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Dark Energy, Modified Gravity
and
The Accelerating Universe
Dragan Huterer
Kavli Institute for Cosmological PhysicsUniversity of Chicago
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Makeup of universe today
Dark Matter(suspected since 1930sestablished since 1970s)
Dark Energy(suspected since 1980s
established since 1998)
Also:
radiation (0.01%)
Baryonic Matter(stars 0.4%, gas 3.6%)
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Some of the earlyhistory of the Universe
is actually understood better!
Physics quite wellunderstood
95% of contents onlyphenomenologically
described
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DE status ~8 years after discovery
Supernova Cosmology Project
=0.3, =0.7
=0.3, =0.0
=1.0, =0.0
m - M ( m
a g )
High-Z SN Search Team
0.01 0.10 1.00z
( m
- M ) ( m a g )
Matter dominated
Vacuum energy dominated
Measurements muchbetter, LCDM still a good fit
Physical mechanism responsible
completely unknown
Strong indirect (non-SNa Ia)
evidence for DE from CMB+LSS
A lot of work on
modified gravity proposals
and observational signatures
Riess et al 1998; Perlmutter et al 1999
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Current constraints
ΩDE ≈ 0.
7
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What if gravitydeviates from GR?
H 2−F (H ) = 8πG
3ρ, or H 2 = 8πG
3
ρ + 3F (H )
8πG
For example:
Modified gravity Dark energy
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Modified gravity proposals
• Introduce modifications to GR (typicallynear horizon scale) to explain the observed
acceleration of the universe• Make sure Solar System tests are passed
(can be hard)
• Constrain the MG theory using thecosmological data
• Try to distinguish MG vs. “standard” DE
(can be hard!)
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Example: f(R) gravity
•Einstein equations are now 4th order
• Two classes
• f RR<0 (never Matter Dominated, long rangeforces)
• f RR>0 (MD in the past, can evade Solar systemtests)
Carroll, Duvvuri, Trodden, Turner 2005; Mena, Santiago & Weller 2006;
Navarro & van Acoleyen 2006; Song, Hu & Sawicki 2006; many others....
S = 116πG
d4x√−g [R+ f (R)]
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• 1 extra dimension(“bulk”) in which onlygravity propagates
• matter lives on the“brane”
• weakening of gravityat large distances =appearance of DE
Example: DGP braneworld theory
Credit: Iggy SawickiDvali, Gabadadze & Porrati 2000; Deffayet 2001
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The structure of DGP
2GM=r g
r * r c
5D GR
5D GR
Scalar-Tensor
4D GR
New scale r∗ =
rgr
2
c
1/3
Credit: Iggy Sawicki
rc is a free parameter(to be consistent with
observation, rc ~ 1/H0)
Dvali, Gabadadze & Porrati 2000; Deffayet 2001
H 2−
H
rc=8πG
3ρ
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DGP linear growth
Lue, Scoccimarro & Starkman; Koyama & Maartens; Sawicki, Song & Hu
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
y
0 0.2 0.4 0.6 0.8 1
x
DGP
LCDM
DGP−4D
dark energy
a
g(a)
Scale factor
G r o w t h r e l a t i v e
t o E d S
DE MimickingDGP expansion DGP
LCDM
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ISW in DGP
Song, Sawicki, & Hu 2007
DGP
LCDM
P h i
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So DGP is (almost) ruled out
• Disfavored at a few sigma from distances (SNe etc)
• Disfavored at a few more sigma from CMB ISW
• Decisive rule-out will come from ISW cross-correlationat high z:
50 100 50 100 50 100 50 100
Song, Sawicki, & Hu 2007
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Dark Energy or Modified Gravity?
• A given DE and modified gravity models may both fit the expansion
history data very well
• But they will predict different structure formation history, i.e.
deviation from δ + 2H δ − 4πρM δ = 0
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• In standard GR, H(z) determines distances and growth of
structure
• So check if this is true by measuring separately
δ + 2H δ − 4πρM δ = 0
Distances(a.k.a. kinematic probes)
(a.k.a. 0th order cosmology)
Growth(a.k.a. dynamical probes)
(a.k.a. 1st order cosmology)
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Price of ignorance of MG
-1.2 -1.15 -1.1 -1.05 -1 -0.95 -0.9 -0.85 -0.8
w0
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
w a
allows for
gravity having !"=0.1neglects modified
modified gravity
Huterer & Linder, astro-ph/0608681
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Cosmological Probes of Dark Energy(and Modified Gravity)
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Kinematic probes: SNe Ia
Supernova Cosmology Project
=0.3, =0.7
=0.3, =0.0
=1.0, =0.0
m - M ( m
a g )
High-Z SN Search Team
0.01 0.10 1.00z
( m - M
) ( m a g )
• Get pure (luminosity) distances
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S o u
nd
h or i z on
D i st anc e t o r e c o mb i nat i o n
T = 2.726 K
δT
T ≈ 10
−5
Bennett et al 2003 (WMAP collaboration)
Credit: WMAP team
Θ 2 - p t c o
r r e l a t i o n
Kinematic probes: CMB and BAO
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Structure formation probes:Galaxy cluster counts
• Essentially fully in the nonlinear regime (scales ~1 Mpc)
d2N
dΩ dz= n(z)
r(z)2
H (z)
Credit: Quinn, Barnes, Babul, Gibson0 0.5 1 1.5 2
z
102
103
104
105
d N
/ d z
( 4 0 0 0 d e g
2 )
!M
=1, !DE
=0
!
M
=0.3, !DE
=0.7, w=-1
w=-0.8
S f i b
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Structure formation probes:Weak Gravitational Lensing
• Mostly in the nonlinear regime (scales ~10 arcmin, or ~1 Mpc)
Credit: Colombi & Mellier1 10 100 1000 10000
Multipole l
10-10
10-8
10-6
10-4
10-2
l ( l + 1 ) P
l ! / ( 2 " )
True, nonlinear
Linear theory
P shear ∞0
W (r)P matter(r)dr
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More general approach
–1.1
–1
–0.9
–0.8
–0.7
–0.6
w_00
0.2
0.4
0.6
0.8
w_1
0.708
0.71
0.712
0.714
0.716
0.718
0.72
0.722
0.724
0.726
O m e g a_
d e
Ishak, Upadhye and Spergel 2006; others...
Measure the DE parameters from distances and growth separately
w0wa
O
m e g a D E
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Still more general approach:measure functions r(z) and g(z)
see if they are consistent
Knox, Song & Tyson 2005
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Minimalist Modified Gravity vs. DE
g(a) ≡δ
a= exp
a0
d ln a[ΩM (a)γ − 1]
Excellent fit to standard DE growth function with
γ = 0.55 + 0.05[1 + w(z = 1)]
Huterer & Linder, astro-ph/0608681see also Linder & Cahn, astro-ph/0701317
∆γ = 0.13 Also fits the DGP braneworld theory with
Describe deviations from GR via a single new parameter
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0 0.5 1 1.5 2
z
0
1000
2000
3000
4000
( d N / d z ) ! z
"=0.55
!"=0.1
!w=0.05
!m#
=0.3 eV
100 1000 10000l
10
-6
10-5
10-4
l ( l + 1 ) P ! i
i / ( 2 " )
# = 0.55# = 0.65
i,i=11
44
22
33
Cluster counts
Weak lensingtomography
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Constraints on the growth index
sig(w0) sig(wa) sig(gamma)
WL 0.33 1.16 0.23
+SNE 0.06 0.28 0.10
+Planck 0.06 0.21 0.044
+Clusters 0.05 0.16 0.037
Huterer & Linder, astro-ph/0608681
Recall, for DGP ∆γ = 0.13
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Discarding the small-scale infoin weak lensing
Using the Nulling Tomography of weak lensing (Huterer & White 2005)
0.1 1 10 100
kcut
(h / Mpc)
0.3
1
3
10
30
( e r r o r o r b i a s
i n ! ) / "
! ,
f i d
Degradation factor in ! error
Pl kS th P l T l
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PlanckSouth Pole Telescope
LSSTSupernova/Acceleration Probe
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Conclusions• distinguishing dark energy from modified gravity is
becoming one of the key goals of cosmology in years tocome
• assuming nonlinear clustering that follows the usualprescription even with MG, we find that future probes canachieve very interesting constraints on this parameter
• restriction to linear scales severely degrades the errors,but well worth pursuing
• ambitious, general approach: measure functions r(z) and
g(z), check if they are consistent
• minimalistic approach: measure a single parameter thatdescribes departures between DE and MG
•bright future with upcoming powerful surveys
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Physically motivated MG parametrization
1 10 100 1000
l: multipole moment
20
40
60
80
[ l ( l + 1
) C l / 2 ! ] 1 / 2
( µ K )
LCDM
!0.1
!0.3
+0.1
Caldwell, Cooray & Melchiorri, astro-ph/0703375
ds2 = a
2(τ )−(1 + 2ψ)dτ 2 + (1 − 2φ)d x2
ψ = (1 + )φ = 0
ρDE
ρM and assume
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