Abstract
We report a new symmetry of the Einstein–Friedmann equations for spatially flat Friedmann- Lemaître-Robertson-Walker universes. We discuss its application to barotropic perfect fluids and its use as a solution-generating technique for scalar field universes.
Highlights
In general-relativistic cosmology, the matter content of the universe is typically modelled by a perfect fluid with energy density ρ(t) and isotropic pressure P(t) related by a barotropic equation of state P = P(ρ)
General symmetries of the Einstein–Friedmann equations involve transformations of the variables a, t, H, ρ, and P
It is common in cosmology to impose the equation of state P = wρ with w = const. while searching for symmetries, in which case one transforms the set of variables (ρ, a, t, P), but the relation imposed between P and ρ restrict the generality
Summary
In comoving coordinates (t, r, θ, φ), where gab is the metric tensor, a(t) is the cosmic scale factor, K is the curvature index, and dΩ(22) = dθ2 + sin θ dφ is the line element on the unit 2-sphere [1] In this geometry, the Einstein field equations. J. C (2020) 80:1002 symmetry of these equations and discuss its possible uses for FLRW universes filled with a perfect fluid with barotropic, linear, and constant equation of state and for scalar fields minimally coupled to the spacetime curvature. C (2020) 80:1002 symmetry of these equations and discuss its possible uses for FLRW universes filled with a perfect fluid with barotropic, linear, and constant equation of state and for scalar fields minimally coupled to the spacetime curvature This symmetry generalizes one previously introduced in Ref. This symmetry generalizes one previously introduced in Ref. [2] (see [3,4,6,10,11,14,15,21]) and studied recently in Ref. [26]
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