Relic Anisotropy as the source of all Evil? Carlo Contaldi Imperial College London + Marco Peloso & Emir Gumrukcuoglu University of Minnesota, Minneapolis astro-ph/ OQSCM, 28 March 2007

Large Scale Anomalies in the CMB  Large scale “missing” power. [Contaldi et al., de Oliveira-Costa et al., Efstathiou, Slosar et al., Weeks et al.,…]  Foregrounds?  Topology?  Infra-red cutoff in primordial perturbations?  etc…  Preferred axis of low multipoles, l = 2, 3, 4, 5. [de Oliveira-Costa et al., Efstathiou, Eriksen et al., Hansen et al., Jaffe et al., Land & Magueijo, Vielva et al.,…]  Power is not evenly distributed between m for each l (m=2,3,0,3).  Correlated in l?  Axis of Evil?  Large scale features in the map are largely unaffected WMAP1  WMAP3.  Quadrupole? Maybe not a big deal.

Isotropic modifications of Power  Low-l reduction in power can be achieved easily e.g. cutoff in primordial spectra. [e.g. Contaldi, Peloso, Kofman & Linde astro-ph/ ]  Likelihood fit is inconclusive (~2σ).  Power is still distributed isotropically in m.  More information lies in the anisotropic distribution of power. V(Ф) ε, η << 1 V(Ф) cf. S. Sarkar talk on Monday

[Tocchini-Valentini et al 05] Short Inflation  oscillations in initial power?

[Nicholson & Contaldi astro-ph/ ] Short Inflation  T/S ratio effect

Anisotropic Contributions to the sky  Topology [Niarchou & Jaffe].  Foreground contamination.  Unknown physics? [ Land & Magueijo 2005] [ Copi et al 2006]

Anisotropy from Inflation…  Inflation isotropizes the universe. Any initial anisotropy in the expansion is wiped out after enough inflation.  Curvature perturbations are imprinted on super-horizon scales as perturbations in the inflaton grow wrt the Hubble radius and ``freeze- out”.  …but…if universe is initially anisotropic, largest scales initially evolved in anisotropic background.   Get infra-red effects with anisotropic signature.  requires short inflation.

Axisymmetric Inflation  Special case  universe expansion is initially axisymmetric.  Residual symmetry  easier to solve perturbation evolution analytically.  Anisotropic but homogeneous.

Toy model motivation n-dim  Microscopic dimension with meta-stable radii.  1-dim starts to inflate.  Drags two other dimensions into inflation (Kasner-like solution) [e.g. Contaldi et al. hep-th/ ].  End up with 3 macroscopic dimensions inflating isotropically.

Background Evolution  Average and difference Hubble rates  Modified background system (Einstein + scalar field eqns.)  e.g. analytical solution for constant V=V 0

Perturbations  To make use of residual symmetries consider longitudinal and transverse modes separately  Longitudinal see an isotropic expansion in the orthogonal directions. longitudinal transverse  Transverse see an anisotropic expansion.

Longitudinal Modes  Perturbed metric seen by modes propagating in x-direction. Extra curvature perturbation which transforms separately  Still have gauge invariant combination  Mukhanov-Sasaki equation.

Transverse Modes  Perturbed metric seen by modes propagating in y, z-directions. One less symmetry  tensor mode couples with scalar.  ``Tensor’’ mode coupled with scalar.  Q is gauge dependent.  Scalar + tensor equation system more complex (Q, Ψ, Φ, h xx ).

Power Spectra  Numerical calculation of axisymmetric power spectrum k iso h ini

Calculation of CMB anisotropies  Expansion has isotropized by end of inflation.  Einstein-Boltzmann integration is unaffected except for initial conditions  Relic Anisotropy.  Most general form of axisymmetric P(k).  Symmetries generate a specific pattern in covariance matrix.

Axisymmetric CMB Covariances  Calculate full covariance matrix for multipoles.

Power Spectra  Numerical calculation of axisymmetric power spectrum

Axisymmetric CMB Covariances

Axisymmetric pixel-pixel correlation

Relic Anisotropy on the Sky  Random realization of an axisymmetric covariance matrix.

Isotropic scale fits  Preliminary fits to data  Marginalize over all axis orientations and initial amplitude.  (fixed initial h)  1-dim marginalized likelihood for k iso [Gumrukcuoglu, Contaldi & Peloso, in prep]

Conclusions  Model gives alignments in multipoles (even).  Slight selection by the data -- ``Axis of Evil’’?  Full anisotropic case (H a, H b, H c ) could fit l by l correlations better.  (short-term) future is NOT miserable!  Large scale modes are special!  Lots of information on anisotropy (temp + polarization)!  Much better constraints on foregrounds soon