Dark Energy, Modified Gravity

and

The Accelerating Universe

Dragan Huterer

Kavli Institute for Cosmological PhysicsUniversity of Chicago

4%

22%

74%

Makeup of universe today

Dark Matter(suspected since 1930sestablished since 1970s)

Dark Energy(suspected since 1980sestablished since 1998)

Also: radiation (0.01%)

Baryonic Matter(stars 0.4%, gas 3.6%)

Some of the earlyhistory of the Universe

is actually understood better!

Physics quite well understood

95% of contents only phenomenologically

described

DE status ~8 years after discovery

Supernova Cosmology Project

=0.3, =0.7

=0.3, =0.0

=1.0, =0.0

m-M

(m

ag

)

High-Z SN Search Team

0.01 0.10 1.00z

(m-M

) (m

ag

)

Matter dominated

Vacuum energy dominated

Measurements much

better, 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

Current constraints

ΩDE ! 0.7

What if gravity deviates from GR?

H2! F (H) =

8πG

3ρ, or H2 =

8πG

3

!

ρ +3F (H)

8πG

"

For example:

Modified gravity Dark energy

Modified gravity proposals

• Introduce modifications to GR (typically near 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 the cosmological data

• Try to distinguish MG vs. “standard” DE (can be hard!)

Example: f(R) gravity

• Einstein equations are now 4th order

• Two classes

• fRR<0 (never Matter Dominated, long range forces)

• fRR>0 (MD in the past, can evade Solar system tests)

Carroll, Duvvuri, Trodden, Turner 2005; Mena, Santiago & Weller 2006;Navarro & van Acoleyen 2006; Song, Hu & Sawicki 2006; many others....

S =1

16πG

!d4x

√

−g [R + f(R)]

• 1 extra dimension (“bulk”) in which only gravity propagates

• matter lives on the “brane”

• weakening of gravity at large distances = appearance of DE

Example: DGP braneworld theory

Credit: Iggy Sawicki

Dvali, Gabadadze & Porrati 2000; Deffayet 2001

The structure of DGP

2GM=rg

r* rc

5D GR

5D GR

Scalar-Tensor

4D GR

New scale r∗ =

!

rgr2

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

H2!

H

rc

=8!G

3"

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

Gro

wth

rel

ativ

e to

EdS

DE Mimicking DGP expansion

DGP

LCDM

ISW in DGP

Song, Sawicki, & Hu 2007

DGP

LCDM

Phi

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-correlation at high z:

50 100 50 100 50 100 50 100

Song, Sawicki, & Hu 2007

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 ! 4πρMδ = 0

• In standard GR, H(z) determines distances and growth of

structure

• So check if this is true by measuring separately

δ + 2H δ ! 4πρMδ = 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)

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

0.8w

a

allows for

gravity having !"=0.1neglects modified

modified gravity

Huterer & Linder, astro-ph/0608681

Cosmological Probes of Dark Energy (and Modified Gravity)

Kinematic probes: SNe Ia

Supernova Cosmology Project

=0.3, =0.7

=0.3, =0.0

=1.0, =0.0

m-M

(m

ag

)

High-Z SN Search Team

0.01 0.10 1.00z

(m-M

) (m

ag

)

• Get pure (luminosity) distances

Sound h

orizo

nDistance to recombination

T = 2.726 K

δT

T≈ 10

!5

Bennett et al 2003 (WMAP collaboration)

Credit: WMAP team

!

2-p

t co

rrel

atio

n

Kinematic probes: CMB and BAO

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

dN

/dz

(4000 d

eg2)

!M

=1, !DE

=0

!M

=0.3, !DE

=0.7, w=-1

w=-0.8

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

Pshear !

∫!

0

W (r)Pmatter(r)dr

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

Omega_de

Ishak, Upadhye and Spergel 2006; others...

Measure the DE parameters from distances and growth separately

w0wa

Om

ega D

E

Still more general approach: measure functions r(z) and g(z)

see if they are consistent

Knox, Song & Tyson 2005

Minimalist Modified Gravity vs. DE

g(a) ≡!

a= exp

[∫ a

0

d ln a[!M (a)!− 1]

]

Excellent fit to standard DE growth function with

! = 0.55 + 0.05[1 + w(z = 1)]

Huterer & Linder, astro-ph/0608681see also Linder & Cahn, astro-ph/0701317

!! = 0.13Also fits the DGP braneworld theory with

Describe deviations from GR via a single new parameter

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 10000

l

10-6

10-5

10-4

l(l+

1)

P! ii /

(2"

)

# = 0.55# = 0.65

i,i=11

44

22

33

Cluster counts

Weak lensingtomography

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 !! = 0.13

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

(err

or

or

bia

s in

!)

/ "!,

fid

Degradation factor in ! error

PlanckSouth Pole Telescope

LSSTSupernova/Acceleration Probe

Conclusions • distinguishing dark energy from modified gravity is

becoming one of the key goals of cosmology in years to come

• assuming nonlinear clustering that follows the usual prescription even with MG, we find that future probes can achieve 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 that describes departures between DE and MG

• bright future with upcoming powerful surveys

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 = a2(!)!

!(1 + 2")d!2 + (1 ! 2#)d$x2"

! = (1 + ")# ! = !0

"DE

"M

and assume

101

102

103

104

l

10!6

10!5

10!4

10!3

l(l+

1)C

l /2!

LCDM

0.1

!0.1

Caldwell, Cooray & Melchiorri, astro-ph/0703375

Physically motivated MG parametrization

CMB-galaxy cross-correlationWeak lensing power spectrum