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Scalar perturbations in f(R) cosmologies in the late Universe

Jan Novák (2017)

Archivum Mathematicum

Standard approach in cosmology is hydrodynamical approach, when galaxies are smoothed distributions of matter. Then we model the Universe as a fluid. But we know, that the Universe has a discrete structure on scales 150 - 370 MPc. Therefore we must use the generalized mechanical approach, when is the mass concentrated in points. Methods of computations are then different. We focus on f ( R ) -theories of gravity and we work in the cell of uniformity in the late Universe. We do the scalar perturbations...

Sharp L 1 estimates for singular transport equations

Sergiu Klainerman, Igor Rodnianski (2008)

Journal of the European Mathematical Society

We provide L 1 estimates for a transport equation which contains singular integral operators. The form of the equation was motivated by the study of Kirchhoff–Sobolev parametrices in a Lorentzian space-time satisfying the Einstein equations. While our main application is for a specific problem in General Relativity we believe that the phenomenon which our result illustrates is of a more general interest.

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