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

We systematically investigate shear-free cosmological models realized by p-form gauge fields; a scenario in which anisotropic spatial sections expand isotropically with expansion histories equivalent to standard FLRW models. Specifically, 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 addidtion to standard LCDM 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 $K_\text{eff}$ 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 ($K\text{eff}<0$), flat ($K_\text{eff}=0$) and closed ($K_\text{eff}>0$) FLRW models, respectively. With a collection of gauge fields ($n>1$) also Bianchi type II admits a shear-free solution ($K_\text{eff}>0$). 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. This is a generalization and unification of the shear-free solutions discovered by Carneiro et. al. (2001) with a massless scalar field and by Koivisto et. al. (2011) with a 2-form gauge field, which we show are physically equivalent at the field strength $p+1$ level. Along the way we develop strategies and a framework that can be utilized in a broader class of models.

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M. Thorsrud
Fri, 8 Dec 17

Comments: 52 pages, see page 5-7 for summary of main results