Study of the observational compatibility of an inhomogeneous cosmology with linear expansion according to SNe Ia

Abstract

Most of current cosmological theories are built combining an isotropic and homogeneous manifold with a scale factor that depends on time. If one supposes a hyperconical universe with linear expansion, an inhomogeneous metric can be obtained by an appropriate transformation that preserves the proper time. This model locally tends to a flat Friedman-Robertson-Walker metric with linear expansion. The objective of this work is to analyse the observational compatibility of the inhomogeneous metric considered. For this purpose, the corresponding luminosity distance was obtained and was compared with the observations of 580 SNe Ia, taken from the Supernova Cosmology Project (SCP). The best fit of the hyperconical model obtains χ 2 0 = 562, the same value that the standard ΛCDM model. Finally, a possible relationship is found between both theories.

Geometric interpretation of the dark energy from projected hyperconical universes

“…For example, hyperconical universes produce inhomogeneous metrics compatible with the observed expansion and they locally approach to the flat FRW metric. To be consistent with the ΛCDM model, it can be assumed as a local perturbation theory in inhomogeneous universes expanding regardless of the matter content [7]. On the other hand, physical properties of inhomogeneous spaces are interesting because they can be used to trace dark energy and dark matter [8].…”

“…Metric. From the above hypotheses, a radially inhomogeneous metric g is obtained with the same local Ricci curvature as the flat FRW metric [7]. The nonzero elements in comoving polar coordinates (t, r , θ, φ) are g 00 = 2k −1 (b−1)+1, g r r = −a 2 /b 2 , g 0r = −ar /tôb, g θθ = −a 2 r 2 and g φφ = −a 2 r 2 sin 2 θ; where k −1 := 1 − β 2 ± is the spatial curvature, a(t) := t/tô is the scale factor and b(r ) 2 := 1 − kr 2 /t 2 o is an auxiliary function.…”

Lagrangian density and local symmetries of inhomogeneous hyperconical universes

“…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).…”