Cosmological perturbations in the Palatini formulation of modified gravity

By Tomi Koivisto, H. Kurki-Suonio. 2005

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Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the homogeneous and isotropic but possibly spatially curved background. The results are presented in a unified form applicable to a broad class of gravity theories allowing arbitrary scalar–tensor couplings and nonlinear dependence on the Ricci scalar in the gravitational action. The gauge-ready formalism exploited here makes it possible to obtain the equations immediately in any of the commonly used gauges. Of the three type of perturbations, the main attention is on the scalar modes responsible for the cosmic large-scale structure. Evolution equations are derived for perturbations in a late universe filled with cold dark matter and accelerated by curvature corrections. Such corrections are found to induce effective pressure gradients which are problematical in the formation of large-scale structure. This is demonstrated by analytic solutions in a particular case. A physical equivalence between scalar–tensor theories in metric and in Palatini formalisms is pointed out.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d4cc617df02c9556b797920ba19482b2adb10a9c

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Citations in the corpus

Modified Gravity and Cosmology (2011, unknown): “For studies of weak field gravity in the Palatini formalism the reader is referred to [92, 429, 881, 999, 30, 1000, 1163, 1001, 1078, 224, 665, 31, 1077], and for cosmology to [1251, 509, 883, 28, 882, 884, 29, 1162, 1164, 724, 34, 727, 258, 793, 1232, 725, 781, 782, 497].”
f(R) Theories (2010, background): “Koivisto and Kurki-Suonio [359] derived perturbation equations in Palatini f (R) gravity.”
Hybrid Metric-Palatini Gravity (2015, background): “One then finds that the scalar φ turns out to be an algebraic function of the trace of the stress-energy tensor of the matter, φ = φ(T ), which may lead, in models of late-time cosmic speed-up, to undesired gradient instabilities at various contexts, as has been shown by studies of cosmological pert”
f(R) Theories Of Gravity (2008, methodology): “Cosmological density perturbations in the Palatini formalism have been studied in (Amarzguioui et al., 2006; Carroll et al., 2006; Koivisto, 2006b, 2007; Koivisto and Kurki-Suonio, 2006; Lee, 2007, 2008; Li et al., 2007b; Uddin et al., 2007).”