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Dark Energy and Modified Gravity

IGC Penn State May 2008

Roy Maartens ICG Portsmouth

R Caldwell

LCDM fits the high-precision data

galaxy distribution

cosmic microwave background

WMAP

LCDM

SDSS

supernovae

- 3 independent data sets intersect

CMB

galaxies

the improbable, mysterious universe

there are particle physics candidates

0.2

or Modified Gravity?

0.75

LCDM fits the data well but we cannot explain i

t

- its the simplest model
- compatible with all data up to now
- no other model gives a better statistical fit
- but . theory cannot explain it
- why so small?
- and why
- so fine-tuned?

coincidence problem

radiation (? 1/a4)

log ?

matter (? 1/a3)

cosmological constant

log a

Radiation dominated

Matter dominated

Dark energy dominated

String theory and vacuum energy

- string landscape and
- multiverse to explain
- fine-tuned small value?
- speculative controversial

- . or from spacetime topology?
- self-tuning braneworld
- the higher-dimensional vacuum energy is large, as

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

4D brane universe

(4n)D spacetime with a cut

- Other quantum gravity approaches to the vacuum

energy - Loop Quantum Gravity
- ask Abhay and Martin
- Causal sets
- Others

minimalist attitude

- LCDM is
- the best model
- test this against data
- wait for particle physics/QG to explain why
- focus on
- the best tests for w-1
- the role of theoretical assumptions
- e.g. wconst,
- w(z) parametrizations,
- curvature0

but we can do more with the data We

can test alternatives

some alternatives to LCDM

- Dynamical Dark Energy in General Relativity
- quintessence, coupled DE-dark matter,...
- effective Dark Energy via nonlinear effects of

structure formation? - Dark Gravity Modify GR on large scales
- 4D scalar-(vector)-tensor theories e.g. f(R)
- higher-D braneworld models e.g. DGP

- NB all these alternatives require that the
- vacuum energy does not gravitate
- - they address the coincidence problem not

the vacuum energy problem - Dark Energy dynamics
- Modified Gravity dynamics

quintessence

- tracker scalar field, to solve the coincidence

problem - but

parameters in the -

potential must be -

highly 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?)

coupled 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

effective DE from structure formation?

- more radical approach to the coincidence problem

- structure formation implies acceleration
- nonlinear averaging/ backreaction?
- voids dominate over filaments accelerating

effect? - averaging effects are real and important

but probably too small to give

acceleration - abandon Copernican principle?

is GR wrong on large scales ? GR acceleration

via the anti-gravity of DE (or perhaps via

nonlinear effects) modified gravity

acceleration via the weakening of gravity

on large scales

Modified (dark) gravity

- Challenge the standard theory?
- Example from history
- Mercury perihelion
- Newton dark planet ?
- no modified gravity!
- But very hard to consistently modify GR in the

IR - and must pass local as well as cosmological

tests

- Key assumptions on MG theories
- metric theory
- energy-momentum conservation
- Key requirements
- on small nonlinear scales must recover GR
- on superhorizon scales perturbations must

evolve compatibly with the background (separate

universe) - On intermediate scales Poisson equation is

modified - GR spin-2 graviton minimal coupled matter
- MG changes both features

- Background
- modified
- Friedman
- Examples
- f(R) modified gravity (R Ricci scalar)
- DGP modified gravity (braneworld model)

- Geometric tests
- (eg supernovae, BAO)
- probe the background
- expansion history
- general feature
- geometric tests on their own cannot distinguish

modified gravity from GR - why?
- geometric tests are based on the comoving

distance - - the same H(z) gives the same expansion history

- we can find a GR model of DE
- to mimic the H(z) of a modified gravity theory
- how to distinguish DG and DE models that both

fit the observed H(z)? - they predict different rates of growth of

structure

structure formation is suppressed by acceleration

in different ways in GR and modified gravity

in GR because DE dominates over matter

in MG because gravity weakens

(G determined by local physics)

d/a

Distinguish DE from MG via growth of structure

DE MG models LCDM

- DE and MG with
- the same H(z)
- rates of growth of structure differ
- (bias evolution?)

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

f

Y Wang

L Guzzo et al

CMB photons carry the signature of the

effect of DE or MG on structure formation

R Caldwell

integrated Sachs-Wolfe effect

Lensing also carries a signature

of the effect of DE or MG

complication linear to nonlinear transition

(need N-body simulations)

f(R) gravity

- simplest scalar-tensor gravity
- implies a new light scalar degree of freedom in

gravity - eg. at low energy,
- 1/R dominates
- This produces late-time self-acceleration
- but the light scalar strongly violates solar

system/ binary pulsar constraints - all f(R) models have this problem
- Possible way out chameleon mechanism,

i.e. the scalar becomes massive in the

solar system - - too contrived?

Modified gravity from braneworlds?

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

branes - perhaps these could dominate at low energies

our brane

different possibilities bulk fields as effect

ive DE on the brane

(eg ekpyrotic/ cyclic) effective 4D gravity on

the brane modified on large scales (eg DGP)

extra dimension

shadow brane

gravity dilaton, form fields

matter

DGP the simplest example

Friedman on the brane

early universe recover GR dynamics

late universe acceleration without DE

gravity leaks off the brane

therefore gravity on the brane weakens

passes the solar system test DGP GR

The background is very simple like LCDM

too good to be true

analysis of higher-D perturbations shows

- there is a ghost in the scalar sector of the

gravitational field This ghost is from higher-

D gravity It is not apparent in the background

It is the source of suppressed growth

The ghost makes the quantum vacuum unstable Can

DGP survive as a classical toy model?

The simplest models fail

- f(R) and DGP simplest in their class
- simplest modified gravity models
- both fail because of their scalar degree of

freedom - f(R) strongly violates solar system constraints
- DGP has a ghost in higher-D gravity
- Either GR is the correct theory on large scales
- Or Modified gravity is more complicated

THEORY find a ghost-free generalized DGP or

find a non-ugly f(R) model

or find

a new MG model?

PHENOMENOLOGY model-independent tests

of the failure of GR ?

structure formation

- Poisson

equation

- Euler

equation -

stress constraint - GR
- MG modified gravity strength dark

anisotropic stress - examples

Testing for MG

- In principle
- Total density perturbation gives
- Galaxy velocities give
- Lensing gives
- Then determines
- We can also derive a consistency test for GR vs

MG -

- Song Koyama

MG versus Coupled DE?

- Coupled DE in GR introduces complications
- MG all fields feel modified gravity equally, so

equivalence principle is not violated - Coupled DE CDM breaks EP because of the

coupling - Poisson equation is the same
- But Euler equation
- is modified
- This can be detected in principle via peculiar

velocities

some conclusions

- observations imply acceleration
- theory did not predict it and cannot yet

explain it - GR with dynamical DE no natural model
- modifications to GR theory gives no natural

model - simplest models fail f(R), DGP
- Observations cannot find a theory
- Too many models to test each one
- Need model-independent approaches
- key questions
- 1. is ? the dark energy?
- 2. if not, is it GRdynamical DE or Dark

Gravity? - In principle expansion history structure

formation - test can answer 12
- As a by-product we understand GR and gravity

better