Isotropic universes with a preferred direction

Abstract

We present a class of cosmological scenarios in which a preferred spatial direction in the matter sector coexists with an exactly homogeneous and isotropic Friedmann--Lema\^ıtre--Robertson--Walker (FLRW) geometry. The Cosmological Principle is realized on shell, with the vector-field equations enforcing a vanishing momentum density and suitable interactions eliminating the anisotropic stress. Consequently, the construction yields an entire FLRW branch without tuning the matter-field initial conditions. The preferred direction reemerges in perturbations, producing direction-dependent propagation and mixing among scalar, vector, and tensor modes already at linear order. In particular, the mixing opens a linear channel through which perturbations in the scalar sector can in principle source gravitational waves. Our construction thus reveals a new route by which preferred-direction physics can leave observable cosmological signatures while remaining hidden in the background geometry.