modified (dark) gravity roy maartens, portsmouth or dark gravity? 0.75 0.2
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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?)