Geometric interpretation of the dark energy from projected hyperconical universes

Abstract

This letter explores the derivation of dark energy from a locally conformal projection of hyperconical universes. It focuses on the analysis of theoretical compatibility between the intrinsic view of the standard cosmology and an adequate transformation of hyperconical manifolds. Choosing some parametric family of locally conformal transformations and taking regional (second order) equality between the Hubble parameter of both theories, it is predicted that the dark energy density is ΩΛ = 0.6937181(2). In particular, we used a radially distorted stereographic projection, the distortion parameter of which is theoretically predicted about α = 0.325 ± 0.005 and empirically fitted as α = 0.36 ± 0.02 (χ 2 0 = 562) according to 580 SNe Ia observations.PACS numbers: 98.80.Es, 98.80.Jk

Lagrangian density and local symmetries of inhomogeneous hyperconical universes

“…Moreover, there exists a family of locally conformal transformations that lead the (linearly expanding and curved) metrics to become the flat FRW metric, absorbing the spatial inhomogeneity as an acceleration in time. That predicted a dark energy density about Ω Λ = 0.6937181(2) (presented in [17]), compatible with the standard-model-dependent observation (Ω Λ = 0.690( 6)) [21,22]. The relation between radial inhomogeneity, Lagrangian curvature terms and effective dark energy is also found in other modified gravities, but without a prediction of its value [23,24,25,26,7,27].…”

“…The aim of this paper is to analyse the symmetry properties of a radially inhomogeneous hyperconical model according to the Killing vectors of the metric, the Lagrangian formalism and the Arnowitt-Deser-Misner (ADM) equations [18,19,20]. This work expands new results obtained from the family of metrics proposed in [16,17]. The model is also based on the same hypothesis of linear expansion as [14,15], but analyses the curvature tensor according to the point of view of a hypothetical observer located in the hypersurface of an expanding universe (hypercone section), which can have both positive or negative curvature.…”

“…If the Hubble parameter is defined as H :=ȧ/a, this linear expansion corresponds to H = 1/t, which is compatible with the empirical age of the universe [10,13,11,12]. For this reason, alternative cosmological models are based on the equality 1/H = t, such as the Dirac-Milne model and the inhomogeneous hyperconical model [14,15,16,17]. However, symmetry properties of these universes have not been analysed yet, so it is necessary to explore conserved quantities and contrast them with physical observables.…”

“…A summary of the used model is described in this section, according to [16,17]. Let M ⊂ R 1,4 η be a support manifold contained in the 5-dimensional Minkowski space, more specifically M := (R ≥0 × R 4 , η 1,4 ), with inner product (•) given by the usual Lorentzian metric η of signature (1,4).…”

“…Let y (t) := (t, 0, −νt) O be antipodal in S 3 t of the comoving observer x (t) = (t, 0, νt), with t ∈ R ≥0 . [17] analysed the locally conformal family of azimuthal projections f α : T t (S 3…”