Accelerated cosmological models in Ricci squared gravity

By G. Allemandi, A. Borowiec, Mauro Francaviglia. 2004

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Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of the Universe at present time. In this paper we proceed further in this analysis of cosmological applications of alternative gravitational theories depending on (other) curvature invariants. We introduce Ricci squared Lagrangians in minimal interaction with matter (perfect fluid); we find modified Einstein equations and consequently modified Friedmann equations in the Palatini formalism. It is striking that both Ricci scalar and Ricci squared theories are described in the same mathematical framework and both the generalized Einstein equations and generalized Friedmann equations have the same structure. In the framework of the cosmological principle, without the introduction of exotic forms of dark energy, we thus obtain modified equations providing values of ${w}_{\mathrm{e}\mathrm{f}\mathrm{f}}l\ensuremath{-}1$ in accordance with the experimental data. The spacetime bi-metric structure plays a fundamental role in the physical interpretation of results and gives them a clear and very rich geometrical interpretation.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/eac5a2402a11e4c926f9ac9bc07bb1f2ca2a99a4

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Citations in the corpus

f(R) Theories (2010, background): “Originally the model f(R) = R − α/R (α > 0, n > 0) was proposed to explain the late-time cosmic acceleration [113, 120, 114, 143] (see also [456, 559, 17, 223, 212, 16, 137, 62] for related works).”
Cosmological constraints on f(R) gravity theories within the Palatini approach (2005, background): “…system constraints in its weak field limit (Clifton & Barrow 2005; Barrow & Clifton 2006; Quandt & Schmidt 1991; Dominguez & Barraco 2004; Sotiriou 2005a,b; Olmo 2005a,b; Capozziello 2002; Carloni et al. 2005; Barraco et al. 2002; Hwang & Noh 2001; Mena et al. 2005; Allemandi et al. 2004a,b, 2005).”