b) change the symmetries
i.e. inhomogeneous non-linear effects, void models, etc
ISAPP 2011
Simplest MG (I): DGP
(Dvali, Gabadadze, Porrati 2000)
S   d 5 x  g ( 5 ) R ( 5)  L  d 4 x  g R
H2
H 8 G


L
3
brane
L = crossover scale:
1
r  L  V 
r
1
r  L  V  2
r
5D Minkowski
bulk:
infinite volume
extra dimension
gravity
leakage
• 5D gravity dominates at low energy/late times/large scales
• 4D gravity recovered at high
energy/early times/small scales
ISAPP 2011
Simplest MG (II): f(R)
The simplest MG in 4D: f(R)
 dx
4
eg higher order corrections
g  f R + Lmatter 
4
d
x


 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 higherorder terms
 particular case of scalar-tensor and extra-dimensional theory
ISAPP 2011

g R + R 2  R 3  ...
Faces
ofofthe
Faces
thesame
samephysics
physics
Extra-dim.
degrees of freedom
Higher order
gravity
Coupled scalar field
4




d
x
g
f
φ,
R
+
L
matter

Scalar-tensor gravity
ISAPP 2011
Is this already ruled out by local gravity?
4
d
x

g  f ( R) + Lmatter 
is a scalar-tensor theory with Brans-Dicke
parameter ω=0 or
a coupled dark energy model with coupling β=1/2
2  m r
G  G (1   e
*
m
2

)  G (1   2e  r /  )
β
1

f ''
λ
ISAPP 2011
Adelberger et al. 2005
The fourfold way out of local constraints
G*  G (1   2 e
m , 
{
 m r
)
depend on time
depend on space
depend on local density
depend on species
ISAPP 2011
The simplest case
4
d
x



μ4
g
 R  R + Lmatter 



In Einstein Frame
3



  3H  V ( )' 
m



  3H  V ( )' 20
  3H  0 3 
 m m 3H m m 
  m
2
β = 1/ 2
ISAPP 2011
Turner, Carroll, Capozziello
etc. 2003
ĝ   ( f ' ) 2 g 
fR  f '
f '2
  log f '
V ( )' 
…a particular case of
coupled dark energy
R-1/R model : the φMDE
  3H  V ( )' 
 m  3H m  
H2 
3
m
2
3 
 m
2
8
(  m   )
3
rad
mat
field
β = 1/ 2
Ωφ = 1 / 9
1/2
In Jordan frame: a= t
instead of
a = t 2/3
rad
MDE field
ISAPP 2011
!!
mat
Caution:
Plots in the
Einstein frame!
Sound horizon in R+R - n model
 dx


μ4

gR
+ Lmatter 

R


4
at
1/ 2

in the Matter Era !
cs dz
 
/
H ( z)
z dec
z dec

0
dz
H ( z)
ISAPP 2011
L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302,
astro-ph/0603173
A recipe to modify gravity
Can we find f(R) models that work?
ISAPP 2011
c
LGC+Cosmology
Take for instance the ΛCDM clone
f (R )  (R a   )b
Applying the criteria of
LGC and background cosmology
a  b  1  10
23
i.e. ΛCDM to an incredible precision
ISAPP 2011
Space-time geometry
The most general (linear, scalar) metric at first-order
ds 2  a 2 [(1  2)dt 2  (1  2)(dx 2  dy 2  dz 2 )]
background
Full metric reconstruction
at first order requires 3 functions
H ( z ) (k , z )  (k , z )
ISAPP 2011
perturbations
Two free functions
ds  a [(1  2)dt  (1  2)(dx  dy  dz )]
2
2
2
2
2
At linear order we can write:
 Poisson equation
   4 Ga  m m
 zero anisotropic stress
  
2
ISAPP 2011
2
2
Two free functions
ds  a [(1  2)dt  (1  2)(dx  dy  dz )]
2
2
2
2
2
2
At linear order we can write:
 modified Poisson equation
 non-zero anisotropic stress
 '' (1 
   4 Ga Q(k , a)  m m
2
2

 (k , a) 

H'
3
) ' [1  Q(k , z )] m  0
H
2
ISAPP 2011
Modified Gravity at the linear level
 standard gravity
 scalar-tensor models
Q(k , a)  1
 (k , a)  0
G * 2( F  F '2 )
Q(a) 
FGcav, 0 2 F  3F '2
Boisseau et al. 2000
Acquaviva et al. 2004
Schimd et al. 2004
L.A., Kunz &Sapone 2007
F '2
 (a) 
F  F '2
 f(R)
 DGP
 coupled Gauss-Bonnet
Q(a ) 
G*
FGcav,0
k2
a2R ,
k2
1  3m 2
a R
1  4m
k2
a2R
 (a) 
k2
1  2m 2
a R
1
;   1  2 Hrc wDE
3
2
 (a) 
3  1
m
Bean et al. 2006
Hu et al. 2006
Tsujikawa 2007
Q(a )  1 
Q (a )  ...
 (a )  ...
Lue et al. 2004;
Koyama et al. 2006
see L. A., C. Charmousis,
S. Davis 2006
ISAPP 2011
Reconstruction of the metric
ds 2  a 2 [(1  2)dt 2  (1  2)(dx 2  dy 2  dz 2 )]
massive particles respond to Ψ
v  Hv 
massless particles respond to Φ-Ψ
    perp (  )dz
ISAPP 2011
Reality check

 ( x)  0
0
ds 2  a 2 [(1  2)dt 2  (1  2)(dx 2  dy 2 2dz 2 )]
Density fluctuation in space
 k  P( k , z )
θ
Matter power spectrum
Galaxy power spectrum
Galaxy power spectrum
in redshift space
Pmatter (k , z )
2
b (k , z ) Pmatter (k , z )
(1   (k , z ) cos 2  ) 2 b 2 (k , z ) Pmatter (k , z )
ISAPP 2011
Peculiar velocities
r = v/H0
.
ISAPP 2011
Peculiar velocities
Pz  (1   2 ) 2 Pr
redshift distortion parameter
'

b
Kaiser 1987
ISAPP 2011
Weak lensing
Dark matter halos
Background
sources
Observer
Radial distances depend on
geometry of Universe
Foreground mass distribution depends on
growth/distribution of structure
ISAPP 2011
The Euclid theorem
4 unknown functions:
b(k , z ),  (k , z ),  (k , z ), (k , z )
Observables:
Conservation equations:
b  P(ktransv )

P(kradial )
'

1
b
P(ktransv )
 '' (1 
H'
3
) ' [1  Q(k , z )] m  0
H
2
z
Pellipt (k , z )   dz ' K ( z ')(k   k )2
0
We can measure 3 combinations and we have 1 theoretical relation…
Theorem: lensing+galaxy clustering allows to measure all
(total matter) perturbation variables at first order
without assuming any specific gravity theory
ISAPP 2011
The Euclid theorem
b(k , z ),  (k , z ),  (k , z ), (k , z )
From these we can derive the deviations from Einstein’s gravity:
4 Ga 2 
Q( k , a )  
2
k 

 (k , a) 

ISAPP 2011
Euclid in a nutshell
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
satellite
Real-time cosmology
Bertinoro 2011
One null cone
time
H0
a 
H0
comoving dist.
now
z0
H ( z)
1 z
z1
ISAPP 2011
One null cone
One null cone
time
H out
a 
H in
com. dist.
now
z0
H ( z, r )
1 z
z1
VOID
ISAPP 2011
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
ISAPP 2011
Two null cones are better than one!
time
H out
a 
H in
tnow  t
com. dist.
now
z0
H ( z, r )
1 z
H (z )
z1
VOID
ISAPP 2011
Mashhoon & Partovi 1985
Uzan, Clarkson & Ellis 2007
Quartin, Quercellini, L.A. 2009
Sandage 1962
H ( z1 )
H ( z2 )
v  1cm / sec/ year
ISAPP 2011
Loeb 1998
ISAPP 2011
The Sandage effect
H 0 t  10 9
(10 yrs )
10 9 c  30cm / sec
a (t0  t0 ) a (t0 )
z 

a (t s  t s ) a (t s )
H ( z)
z  H 0 t0 (1  z 
)
H0
v 
cz
|1 yr  1 cm / sec
1 z
Corasaniti, Huterer, Melchiorri 2007
Balbi & Quercellini 2007
ISAPP 2011
EELT
ISAPP 2011
CODEX at EELT
2010
today...
...ten years later
ISAPP 2011
CODEX at EELT
1/ 2
1.8


2350
30
5



 
  2

 cm / s

 S / N  N QSO   1  z 
Liske et al. 2008
ISAPP 2011
• large colleting area
• high resolution spetrographs
• stable, low-peculiar motion
targets: Lyman-alpha lines
Two null cones are better than one!
time
H out
H in
tnow  t
com. dist.
now
5yrs
z0
10yrs
z1
VOID
15yrs
ISAPP 2011
M. Quartin & L. A. 2009
Evolution
Rest of the Universe
Rest of the Universe
Us
Us
Ptolemaic system, I century
ISAPP 2011
LTB void model, XXI century
Cosmic Parallax
H 0 t  109
109 rad  200as
astrometric satellites
GAIA, SIM, Jasmine etc:
1-100 µas
LTB void model
ISAPP 2011
Quercellini, Quartin & LA,
Phys. Rev. Lett. 2009
arXiv 0809.3675
Lemaitre-Tolman-Bondi models
2
[
R
'
(
t
,
r
)]
ds 2  dt 2 
dr 2  R 2 (t , r )d2
1   (r )
Exact solution in matter-dominated universe:

R (r , t )  (cosh   1)
2

 t  (sinh    )
2
Garcia-Bellido & Haugbolle 2008
ISAPP 2011
Garcia-Bellido & Haugbolle 2008
Quercellini, Quartin & LA,
arXiv 0809.3675
ISAPP 2011
Gaia: Complete, Faint, Accurate
Hipparcos
Gaia
Magnitude limit
Completeness
Bright limit
Number of objects
12
7.3 – 9.0
0
120 000
Effective distance
limit
Quasars
Galaxies
Accuracy
1 kpc
None
None
1 milliarcsec
Photometry
photometry
velocity
Radial
Observing
programme
2-colour (B and V)
None
Pre-selected
20 mag
20 mag
6 mag
26 million to V = 15
250 million to V = 18
1000 million to V = 20
50 kpc
5 x 105
106 – 107
7 µarcsec at V = 10
10-25 µarcsec at V = 15
300 µarcsec at V = 20
Low-res. spectra to V = 20
15 km/s to V = 16-17
Complete and unbiased
ISAPP 2011
Cosmic Parallax
Quercellini, Quartin & LA,
arXiv 0809.3675
ISAPP 2011
Garcia-Bellido & Haugbolle 2008
Quercellini, Quartin & LA,
arXiv 0809.3675
ISAPP 2011
Garcia-Bellido & Haugbolle 2008
Quercellini, Quartin & LA,
arXiv 0809.3675
ISAPP 2011
Not only LTB
a(t)
Bianchi I
1
2
b(t)
c(t)
ISAPP 2011
Current limits on anisotropy
H
R
 10  4
H
H
 10 8
H
H
?
H
at z = 1000
at z = 0 in a ΛCDM universe
at z = 0 in anisotropic dark energy
ISAPP 2011
Anisotropic dark energy
Mota & Koivisto 2008,
Barrow, Saha, Bruni, Rodrigues and many others..
 DE
C. Quercellini, P. Cabella, L.A.,
M. Quartin, A. Balbi 2009
R
ISAPP 2011
H
 10  4
H
, at any z
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
a pec  sin 
GM (r )
r2
The PA is a direct probe of the
gravitational potential: it
does not assume virialization or
hydrostatic equilibrium.
ISAPP 2011
Peculiar Acceleration
 c c
 NFW (r ) 
r
rs

r
1  
 rs 
2
, rs  rv / c
M v  rs 
cm 
T



s (  )  v   0.44
 sin 
14
sec 
10 yr 10 M   1Mpc 

Mass
Andromeda
1011
2
r


 log( 1  )

r
1
s

C

2
 (r / rs )
r
r 
(
1

)

rs
rs  r  R  / cos 

c
rs
20 kpc
Virgo
1.2  1015
0.55 Mpc
Coma
15
1.ISAPP
2  102011
0.29 Mpc
Peculiar Acceleration
M v  rs 
cm 
T



s (  )  v   0.44
 sin 
14
sec
10
yr
10
M
1
Mpc



 
2
r


 log( 1  )

r
1
s

C

2
 (r / rs )
r
r 
(
1

)

r
r
s
s 

different
lines of sight
ISAPP 2011
L.A., A. Balbi, C. Quercellini,
astro-ph arXiv/0708.1132
Phys.Lett.B660:81,2008
local versus global
pec. acc.
1015
1014
Cluster
Mass
LCDM
redshift drift
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
test particle outside the disc, where the
presence/absence of a CDM halo is more
influent.
• Disc: Kuzmin potential,
aK  
R
MG
2
 | z | h 
2

• CDM halo: logarithmic

1 2  2
z 2 
 L  v o log Rc  R 2  2 
2
q 

• The total line of sight acceleration:
C. Quercellini, L.A., A. Balbi 2008

arXiv:0807.3237
as,K 
MG
sin 
2 
 

h 
Rg2 2 1 
| tan  | 


 
Rg 
 



tan 
q2
as,L 
sin 
 tan 2  
2
2 2
ISAPP
2011
Rc  Rg 1

q 2 

v 02 Rg 1
2
v  as,K  as,L t
spiral galaxy: MOND
• Beckenstein-Milgrom modified Poisson equation
 |  | 

 4G
a



0 
• For configurations with spherical, cylindrical or plane symmetry
 |  | 

 N
a



0 

• Assuming

(x) 
x
1 x 2

and solving for
aM  
1/ 2

4a02 

1 1 | a |2 

K
 

aM  aK
2
ISAPP 2011
spiral galaxy: MOND
• peculiar acceleration in MOND:
as,M
1/ 2
2 

2



4a02 4 4  
h   
MG1 1 2 2 Rg  1 
| tan  |  R  
  

M
G

g
  





 sin 
 


h
2Rg2 2 1 
| tan  |  R  



g 
 


ISAPP 2011

Most accelerated globular clusters
v  1.5 cm / sec/ yr
ISAPP 2011
Newton vs. MOND
ISAPP 2011
Proper Acceleration

a
a pec  cos 
GM (r )
r2
The PropAcc could be seen by averaging
over many stars in open and globular
clusters
ISAPP 2011
Cambridge UP
ISAPP 2011
!!! COMING SOON !!!
New full Professorship in Heidelberg
in theoretical astroparticle physics
for inquiries, write to
[email protected]
[email protected]
ISAPP 2011