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arXiv · 1908.06654

Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) Polynomial Affine Gravity

Oscar Castillo-Felisola·Jose Perdiguero·Oscar Orellana·Alfonso R. Zerwekh
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Abstract

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 \emph{emergent} metric on the manifold. We show that there exists a parametrization in which the \((r,\varphi)\)-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 \emph{trajectories} of massive and massless particles.

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Oscar Castillo-Felisola, Jose Perdiguero, Oscar Orellana, Alfonso R. Zerwekh. 2019-08-19. Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) Polynomial Affine Gravity. https://doi.org/10.1088/1361-6382%2Fab58ef

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