An Anisotropic Cosmological Model with Isotropic Background Radiation

Abstract

Abstract. We present an exact solution of Einstein equations that describes a Bianchi type III spacetime with conformal expansion. The matter content is given by an anisotropic scalar field and two perfect fluids representing dust and isotropic radiation. Based on this solution, we construct a cosmological model that respects the evolution of the scale factor predicted in standard cosmology.A crucial question in cosmology is whether the observed isotropy of the cosmic microwave background (CMB), together with the apparent homogeneity and isotropy of clustering matter, suffices to guarantee the Cosmological Principle. An affirmative answer is strongly supported by a theorem proved by Ehlers, Geren and Sachs [1]. The EGS theorem ensures that a spacetime region satisfying Einstein equations and containing only dust and radiation has a Friedmann-Robertson-Walker (FRW) geometry provided that the dust velocity field u µ is (geodesic and) expanding, and that the distribution function of the photons is a solution to the Liouville equation which is isotropic with respect to u µ . In fact, the result that the geometry is FRW depends critically on the hypotheses of the theorem, and there exist counterexamples in which all but one of the assumptions are satisfied [2][3][4]. The theorem admits generalizations for matter consisting in a generic (barotropic) perfect fluid [2], and for an almost isotropic CMB [5], case in which the geometry is approximately of the FRW form.We will concentrate our discussion on the validity of the EGS theorem when one relaxes the assumption about the kind of matter content. This is important in modern cosmology because, in order to explain the observed acceleration detected with type Ia supernovae, scalar fields are often introduced to generate a quintessence component. It was recently shown that the conclusions of the EGS theorem remain valid in the presence of a quitessence field unless the gradient of the field is orthogonal to the dust congruence [4]. This alternative to the FRW geometry has been neglected so far because it is believed to lead to unphysical situations. We will show, nevertheless, that it is possible to find physically acceptable systems in which the commented alternative allows one to circumvent the Cosmological Principle.The most general line-element and Einstein tensor compatible with an isotropic radiation can be found in [2]. The aim of the present work is to explicitly construct a feasible solution to the Einstein equations respecting this isotropy of the CMB. This task includes determining not only the metric, but also the matter content. Furthermore, we want such a content to be of cosmological and physical interest, in the sense that it must be composed of dust, radiation, and a scalar field, and that none of the energy conditions (weak, strong or dominant) is violated. In addition, we will accept that both the perfect fluid components and the spatial sections of the spacetime are homogeneous.Our ansatz for the metric isThis is a Bianchi type III metric, with Killing...

SNe Ia tests of quintessence tracker cosmology in an anisotropic background

“…It possesses the Killing vectors ξ 1 = ∂ x − y∂ y , ξ 2 = ∂ y , ξ 3 = ∂ z . It has also an additional conformal Killing vector ξ µ C = δ µ 0 , which guarantees the isotropy of CMB on this background [26]. This spacetime is the product of the real line and a hyperbolic manifold, R×H 2 .…”

Tensor perturbations in anisotropically curved cosmologies

“…The interplay between the energy-momentum tensor and the shear-free condition was further explored in [36,37]. An analogous result was also found by Carneiro and Marugán [38,39] who deployed a clever use of an anisotropic scalar field to balance the anisotropy of the spatial curvature. Under this condition the scale factor has the same dynamics of a spatially curved Friedmann-Lemaître-Robertson-Walker (FLRW) universe and the metric can be brought to a conformally static form.…”

Cosmological signatures of anisotropic spatial curvature

“…This can be done either by introducing a stress component in the energy-momentum tensor [21] or a two-form field [24]. We can also take the simpler route provided by the choice of scalar fields, which can be chosen to be a real massless field in the BIII case [22,23], or a complex massless field in the KS case [33]. Thus, our matter sector is composed of two fields: the inflaton, whose perturbations can be introduced exactly as in the FLRW case (see, for example, [34]), and the above anisotropic and massless scalar field φ(η, x).…”

“…However, once we are willing to abandon the isotropy hypothesis of the cosmological principle, much richer models can be constructed besides the Bianchi I solution [16][17][18][19][20]. In fact, it has been demonstrated in references [18,[21][22][23] that the anisotropy of the universe does not need to emerge from its dynamical expansion; instead, it could result from the curvature of spatial sections, while having the expansion controlled by one scale factor, at the cost of having an imperfect fluid sourcing the anisotropic curvature. This idea has been successfully applied in the context of late-time anisotropies in references [24][25][26].…”