Non-perturbative scalar gauge-invariant metric fluctuations from the Ponce de Leon metric in the STM theory of gravity

We study our non-perturbative formalism to describe scalar gauge-invariant metric fluctuations by extending the Ponce de Leon metric.Comment: accepted in Eur. Phys. J.

Scale invariant scalar metric fluctuations during inflation: non-perturbative formalism from a 5D vacuum

We extend to 5D an approach of a 4D non-perturbative formalism to study scalar metric fluctuations of a 5D Riemann-flat de Sitter background metric. In contrast with the results obtained in 4D, the spectrum of cosmological scalar metric fluctuations during inflation can be scale invariant and the background inflaton field can take sub-Planckian values.Comment: final version to be published in Eur. Phys. J.

Seminal magnetic fields from Inflato-electromagnetic Inflation

We extend some previous attempts to explain the origin and evolution of primordial magnetic fields during inflation induced from a 5D vacuum. We show that the usual quantum fluctuations of a generalized 5D electromagnetic field cannot provide us with the desired magnetic seeds. We show that special fields without propagation on the extra non-compact dimension are needed to arrive to appreciable magnetic strengths. We also identify a new magnetic tensor field $B_{ij}$ in this kind of extra dimensional theories. Our results are in very good agreement with observational requirements, in particular from TeV Blazars and CMB radiation limits we obtain that primordial cosmological magnetic fields should be close scale invariance.Comment: Improved version. arXiv admin note: text overlap with arXiv:1007.3891 by other author

A Note On Stochastic Calculus In Vector Bundles

The aim of these notes is to relate covariant stochastic integration in a vector bundle E [as in Norris (Séminaire de Probabilités, XXVI, vol. 1526, Springer, Berlin, 1992, pp. 189-209)] with the usual Stratonovich calculus via the connector [cf. e.g. Paterson (Canad. J. Math. 27(4):766-791, 1975) or Poor (Differential Geometric Structures, McGraw-Hill, New York, 1981)] which carries the connection dependence. © 2013 Springer International Publishing Switzerland.2078353364Arnaudon, M., Thalmaier, A., Hoizontal martingales in vector bundles. Séminaire de Probabilit ́es XXXVI (2003) Lecture Notes in Math, 1801, pp. 419-456. , Springer, BerlinCatuogno, P.J., Stelmastchuk, S., Martingales on frame bundles (2008) Potential Anal, 28 (1), pp. 61-69Driver, B.K., Thalmaier, A., Heat equation derivative formulas for vector bundles (2001) J. Funct. Anal, 183 (1), pp. 42-108Eells, J., Lemaire, L., Selected topics in harmonic maps (1983) CBMS Regional Conference Series in Mathematics, 50. , American Mathematical Society, Providence, RIEmery, M., (1989) Stochastic Calculus in Manifolds, , With An Appendix By P. A. Meyer. Universitext Springer BerlinNorris, J.R., A complete differential formalism for stochastic calculus in manifolds. Séminaire de Probabilités XXVI (1992) Lecture Notes in Math, 1526, pp. 189-209. , Springer, BerlinPatterson, L.N., Connexions and prolongations (1975) Canad. J. Math, 27 (4), pp. 766-791Poor, W.A., (1981) Differential Geometric Structures, , McGraw-Hill New YorkXin, Y., Geometry of harmonic maps (1996) Progress in Nonlinear Differential Equations and Their Applications, 23. , Birkhäuser Boston, Boston, M

Harmonic Measures In Embedded Foliated Manifolds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We study harmonic and totally invariant measures in a foliated compact Riemannian manifold. We construct explicitly a Stratonovich differential equation for the foliated Brownian motion. We present a characterization of totally invariant measures in terms of the flow of diffeomorphisms associated to this equation. We prove an ergodic formula for the sum of the Lyapunov exponents in terms of the geometry of the leaves. © 2017 World Scientific Publishing Company.17411/50151, FAPESP, Fundação de Amparo à Pesquisa do Estado de São Paulo15/07278-0, FAPESP, Fundação de Amparo à Pesquisa do Estado de São PauloFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP