Recovering the cosmological constant from affine geometry

Boskoff, Wladimir-Georges; Capozziello, Salvatore

doi:10.1142/s0219887819501615

Cited by 6 publications

(2 citation statements)

References 23 publications

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“…Further studies, which take the nature of the dark sector into account, will need to be undertaken. Interesting proposals-in models other than the polynomial affine model of Gravitycould be found in [71,[75][76][77][78][79][80][81].…”

Section: Conclusion and Remarksmentioning

confidence: 99%

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Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) polynomial affine gravity

Castillo-Felisola

Perdiguero

Orellana

et al. 2020

Class. Quantum Grav.

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Starting from an affinely connected space, we consider a model of gravity whose fundamental field is the connection. We build up the action using as sole premise the invariance under diffeomorphisms, and study the consequences of a cosmological ansatz for the affine connection in the torsion-free sector. Although the model is built without requiring a metric, we show that the nondegenerated Ricci curvature of the affine connection can be interpreted as an emergent metric on the manifold. We show that there exists a parametrization in which the (r, ϕ)-restriction of the geodesics coincides with that of the Friedman-Robertson-Walker model. Additionally, for connections with nondegenerated Ricci we are able to distinguish between space-, time-and null-like self-parallel curves, providing a way to differentiate trajectories of massive and massless particles.

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Section: Conclusion and Remarksmentioning

confidence: 99%

“…Very recently, it has been pointed that from an affine point of view, the nature of the cosmological constant is related with the volume preserving property (instead of being related to the sectional curvature)[71] 22. See[57,72,73] 23.…”

mentioning

confidence: 99%

Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) polynomial affine gravity

Castillo-Felisola

Perdiguero

Orellana

et al. 2020

Class. Quantum Grav.

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Emerging hyperbolic spaces and some considerations in AdS cosmology

Pigazzini¹,

Pinčák

Jafari

et al. 2022

Int. J. Geom. Methods Mod. Phys.

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Recently, PNDP-manifolds have been introduced, and these have shown to be useful in applicative aspects especially in the field of cosmology, introducing a new geometric/topological approach to the concept of “emerging space”. However, the applications considered so far concern only trivial and flat PNDP-manifolds. Therefore, we show the existence of non-Ricci-flat solutions for PNDP-manifolds with positive “virtual” dimension which have hyperbolic [Formula: see text]-manifold. Based on this, we have advanced an applicative hypothesis, accompanied by some open considerations, in the context of [Formula: see text] cosmology.

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Cosmological constant and AdS spacetimes from Minkowski spheres

Boskoff

Capozziello

2022

Int. J. Geom. Methods Mod. Phys.

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A theory of gravity without masses can be constructed starting from Minkowski [Formula: see text] spaces. The corresponding adapted [Formula: see text] Minkowski potentials, gradients and Laplacians built on each signature lead to a field equation similar to the Newton-Laplace one. In this framework, the anti-de Sitter spacetime is a hypersurface described by a constant potential of Minkowski gravitational force in absence of matter. We show that the cosmological constant of the anti-de Sitter spacetimes is related to a geometric property of Minkowski spheres: the centro-affine conservation of volumes defined from the so-called Minkowski–Tzizteica affine spheres. It is possible to show the connection between the anti-de Sitter [Formula: see text] space, the non-Euclidean geometry and the difference between Minkowski [Formula: see text] sphere and the pseudosphere seen as a surface of the [Formula: see text]-Euclidean space. According to a suitable parameterization, the relation between de Sitter and anti-de Sitter spacetimes in any dimension is fixed. As a consequence, the light can travel in any anti-de Sitter spacetime defining the geodesic structure. These considerations can be recast in terms of Einstein field equations with cosmological constant and extended to [Formula: see text] gravity.

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Recovering the cosmological constant from affine geometry

Cited by 6 publications

References 23 publications

Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) polynomial affine gravity

Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) polynomial affine gravity

Emerging hyperbolic spaces and some considerations in AdS cosmology

Cosmological constant and AdS spacetimes from Minkowski spheres

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