Dark Energy and Modified Gravity IGC Penn State May 2008 Roy Maartens ICG Portsmouth R Caldwell.
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Transcript of Dark Energy and Modified Gravity IGC Penn State May 2008 Roy Maartens ICG Portsmouth R Caldwell.
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