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Dark matter problem and effective curvature Lagrangians. (English) Zbl 1080.83024

It is shown that the dependence of the effective Lagrangian \(L\) on the scalar curvature \(R\) is generically singular and cannot always be represented analytically in the \((R,L)\) plane. It is found that, although nonlinear, \(L=L(R)\) bifurcates in several branches of almost linear Lagrangians distinguished only by the effective gravitational constant \(k_{\text{eff}}\) and a cosmological constant \(\Lambda_{\text{eff}}\).

MSC:

83F05 Relativistic cosmology
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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