Dragan Huterer- Dark Energy, Modified Gravity and The Accelerating Universe

8/3/2019 Dragan Huterer- Dark Energy, Modified Gravity and The Accelerating Universe

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Dark Energy, Modified Gravity

and

The Accelerating Universe

Dragan Huterer

Kavli Institute for Cosmological PhysicsUniversity of Chicago



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%)



Some of the earlyhistory of the Universe

is actually understood better!

Physics quite wellunderstood

95% of contents onlyphenomenologically

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

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



Current constraints

ΩDE ≈ 0.

7



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



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!)



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)]



• 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



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



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



ISW in DGP

Song, Sawicki, & Hu 2007

DGP

LCDM

P h i



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



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



• 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)



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



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

a g )

High-Z SN Search Team

0.01 0.10 1.00z

( m - M

) ( m a g )

• Get pure (luminosity) distances



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



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



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



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



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) ≡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



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



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



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



PlanckSouth Pole Telescope

LSSTSupernova/Acceleration Probe



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



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

Dragan Huterer- Dark Energy, Modified Gravity and The Accelerating Universe

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