Abstract
We study the wave equation for the gravitational fluctuations in the Randall–Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L1-L∞, L2-L∞ decay estimates and global Lp Strichartz type inequalities. We develop the complete scattering theory: existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.
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