We study in detail the equations of the geodesic deviation in multidimensional theories of KaluzaKlein type. We show that their 4-dimensional space-time projections are identical with the equations obtained by direct variation of the usual geodesic equation in the presence of the Lorentz force, provided that the fifth component of the deviation vector satisfies an extra constraint derived here.

General relativity, black holes, and cosmology: A course for nonscientists Am.

Moduli fields generically produce strong dark matter -radiation and baryon -radiation isocurvature perturbations through their decay if they remain light during inflation. We show that existing upper bounds on the magnitude of such fluctuations can thus be translated into stringent constraints on the moduli parameter space mσ (modulus mass)σ inf (modulus vacuum expectation value at the end of inflation). These constraints are complementary to previously existing bounds so that the moduli problem becomes worse at the perturbative level. In particular, if the inflationary scale H inf ∼ 10 13 GeV, particle physics scenarios which predict high moduli masses mσ 10 − 100 TeV are plagued by the perturbative moduli problem, even though they evade big-bang nucleosynthesis constraints.PACS numbers: 98.80.Cq, 98.70.Vc

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