A Model of Universe Anisotropization

TL;DR

The paper investigates how a Lorentz-violating term in the photon sector, the Kostelecký term, can amplify magnetic fluctuations during inflation when a specific anisotropic form of the external tensor $(k_F)_{\alpha\beta\mu\nu}$ is assumed. This leads to a plane-symmetric (planar) cosmic magnetic field whose present-day strength can be of order nanogauss, potentially explaining galactic and intergalactic magnetic fields and inducing a small anisotropy described by a Bianchi I metric. The anisotropic expansion generates a modified CMB quadrupole, offering a natural mechanism for the observed low quadrupole and an axis of evil alignment, while leaving higher multipoles largely unaffected at leading order. The authors further analyze the post-inflation evolution of the field through reheating and the primordial plasma, derive the quadrupole solutions, and discuss observational constraints from CMB polarization, outlining testable predictions for future polarization data.

Abstract

The presence of a nonconformally invariant term in the photon sector of the Lorentz-violating extension of Standard Model of particle physics, the "Kostelecký term" $\mathcal{L}_K \propto (k_F)_{αβμν} F^{αβ} F^{\m ν}$, enables a superadiabatic amplification of magnetic vacuum fluctuations during de Sitter inflation. For a particular form of the external tensor $k_F$ that parameterizing Lorentz violation, the generated field possesses a planar symmetry at large cosmological scales and can have today an intensity of order of nanogauss for a wide range of values of parameters defining inflation. This peculiar magnetic field could account for the presently-observed galactic magnetic fields and induces a small anisotropization of the universe at cosmological scales. The resulting Bianchi I model could explain the presumedly low-quadrupole power in the Cosmic Microwave Background radiation.

Figures (2)

• Figure 1: The plane-symmetric, scale-invariant, inflation-produced magnetic field has an actual intensity of order of nanogauss if the values of parameter defining inflation, i.e. the energy scale of inflation $M$ and the reheat temperature $T_{\rm RH}$, stay on the curves. $k_F \sim ||(k_F)_{\alpha \beta \mu \nu}||$ estimates the magnitude of the (constant) external tensor which parametrizes Lorentz violation [see Eqs. (\ref{['Action']}) and (\ref{['k3003']})].
• Figure 2: Numerical solutions of Eq. (\ref{['alm']}) obtained by using the three maps in Table I. Note that $b = 90^{\circ} - \vartheta$, and $l = \varphi$, where $(b,l)$ are the galactic coordinates. The two open circles at $(b,l) \simeq (20^{\circ},130^{\circ})$ and $(b,l) \simeq (10^{\circ},110^{\circ})$ define the direction of the axis of evil determined in Ref. Groeneboom for the 5-year WMAP temperature sky maps in V-band and W-band, respectively.