ANISOTROPIC

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ANISOTROPIC PERTURBATIONS DUE TO DARK ENERGY
RICHARD BATTYE ADAM MOSS astro-ph/0602377
JODRELL BANK OBSERVATORY UNIVERSITY OF MANCHESTER
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DOMAIN WALL DOMINATED UNIVERSE
w -2/3
DIMENSIONS
SHOWED THERE EXIST LOCALLY STABLE
CONFIGURATIONS BUT THEY DON'T APPEAR TO BE
ATTRACTORS IN THE SIMPLE MODELS WE CONSIDERED
WORK CONTINUES
ADAM MOSS TALK
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PLAN OF TALK

• MOTIVATION
• COSMOLOGICAL PERTURBATIONS
• ELASTIC DARK ENERGY
• ANISOTROPIC PERTURBATIONS
• CORRELATED MODES ON LARGE SCALES

THE STANDARD LORESCALAR-VECTOR-TENSOR SPLIT
(THE MODEL FORMERLY KNOWN AS SOLID DARK
MATTER/ENERGY)
BASIC IDEA ISOTROPIC AND ANISOTROPIC
ELASTICITY SPEED SOUND FOR CUBIC SYMMETRY
ANISOTROPY FROM ADIABATIC INITIAL
CONDITIONS ANALYTIC NUMERICAL CALCULATIONS
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ALIGNMENT IN CMB MAPS
D'Oliveria-Costa et al
Alignment of the l2 and l3 multipoles

Eriksen et al
North-South ratio of Ppower spectrum 3-pt
correlation fn
Land Magueijo
Axis of Evil - correlated multipoles
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(T. Jaffe et al)
BIANCHI TYPE VIIh UNIVERSE
BASIC IDEA
WMAP
ADD STANDARD ADIABATIC MODEL AND BEST FITTING
BIANCHI TEMPLATE
BIANCHI MODEL
WMAP -BIANCHI
now compatible with Gaussianity and isotropy
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SCALAR-VECTOR-TENSOR SPLIT
ENERGY-MOMENTUM TENSOR
VECTOR
SCALAR
VELOCITY
ANISOTROPICSTRESS
SCALAR
TENSOR
VECTOR
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LAGRANGIAN, EM TENSOR
STANDARD ASSUMPTION
ACTION
EM-TENSOR
STANDARDDEFINITIONS
RELATIVISTIC ELASTICITY TENSOR
PARAMETERIZES FLUID PERTS
HENCE
THEORY DEVELOPED BY CARTER AND OTHERS IN 1970s TO
MODEL NEUTRON STARS
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STANDARD ELASTICITY TENSOR

31 SPLIT
WHERE
LAGRANGIAN EULERIAN PERTURBATIONS
STANDARD 21 COMPONENTS
LAGRANGIAN
EULERIAN
1 BULK MODULUS 20 SHEAR MODULI
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NB w0, IS CDM
ISOTROPY
(BUCHER SPERGEL 1998, BATTYE, BUCHER SPERGEL
1999)
ISOTROPIC TENSORS
P PRESSURE
DOMAIN WALLS
BULK MODULUS
w -2/3 ?????????
STABILITY
? SHEAR MODULUS
SOUND SPEEDS
LONGITUDINAL (SCALAR)
TRANSVERSE (VECTOR)
ADIABATIC
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POINT SYMMETRIES
EG CUBIC CASE
POSSIBLE SYMMETRIES ARE CLASSIFIED BY THE
BRAVAIS LATTICES
PRESSURE ISOTROPIC
eg FROM LANDAU LIFSCHITZ
ELASTICITY TENSOR
1 xx, 2 yy, 3 zz 4 xy, 5 yz, 6 zx
WHERE
BULK MODULUS 2 SHEAR MODULI
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(BATTYE, CHACHOUA MOSS 2005)
VARIABLE SOUND SPEEDS
SIMPLE CUBE
FCC
BCC
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ANISOTROPY FROM ADIABATIC PERTS
- ie. FROM INFLATION

• INITIAL CONDITIONS
• POWER SERIES SOLUTION
• "WOULD-BE SCALAR MODE"

THOSE USED FOR INFLATION
??
CUBIC SYMMETRY
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TIME EVOLUTION ?????????????????????????????k0
.001Mpc
-1
SCALAR
VECTOR
VECTOR
TENSOR
VELOCITY
METRIC PERTS
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-1
SPATIAL DISTRIBUTION k0.001Mpc
WHERE
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AMPLITUDE OF EFFECT
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CMB ANISOTROPIES IN PROGRESS
ROTATION
ISOTROPIC (COMPUTE USING CAMB)
ANISOTROPIC
SYMMETRY ADAPTED SPHERICAL HARMONICS (SASH) eg
VON DE LAGE BETHE 1947
EXAMPLE OF SASH l 4
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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