ANISOTROPIC PERTURBATIONS DUE TO DARK ENERGY JODRELL BANK OBSERVATORY UNIVERSITY OF MANCHESTER RICHARD BATTYE & ADAM MOSS astro-ph/

DOMAIN WALL DOMINATED UNIVERSE ADAM MOSS TALK : SHOWED THERE EXIST LOCALLY STABLE CONFIGURATIONS BUT THEY DON'T APPEAR TO BE ATTRACTORS IN THE SIMPLE MODELS 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 LORE SCALAR-VECTOR-TENSOR SPLIT BASIC IDEA ISOTROPIC AND ANISOTROPIC ELASTICITY SPEED SOUND FOR CUBIC SYMMETRY ANISOTROPY FROM ADIABATIC INITIAL CONDITIONS ANALYTIC & NUMERICAL CALCULATIONS (THE MODEL FORMERLY KNOWN AS SOLID DARK MATTER/ENERGY)

ALIGNMENT IN CMB MAPS D'Oliveria-Costa et al Eriksen et al Land & Magueijo Alignment of the l=2 and l=3 multipoles North-South ratio of Ppower 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 ADIABATIC MODEL AND BEST FITTING BIANCHI TEMPLATE

SCALAR-VECTOR-TENSOR SPLIT ENERGY-MOMENTUM TENSOR VELOCITY : ANISOTROPIC STRESS : SCALAR VECTOR SCALAR VECTOR TENSOR

LAGRANGIAN, EM TENSOR ACTION : EM-TENSOR : RELATIVISTIC ELASTICITY TENSOR : HENCE PARAMETERIZES FLUID PERTS STANDARD DEFINITIONS THEORY DEVELOPED BY CARTER AND OTHERS IN 1970s TO MODEL NEUTRON STARS STANDARD ASSUMPTION

STANDARD ELASTICITY TENSOR WHERE STANDARD : 21 COMPONENTS LAGRANGIAN & EULERIAN PERTURBATIONS 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 TRICLINIC18 MONOCLINIC12 ORTHORHOMIBIC 9 TETRAGONAL 6 RHOMBOHEDRAL 6 HEXAGONAL 5 CUBIC 3 ISOTROPIC 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 = zz 4 = xy, 5 =yz, 6 = zx BULK MODULUS + 2 SHEAR MODULI

SIMPLE CUBE 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 CUBIC SYMMETRY 

TIME EVOLUTION :  k=0.001Mpc VELOCITY METRIC PERTS SCALAR VECTOR TENSOR

SPATIAL DISTRIBUTION : k=0.001Mpc WHERE

AMPLITUDE OF EFFECT

CMB ANISOTROPIES : IN PROGRESS ISOTROPIC (COMPUTE USING CAMB) ANISOTROPIC EXAMPLE OF SASH : l =4 SYMMETRY ADAPTED SPHERICAL 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