ANISOTROPIC PERTURBATIONS

DUE TO DARK ENERGY

JODRELL BANK OBSERVATORYUNIVERSITY OF MANCHESTER

RICHARD BATTYE & ADAM MOSS astro-ph/0602377

DOMAIN WALL DOMINATED UNIVERSE

ADAM MOSS TALK : SHOWED THERE EXIST LOCALLY STABLE CONFIGURATIONS

BUT THEY DON'T APPEAR TO BE ATTRACTORS IN THE SIMPLEMODELS WE CONSIDERED – WORK CONTINUES

w = -2/3

DIMENSIONS :

PLAN OF TALK● MOTIVATION

● COSMOLOGICAL PERTURBATIONS

● ELASTIC DARK ENERGY

● ANISOTROPIC PERTURBATIONS

● CORRELATED MODES ON LARGE SCALES

THE STANDARD LORESCALAR-VECTOR-TENSOR SPLIT

BASIC IDEAISOTROPIC AND ANISOTROPIC ELASTICITYSPEED SOUND FOR CUBIC SYMMETRY

ANISOTROPY FROM ADIABATIC INITIAL CONDITIONSANALYTIC & NUMERICAL CALCULATIONS

(THE MODEL FORMERLY KNOWNAS SOLID DARK MATTER/ENERGY)

ALIGNMENT IN CMB MAPS

D'Oliveria-Costa et al

Eriksen et al

Land & Magueijo

Alignment of thel=2 and l=3 multipoles

North-South ratio ofPpower spectrum & 3-pt correlation fn

“Axis of Evil” -correlated multipoles

BIANCHI TYPE VIIh UNIVERSE (T. Jaffe et al)

WMAP

BIANCHI MODEL

WMAP-BIANCHI

now compatible with Gaussianity and isotropy

BASIC IDEA

ADD STANDARD ADIABATICMODEL AND BEST FITTING

BIANCHI TEMPLATE

SCALAR-VECTOR-TENSOR SPLIT

ENERGY-MOMENTUM TENSOR

VELOCITY :

ANISOTROPICSTRESS :

SCALARVECTOR

SCALAR

VECTORTENSOR

LAGRANGIAN, EM TENSOR

ACTION :

EM-TENSOR :

RELATIVISTIC ELASTICITY TENSOR :

HENCE PARAMETERIZES FLUID PERTS

STANDARDDEFINITIONS

THEORY DEVELOPED BY CARTER AND OTHERS IN 1970s TO MODEL NEUTRON STARS

STANDARD ASSUMPTION

STANDARD ELASTICITY TENSOR

WHERE

STANDARD : 21 COMPONENTS

LAGRANGIAN & EULERIANPERTURBATIONS

EULERIAN LAGRANGIAN

1 BULK MODULUS 20 SHEAR MODULI

3+1 SPLIT}

ISOTROPY

ISOTROPIC TENSORS

P = PRESSURE

= BULK MODULUS

= SHEAR MODULUS

SOUND SPEEDS

LONGITUDINAL(SCALAR)

TRANSVERSE(VECTOR)

DOMAIN WALLS

w = -2/3

STABILITY

NB w=0, IS CDM

(BUCHER & SPERGEL 1998,BATTYE, BUCHER & SPERGEL 1999)

ADIABATIC

POINT SYMMETRIES

NON-ZERO MODULI

TRICLINIC 18MONOCLINIC 12ORTHORHOMIBIC 9TETRAGONAL 6RHOMBOHEDRAL 6HEXAGONAL 5CUBIC 3ISOTROPIC 2

eg FROM LANDAU & LIFSCHITZ

EG CUBIC CASE

PRESSURE ISOTROPIC :

POSSIBLE SYMMETRIES ARE CLASSIFIED BY

THE BRAVAIS LATTICES

ELASTICITY TENSOR :

WHERE 1 = xx, 2 = yy, 3 = zz4 = xy, 5 =yz, 6 = zx

BULK MODULUS +2 SHEAR MODULI

SIMPLECUBE

FCC

BCC

VARIABLE SOUND SPEEDS : (BATTYE, CHACHOUA & MOSS 2005)

ANISOTROPY FROM ADIABATIC PERTS- ie. FROM INFLATION

● INITIAL CONDITIONS

● POWER SERIES SOLUTION

● "WOULD-BE SCALAR MODE"

THOSE USED FOR INFLATION

CUBICSYMMETRY

TIME EVOLUTION : k=0.001Mpc

VELOCITY METRIC PERTS

SCALAR

VECTOR

VECTOR

TENSOR

-1

SPATIAL DISTRIBUTION : k=0.001Mpc-1

WHERE

AMPLITUDE OF EFFECT

CMB ANISOTROPIES : IN PROGRESS

ISOTROPIC(COMPUTE USING CAMB)

ANISOTROPIC

EXAMPLE OF SASH : l =4

SYMMETRY ADAPTEDSPHERICAL HARMONICS (SASH) eg VON DE LAGE & BETHE 1947

ROTATION

CONCLUSIONS● PERTURBATIONS IN DARK ENERGY ARE IMPORTANT

● ADIABATIC ELASTIC DARK ENERGY MODELS CAN BE STABLE

● THERE APPEAR TO BE ALIGNMENTS IN THE CMB

● QUALITATIVELY, THEY MAYBE DUE TO ANISOTROPIC DARK ENERGY

● WE HAVE INVESTIGATED THE CASE OF CUBIC SYMMETRY

● NEXT (AND VERY IMPORTANT STEP) IS TO COMPUTE

● THEN WE CAN INVESTIGATE THE FIT TO THE DATA

● NB ONE IS NOT RESTRICTED TO CUBIC SYMMETRY