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BRANEWORLD COSMOLOGICAL PERTURBATIONS

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Title: BRANEWORLD COSMOLOGICAL PERTURBATIONS


1
Dark Energy and Modified Gravity
IGC Penn State May 2008
Roy Maartens ICG Portsmouth
R Caldwell
2
LCDM fits the high-precision data
galaxy distribution

cosmic microwave background

WMAP
LCDM

SDSS
3
supernovae
  • 3 independent data sets intersect

CMB
galaxies
4
the improbable, mysterious universe
there are particle physics candidates
0.2
or Modified Gravity?
0.75
5
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?

6
coincidence problem
radiation (? 1/a4)
log ?
matter (? 1/a3)
cosmological constant
log a
Radiation dominated
Matter dominated
Dark energy dominated
7
String theory and vacuum energy
  • string landscape and
  • multiverse to explain
  • fine-tuned small value?
  • speculative controversial

8
  • . 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
9
  • Other quantum gravity approaches to the vacuum
    energy
  • Loop Quantum Gravity
  • ask Abhay and Martin
  • Causal sets
  • Others

10
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

11
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

12
  • 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

13
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?)

14
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

15
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?

16
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


17
  • 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


18
  • Background
  • modified
  • Friedman
  • Examples
  • f(R) modified gravity (R Ricci scalar)
  • DGP modified gravity (braneworld model)

19
  • 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

20
  • 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

21
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
22
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
23
L Guzzo et al
24
CMB photons carry the signature of the
effect of DE or MG on structure formation
R Caldwell
integrated Sachs-Wolfe effect
25
Lensing also carries a signature
of the effect of DE or MG
complication linear to nonlinear transition
(need N-body simulations)
26
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?

27
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
28
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
29
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?
30
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 ?
31
structure formation
  • Poisson
    equation

  • Euler
    equation

  • stress constraint
  • GR
  • MG modified gravity strength dark
    anisotropic stress
  • examples

32
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

33
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

34
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
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