We calculate the probability of pair creation in vacuum in d + 1 dimensions (with d = 3,2,1), by an alternating electromagnetic field, in three cases. First, we consider an electromagnetic field composed of an alternating electric field and of a constant uniform magnetic field. Next, we consider the situation when both the electric and magnetic fields are purely alternating. Finally, we complete this analysis with the case of production of Dirac particles in vacuum by a constant uniform electromagnetic field and a plane wave.

We propose a new potential in brane inflation theory, which is given by the arctangent of the square of the scalar field. Then we perform an explicit computation for inflationary quantities. This potential has many nice features. In the small field approximation, it reproduces the chaotic and MSSM potentials. It allows one, in the large field approximation, to implement the attractor mechanism for bulk black holes where the geometry on the brane is de Sitter. In particular, we show, up to some assumptions, that the Friedman equation can be reinterpreted as a Schwarzschild black hole attractor equation for its mass parameter.

We consider a Minimal Supersymmetric Standard Model (MSSM) inflation in the context of the Randall-Sundrum type-2 braneworld model. We apply the slow-roll approximations, in high-energy limit, to constraint various inflationary spectrum parameters in relation with recent WMAP9 data. We show that, for some values of the number of efolding N , the MSSM braneworld inflation provides the best fit results according to recent observations.

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