Modified (dark) gravity Modified (dark) gravity Roy Maartens, PortsmouthRoy Maartens, Portsmouth

or Dark Gravity?0.75

0.2

it’s the it’s the simplestsimplest model model compatible with compatible with allall data so far data so far nono other model is a better fit other model is a better 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?

obs

44susy

4physics newtheory

43228233220obs

TeV) 1(~~energy vacuum

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

MM

MHG p

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

LCDM is LCDM is the best modelthe best model

test this against datatest this against data wait for particle physics/QG to explainwait for particle physics/QG to explain 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, curvature=0curvature=0

““minimalist” approach minimalist” approach

1||10 averagenonlinear

10|~ | inflation big-

-big

K

K

43vac )eV 10(

Dynamical Dark Energy in General Dynamical Dark Energy in General RelativityRelativity

““quintessence”,…quintessence”,… effective ‘Dark Energy’ via nonlinear effects of effective ‘Dark Energy’ via nonlinear effects of

structure formation? structure formation?

Dark Gravity –Dark Gravity – Modify GR on large scalesModify 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]

alternatives to LCDM alternatives to LCDM

… … but we can do more but we can do more with the datawith the dataWe can test We can test gravitygravity

The problem is so big that we need to test alternatives The problem is so big that we need to test alternatives

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

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

Dark Energy dynamicsDark Energy dynamics

Dark Gravity dynamicsDark Gravity dynamics

3

1

field DE varying- time

88

DE

DE

dark

dark

pw

T

GTGTG

expansionmodify to

DOFscalar new

8dark

dark

G

GTGG

0vac

is GR wrong on large scales is GR wrong on large scales ?? i.e. acceleration via the i.e. acceleration via the weakeningweakening of of gravitygravity

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

Today:Today:

Modified Friedman Modified Friedman equations (schematic) equations (schematic)

Modified (dark) gravityModified (dark) gravity

GR on tomodificati

0)(3

dark

A

pH

2darkdark

2dark2

)(42

1)1(

3

8)1(

a

KpGAHAH

a

KGAH

modified modified

Friedman:Friedman:

Examples:Examples:

f(R)f(R) modified gravitymodified gravity

DGP modified gravity (5D braneworld DGP modified gravity (5D braneworld model)model)

2darkdark

2dark2

)(42

1)1(

3

8)1(

a

KpGAHAH

a

KGAH

H

Rf

H

Hf

H

fRA

RfL

RRR

22dark

grav

116

)(

HrA

c

1dark

modified modified

Friedman:Friedman:

general feature general feature

geometric tests on their own cannot geometric tests on their own cannot distinguish modified gravity from GRdistinguish modified 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

2darkdark

2dark2

)(42

1)1(

3

8)1(

a

KpGAHAH

a

KGAH

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 observed H(z)?fit 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 DG – because in DG – because gravity weakensgravity weakens

(G determined (G determined

by local physics)by local physics)

decreases

increases :DG

: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 DG DE from DG via growth via growth of structureof structure

DE and DG with DE and DG with

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

rates of growth of rates of growth of structure differstructure differ

bias evolution?bias evolution?

(Y Wang, 0710.3885)

DE + DG modelsLCDM

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

ad

df

ln

ln f

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

a new light scalar degree of freedoma new light scalar degree of freedom

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 constraintssystem constraints all f(R) models have this problemall f(R) models have this problem way out: ‘chameleon’ mechanism, i.e. the way out: ‘chameleon’ mechanism, i.e. the

scalar becomes massive in the solar system scalar becomes massive in the solar system

- very contrived- very contrived

f(R) gravityf(R) gravity

)( gravGRgrav, RfLRL

0

4

~ ,)( HR

RRf

Scalar-tensor gravity (‘extended Scalar-tensor gravity (‘extended quintessence’):quintessence’):

also a new light scalar degree of freedomalso a new light scalar degree of freedom

But now there are 2 free functions:But now there are 2 free functions:

late-time self-acceleration is possible late-time self-acceleration is possible without violating solar system constraints without violating solar system constraints

(no chameleon is needed)(no chameleon is needed)

Interesting - but the models do not improve Interesting - but the models do not improve on standard GR quintessence modelson standard GR quintessence models

Scalar-vector-tensor gravity – even more Scalar-vector-tensor gravity – even more complicated; no advantage unless it complicated; no advantage unless it solves the DM solves the DM andand DE problems DE problems gravitationally gravitationally

Generalising f(R) gravityGeneralising f(R) gravity

)(2)()( 2grav URFL

String theory - our 4D universe may be String theory - our 4D universe may be moving in 10D spacetimemoving in 10D spacetime

ST unifies the ST unifies the 4 interactions4 interactions

Dark gravity from braneworlds?Dark gravity from braneworlds?

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 brane

different possibilities

* ‘bulk’ fields as effective DE on the brane

(eg ekpyrotic/ cyclic)

* matter on a ‘shadow’ brane as effective DE on the ‘visible’ brane

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

(eg DGP)

shadow brane

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

4D brane universe in 5D bulk 4D brane universe in 5D bulk

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

10

eff

~ and

small )0( SNe

)(1

1)(

Hr

zzw

c

m

mExpansion historyExpansion history

Density perturbations (sub-horizon)Density perturbations (sub-horizon)

(cannot neglect 5D effects!)(cannot neglect 5D effects!)

More suppression of More suppression of

structure than LCDMstructure than LCDM

13

2 , )(1)(

)(42

eff

eff

tGtG

tGH

δ/a

… … too good to be truetoo good to be true

5D analysis of perturbations shows5D analysis of 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 5D gravityThis ghost is from 5D 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 5D gravityDGP has a ghost in 5D 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’ ST model ?find a ‘non-ugly’ ST model ?

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

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

Model-independent tests of Model-independent tests of GRGR

There is no natural DE model in GR There is no natural DE model in GR (but LCDM is preferred by simplicity)(but LCDM is preferred by simplicity) There is no natural or preferred modified MGThere is no natural or preferred modified MG

(theory gives (theory gives nono guidance) guidance) Aim =Aim = without choosing a DE model in GR, without choosing a DE model in GR,

and without specifying a modified DG model, and without specifying a modified DG model, try to find constraints on deviations from GRtry to find constraints on deviations from GR

Problem = Problem = find tests that do not depend on find tests that do not depend on the DE or the DG modelthe DE or the DG model

In parallel:In parallel:1. Test for Lambda vs dynamical DE in GR1. Test for Lambda vs dynamical DE in GR2. Test for GR vs modified DG2. Test for GR vs modified DG

Some complications: Some complications: * modified gravity has ‘dark’ anisotropic stress* modified gravity has ‘dark’ anisotropic stress

examplesexamples

DE (smooth) – only need growth rate for DE (smooth) – only need growth rate for CMB,LSSCMB,LSS

DG – DG – alsoalso need anisotropic stress + G need anisotropic stress + Geffeff

* linear-nonlinear transition * linear-nonlinear transition (nonlinear regime should recover GR)(nonlinear regime should recover GR)can severely complicate WL testscan severely complicate WL tests

R

RR

f

f

dark

dark

: f(R)

: DGP

8)(

3

8)(

eff2

2

darkeff2

2

Ga

k

Ga

k

2222 )21()21( xdadtds

DegeneraciesDegeneracies * DE with clustering and anisotropic stress can * DE with clustering and anisotropic stress can

look like MG – (physical?)look like MG – (physical?)* astrophysical (eg bias evolution vs growth * astrophysical (eg bias evolution vs growth rate)rate)

Approaches:Approaches:(1) Growth rate:(1) Growth rate:

compare the observed growth rate with the compare the observed growth rate with the theoretical rate – is it DE or DG?theoretical rate – is it DE or DG?

we need to know the DE and the DG we need to know the DE and the DG modelsmodels

f

(2) Parameter-splitting:(2) Parameter-splitting:

check for a breaking of GR consistency check for a breaking of GR consistency between between ‘geometry’ and ‘growth’‘geometry’ and ‘growth’

egeg

inconsistency could inconsistency could

mean a more mean a more

complicated DEcomplicated DE

model or data model or data

problemsproblems

0

1(grow)(geom)

K

ww CMBCMB+GalCMB+SNCMB+WLAll

(S Wang et al, 0705.0165)

(3) Parametrised post-Friedman approach(3) Parametrised post-Friedman approach

Parametrised post-Newtonian formalism has Parametrised post-Newtonian formalism has been very successful for testing deviations been very successful for testing deviations from GR in the solar systemfrom GR in the solar system

Develop a PPF for modified DG?Develop a PPF for modified DG? Need basic assumptions:Need basic assumptions:

* * DE is smoothDE is smooth

* * modified gravity is a metric theory with modified gravity is a metric theory with energy conservationenergy conservation

To close the system – 3 functions To close the system – 3 functions

(Hu, Sawicki 0708.1190; Jain, Zhang 0709.2375)(Hu, Sawicki 0708.1190; Jain, Zhang 0709.2375)

00

8

dark

dark

GT

GGTG

darkeff ,, G

some conclusionssome conclusions

observations observations imply accelerationimply acceleration theorytheory did not predict it – and cannot explain it did not predict it – and cannot explain it simplest model LCDM is the best we havesimplest model LCDM is the best we have GR with dynamical DE – no natural modelGR with dynamical DE – no natural model modifications to GR – dark gravity:modifications to GR – dark gravity:

* theory gives no natural model* theory gives no natural model* simple f(R) model fails solar system test* simple f(R) model fails solar system test* simplest braneworld model DGP has a * simplest braneworld model DGP has a

ghostghost theorists need to keep exploringtheorists need to keep exploring

* better models* better models* better observational tests * better observational tests (model-independent?)(model-independent?)