Following the density perturbations through a bounce with AdS/CFT Correspondence

A bounce universe model, known as the coupled-scalar-tachyon bounce (CSTB) universe, has been shown to solve the Horizon, Flatness and Homogeneity problems as well as the Big Bang Singularity problem. Furthermore a scale invariant spectrum of primordial density perturbations generated from the phase of pre-bounce contraction is shown to be stable against time evolution. In this work we study the detailed dynamics of the bounce and its imprints on the scale invariance of the spectrum. The dynamics of the gravitational interactions near the bounce point may be strongly coupled as the spatial curvature becomes big. There is no a prior reason to expect the spectral index of the primordial perturbations of matter density can be preserved. By encoding the bounce dynamics holographically onto the dynamics of dual Yang-Mills system while the latter is weakly coupled, via the AdS/CFT correspondence, we can safely evolve the spectrum of the cosmic perturbations with full control. In this way we can compare the post-bounce spectrum with the pre-bounce one: in the CSTB model we explicitly show that the spectrum of primordial density perturbations generated in the contraction phase preserves its stability as well as scale invariance throughout the bounce process.Comment: 19 pages, 4 figure

On-Shell Gauge Invariant Three-Point Amplitudes

Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches. Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field $\phi$ and an antisymmetric rank-2 tensor field $A_{\mu\nu}$. Despite the well-known fact that in 4 dimensions rank-2 anti-symmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.Comment: significantly revised, final version published in JHE