Extending the ΛCDM model through shear-free anisotropies

Abstract

If the spacetime metric has anisotropic spatial curvature, one can still expand the universe as if it were isotropic, provided that the energy–momentum tensor satisfies a certain constraint. This leads to the so-called shear-free (SF) metrics, which have the interesting property of violating the cosmological principle while still preserving the isotropy of the cosmic microwave background (CMB) radiation. In this work, we show that SF cosmologies correspond to an attractor solution in the space of models with anisotropic spatial curvature. Through a rigorous definition of linear perturbation theory in these spacetimes, we show that SF models represent a viable alternative to explain the large-scale evolution of the universe, leading, in particular to a kinematically equivalent Sachs–Wolfe (SW) effect. Alternatively, we discuss some specific signatures that SF models would imprint on the temperature spectrum of CMB.