Dark Energy and Modified Gravity

IGC

Penn State

May 2008Roy MaartensICGPortsmouth R Caldwell

LCDM fits the high-precision dataLCDM fits the high-precision data

galaxy distribution

cosmic microwave background

SDSS

WMAPLCDM

3 3 independenindependent data sets t data sets intersectintersect

0K

203

8

1

H

G ii

KM

supernovae

CMB

galaxies

or Modified Gravity?

0.75

0.2

the improbable, mysterious the improbable, mysterious universeuniverse

there areparticle physics candidates

it’s the it’s the simplestsimplest model model compatible with compatible with allall data up to now data up to now nono other model gives a better statistical fit other model gives a better statistical fit but ….but …. theory cannot explain it theory cannot explain it

why so small? why so small? and … why and … why

so fine-tuned?so fine-tuned?

LCDM fits the data well…LCDM fits the data well…but we cannot explain itbut we cannot explain it

30

0

whilebut

formation structurefor crucial:~

aa m

obs

44susy

4physics newtheory

43228233220obs

TeV) 1(~)()(~energy vacuum

eV) 10(~)eV 10()eV 10(~~8

MM

MHG p

radiation ( 1/a4)

matter ( 1/a3)

cosmological constant

Radiationdominated

Matterdominated

Dark energydominated

log

log a

‘coincidence’ problem

string “landscape” and string “landscape” and multiverse to explain multiverse to explain fine-tuned small value?fine-tuned small value?

speculative & controversialspeculative & controversial

G 8/vac

String theory and vacuum energyString theory and vacuum energy

43vac eV) 10(~

8

G

gTTTGG vacvacvac ),(8

G 8/vac

0vac

……. or from spacetime topology?. or from spacetime topology?

““self-tuning” braneworldself-tuning” braneworld the higher-dimensional vacuum energy is the higher-dimensional vacuum energy is

large, as expectedlarge, as expected

- but the 4D brane is protected from it- but the 4D brane is protected from it However: unstableHowever: unstable

nn M 4physics new

)(4vac )(~

(4+n)D spacetimewith a cut

4D brane universe

Other quantum gravity Other quantum gravity approachesapproaches to to the vacuum the vacuum energyenergy

Loop Quantum Gravity:Loop Quantum Gravity:

ask Abhay and Martinask Abhay and Martin

Causal setsCausal sets

OthersOthers

LCDM is LCDM is the best modelthe best model

test this against data test this against data wait for particle physics/QG to explain whywait for particle physics/QG to explain why

focus on focus on * the best tests for w=-1* the best tests for w=-1* the role of theoretical assumptions* the role of theoretical assumptions

e.g. w=const, e.g. w=const, w(z) parametrizations,w(z) parametrizations, curvature=0curvature=0

““minimalist” attitude minimalist” attitude

43vac )eV 10(

Dynamical Dark Energy in General Dynamical Dark Energy in General RelativityRelativity

““quintessence”, coupled DE-dark matter,...quintessence”, coupled DE-dark matter,... effective ‘Dark Energy’ via nonlinear effects of effective ‘Dark Energy’ via nonlinear effects of

structure formation? structure formation?

‘‘Dark Gravity’ – Modify GR on large scalesDark Gravity’ – Modify GR on large scales 4D: scalar-(vector)-tensor theories 4D: scalar-(vector)-tensor theories [e.g. f(R)][e.g. f(R)] higher-D: braneworld models higher-D: braneworld models [e.g. DGP][e.g. DGP]

some alternatives to some alternatives to LCDM LCDM

… … but we can do more but we can do more with the datawith the data

We can test alternatives We can test alternatives

NB –NB – all these alternatives require that the all these alternatives require that the

vacuum energy does not gravitate: vacuum energy does not gravitate:

- - they address the coincidence problem they address the coincidence problem notnot the the vacuum energy problemvacuum energy problem

Dark Energy dynamicsDark Energy dynamics

Modified Gravity dynamicsModified Gravity dynamics

0vac

onaccelerati induce to

DOFscalar new

8dark

dark

G

GTGG

3

1

field DE varying- time

88

DE

DE

dark

dark

pw

T

GTGTG

tracker scalar field, to solve the coincidence problemtracker scalar field, to solve the coincidence problem

but parameters in thebut parameters in the potential must be potential must be highly fine-tunedhighly fine-tuned

more complicated dynamical models are poorly motivated or suffer theoretical problems:

eg phantom scalar field (ghost - vacuum unstable)

k-essence (violates causality)

Chaplygin gas (what phenomenology?)

quintessencequintessence

coupled quintessencecoupled quintessence alternative approach to the coincidence problem:

* DM and DE only detected gravitationally* unavoidable degeneracy* there could be a coupling in the dark sector

(coupling to SM fields strongly constrained) intrinsic CDM bias – Euler equation violated some models ruled out by instabilities others lead to interesting features

eg w<-1 without ghosts

cc

c

HQwH

TQT

3)1(3

)()(

more radical approach to the coincidence more radical approach to the coincidence problem – problem –

“ “structure formation structure formation impliesimplies acceleration” acceleration”

nonlinear averaging/ backreaction?nonlinear averaging/ backreaction? voids dominate over filaments – accelerating voids dominate over filaments – accelerating

effect?effect? averaging effects are real and important – averaging effects are real and important –

but probably too small to give acceleration but probably too small to give acceleration abandon Copernican principle?abandon Copernican principle?

effective ‘DE’ from structure effective ‘DE’ from structure formation?formation?

Mpc 100 wallsbut voids, Mpc 10for 1 11 hh

is GR wrong on large scales is GR wrong on large scales ?? * * GR:GR: acceleration via the acceleration via the anti-anti-gravity of DEgravity of DE

(or perhaps via nonlinear effects)(or perhaps via nonlinear effects)

* * modified gravity:modified gravity: acceleration via the acceleration via the weakening weakening of gravity of gravity on large scaleson large scales

Challenge the standard theory?Challenge the standard theory?

Example from history: Example from history: Mercury perihelionMercury perihelion– – Newton + ‘dark’ planet Newton + ‘dark’ planet ??no –no – modified gravity! modified gravity!

But – very hard to consistently modify GR in the IRBut – very hard to consistently modify GR in the IR

and – must pass local as well as cosmological and – must pass local as well as cosmological teststests

Modified (dark) gravityModified (dark) gravity

Key assumptions on MG theories: metric theorymetric theory energy-momentum conservationenergy-momentum conservation

Key requirements on small nonlinear scales – must recover GRon small nonlinear scales – must recover GR on superhorizon scales – perturbations must on superhorizon scales – perturbations must

evolve compatibly with the background evolve compatibly with the background (‘separate universe’)(‘separate universe’)

On intermediate scales – Poisson equation is On intermediate scales – Poisson equation is modifiedmodified

GR = spin-2 graviton + minimal coupled matterGR = spin-2 graviton + minimal coupled matter

MG changes both featuresMG changes both features

0 T

Background

modified modified

Friedman:Friedman:

Examples:Examples:

f(R)f(R) modified gravity (R = Ricci scalar)modified gravity (R = Ricci scalar)

DGP modified gravity (braneworld model)DGP modified gravity (braneworld model)

)(42

1)1(

3

8)1(

darkdark

dark2

pGAHAH

GAH

H

Rf

H

Hf

H

fRA

RfL

RRR

22dark

grav

116

)(

HrA

c

1dark

GR on tomodificati dark A

Geometric tests Geometric tests

(eg supernovae, BAO)(eg supernovae, BAO)

probe the background probe the background

expansion historyexpansion history

general feature general feature

geometric tests on their own cannot distinguish geometric tests on their own cannot distinguish modified gravity from GRmodified gravity from GR

why?why?

geometric tests are based on the comoving geometric tests are based on the comoving distancedistance

- the same H(z) gives the same expansion - the same H(z) gives the same expansion historyhistory

z

zH

dzzr

0 )'(

')(

we can find a GR model of DE we can find a GR model of DE

to mimic the H(z) of a modified gravity theory:to mimic the H(z) of a modified gravity theory:

how to distinguish DG and DE models that both how to distinguish DG and DE models that both fit the observed H(z)?fit the observed H(z)?

they predict different they predict different rates of growth of rates of growth of structurestructure

)()( and

)()( then

)(8

)(3)( choose

3

8)1(gravity dark

)(3

8 DEGR

dark

2

DE

dark2

DE2

zwzw

zrzr

zAG

zHz

GAH

GH

DGGR

DGGR

structure formation is suppressed by acceleration structure formation is suppressed by acceleration in different ways in GR and modified gravity:in different ways in GR and modified gravity:

** in GR – because DE dominates over matter in GR – because DE dominates over matter

* * in MG – because gravity weakensin MG – because gravity weakens

(G determined (G determined

by local physics)by local physics)

decreases

increases :MG

:DE

42

eff

eff

eff

eff

GG

GG

GG

GH

GG eff

GG eff

δ/a

)( egeff

Rf

GG

DGP egeff GG

GG eff

Distinguish Distinguish DE from MG DE from MG via growth via growth of structureof structure

DE and MG with DE and MG with

the same H(z)the same H(z)

rates of growth of rates of growth of structure differstructure differ

(bias evolution?)(bias evolution?)

DE + MG modelsLCDM

MG model (modification to GR)DE model (GR)LCDM

ad

df

ln

ln f

Y Wang

L Guzzo et al

CMB photons carry the signature of theCMB photons carry the signature of the

effect of DE or MG on structure formation effect of DE or MG on structure formation

integrated Sachs-Wolfe effectintegrated Sachs-Wolfe effect R Caldwell

Lensing also carries a signature Lensing also carries a signature

of the effect of DE or MG of the effect of DE or MG

complication: linear to nonlinear transition(need N-body simulations)

simplest scalar-tensor gravity:simplest scalar-tensor gravity:

implies a new light scalar degree of freedom in implies a new light scalar degree of freedom in gravitygravity

eg.eg. at low energy, at low energy,

1/1/RR dominates dominates

This produces late-time self-accelerationThis produces late-time self-acceleration but the light scalar strongly violates solar but the light scalar strongly violates solar

system/ binary pulsar constraintssystem/ binary pulsar constraints all f(R) models have this problemall f(R) models have this problem Possible way out: Possible way out: ‘chameleon’‘chameleon’ mechanism, mechanism,

i.e. the scalar becomes massive in the solar i.e. the scalar becomes massive in the solar system system

- too contrived?- too contrived?

f(R) gravityf(R) gravity

)( gravGRgrav, RfLRL

0

4

~ ,)( HR

RRf

new massive graviton modesnew massive graviton modes new effects from higher-D fields and other new effects from higher-D fields and other

branesbranes perhaps these could dominate at low perhaps these could dominate at low

energiesenergies

matter

gravity

+ dilaton,

form fields…

extra dimension

our branedifferent

possibilities

* ‘bulk’ fields as effective DE on the brane

(eg ekpyrotic/ cyclic)

* effective 4D gravity on the brane modified on large scales

(eg DGP)

shadow brane

Modified gravity from Modified gravity from braneworlds?braneworlds?

DGP – the simplest exampleDGP – the simplest example

3

8 :early time

10 : timelate

3

8

21

2

GHrH

rH

G

r

HH

c

c

c

early universe early universe – recover GR dynamics – recover GR dynamics

late universe late universe – acceleration – acceleration withoutwithout DE DE

gravity “leaks” off the branegravity “leaks” off the brane

therefore gravity on the brane therefore gravity on the brane weakensweakens

passes the solar system test: DGP GRpasses the solar system test: DGP GR

The background is very simple – like LCDMThe background is very simple – like LCDM

Friedman on theFriedman on the

branebrane

… … too good to be truetoo good to be true

analysis of higher-D perturbations showsanalysis of higher-D perturbations shows

- there is a ghost in the scalar sector of - there is a ghost in the scalar sector of the the gravitational fieldgravitational field

This ghost is from higher-D gravityThis ghost is from higher-D gravity

* It is not apparent in the background* It is not apparent in the background

* It is the source of suppressed * It is the source of suppressed growthgrowth

The ghost makes the quantum vacuum The ghost makes the quantum vacuum unstableunstable

Can DGP survive as a classical toy model?Can DGP survive as a classical toy model?

0 with

)(42

Dicke-Branseff

eff

GG

tGH

The simplest models failThe simplest models fail f(R) and DGP – simplest in their classf(R) and DGP – simplest in their class

– – simplest modified gravity simplest modified gravity modelsmodels both both fail fail because of their scalar degree of because of their scalar degree of freedom:freedom:

f(R) strongly violates solar system f(R) strongly violates solar system constraintsconstraints

DGP has a ghost in higher-D gravityDGP has a ghost in higher-D gravity

Either Either GR is the correct theory on large scalesGR is the correct theory on large scales

Or Or Modified gravity is more complicatedModified gravity is more complicatedTHEORY: find a ghost-free generalized DGP or THEORY: find a ghost-free generalized DGP or

find a ‘non-ugly’ f(R) model – or findfind a ‘non-ugly’ f(R) model – or find

a new MG model?a new MG model?

PHENOMENOLOGY: model-independent PHENOMENOLOGY: model-independent tests tests

of the failure of GR ?of the failure of GR ?

Poisson equationPoisson equation

Euler equationEuler equation

stress constraintstress constraint

GR:GR: MG: modified gravity strength + ‘dark’ anisotropic stressMG: modified gravity strength + ‘dark’ anisotropic stress

examplesexamples

R

RR

f

fGG

GG

darkeff

darkeff

, : f(R)

, : DGP

darkeff2

2

2

2

eff2

2

3

8)(

)(

4

Ga

k

adt

d

a

k

Ga

k

m

2222 )21()21( xdadtds

structure formationstructure formation

0 , darkeff GG

Testing for MGTesting for MG

In principle:In principle: Total density perturbation givesTotal density perturbation gives

Galaxy velocities giveGalaxy velocities give

Lensing givesLensing gives

Then determinesThen determines

We can also derive a consistency test for GR vs We can also derive a consistency test for GR vs MG:MG:

Song & KoyamaSong & Koyama

ds)(

effG

dark

1 :MG ,1 :GR ,

4

)(2

2

Ga

Hak mm

MG versus Coupled DE?MG versus Coupled DE?

Coupled DE in GR introduces complicationsCoupled DE in GR introduces complications

MG:MG: all fields feel modified gravity equally, so all fields feel modified gravity equally, so equivalence principle is not violatedequivalence principle is not violated

Coupled DE:Coupled DE: CDM breaks EP because of the CDM breaks EP because of the couplingcoupling

Poisson equation is the samePoisson equation is the same

But Euler equation But Euler equation

is modifiedis modified

This can be detected in principle via peculiar This can be detected in principle via peculiar velocitiesvelocities

)1()( CDM

)( baryons

2

2

kadt

d

kadt

d

b

b

some conclusionssome conclusions observations observations imply accelerationimply acceleration theorytheory did not predict it – and cannot yet explain it did not predict it – and cannot yet explain it GR with dynamical DE – GR with dynamical DE – nono natural model natural model modifications to GR – theory gives modifications to GR – theory gives nono natural model natural model

simplest models fail [f(R), DGP]simplest models fail [f(R), DGP] Observations cannot ‘find’ a theory Observations cannot ‘find’ a theory Too many models to test each oneToo many models to test each one Need model-independent approachesNeed model-independent approaches key questions:key questions: 1.1. is is ΛΛ the dark energy the dark energy??

2.2. if not, is it GR+dynamical DE – or Dark Gravity? if not, is it GR+dynamical DE – or Dark Gravity? In principle: In principle: expansion history + structure expansion history + structure

formationformation test can answer 1+2test can answer 1+2 As a by-product – As a by-product – we understand GR and gravity we understand GR and gravity

betterbetter