Balancing Anisotropic Curvature with Gauge Fields in a Class of Shear-Free Cosmological Models

Abstract

We present a complete list of general relativistic shear-free solutions in a class of anisotropic, spatially homogeneous and orthogonal cosmological models containing a collection of $n$ independent $p$-form gauge fields, where $p\in \{0,1,2,3\}$, in addition to standard $\Lambda$CDM matter fields modelled as perfect fluids. Here a (collection of) gauge field(s) balances anisotropic spatial curvature on the right-hand side of the shear propagation equation. The result is a class of solutions dynamically equivalent to standard FLRW cosmologies, with an effective curvature constant $K_{\mathrm{eff}}$ that depends both on spatial curvature and the energy density of the gauge field(s). In the case of a single gauge field ($n=1$) we show that the only spacetimes that admit such solutions are the LRS Bianchi type III, Bianchi type VI${}_0$ and Kantowski-Sachs metric, which are dynamically equivalent to open ($K_{\mathrm{eff}}<0$), flat ($K_{\mathrm{eff}}=0$) and closed ($K_{\mathrm{eff}}>0$) FLRW models, respectively. With a collection of gauge fields ($n>1$) also Bianchi type II admits a shear-free solution ($K_{\mathrm{eff}}>0$). We identify the LRS Bianchi type III solution to be the unique shear-free solution with a gauge field Hamiltonian bounded from below in the entire class of models.

33 pages, see pages 4-7 for summary of main results. V3: matches published version, cites V2 for more details and discussion

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Cited by in corpus (8)

• Gauge Field Mimetic Cosmology
• Bianchi cosmologies with $p$-form gauge fields
• Tensor Perturbations in Anisotropically Curved Cosmologies
• Extended FLRW Models: dynamical cancellation of cosmological anisotropies
• Bianchi models with a free massless scalar field: invariant sets and higher symmetries
• Dynamically equivalent ΛCDM equations with underlying Bianchi Type geometry
• Approaching Wonderland
• Collins in Wonderland