Relic Anisotropy as the source of all Evil?

Carlo ContaldiImperial College London

+Marco Peloso & Emir GumrukcuogluUniversity of Minnesota, Minneapolis

astro-ph/0608405

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/0303636 ]

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/0701783]

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/0403270].

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=V0

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, hxx).

Power Spectra

Numerical calculation of axisymmetric power spectrum

kiso

hini

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 kiso

[Gumrukcuoglu, Contaldi & Peloso, in prep]

Conclusions

Model gives alignments in multipoles (even).

Slight selection by the data -- ``Axis of Evil’’?

Full anisotropic case (Ha, Hb, Hc) 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