| We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is sub-dominant otherwise. This is unlike standard perturbation theory, where different loop corrections can become of the same magnitude in the nonlinear regime. We calculate the resummation of the propagator and compare to measurements in numerical simulations, showing a remarkably good agreement well into the nonlinear regime.; Provided with the nonlinear propagator we computed the first diagrams corresponding to mode coupling effects described above. This allows a description of the nonlinear power spectrum down to mildly nonlinear scales that shows an excellent agreement between theory and simulations never accomplished before beyond linear theory for the currently accepted cosmological model.; Additionally we show that this formalism is particularly suitable to understand the nonlinear evolution of the baryon acoustic oscillations in the matter power spectrum. These features, matter counterpart of the famous acoustic peaks in the spectrum of the Cosmic Microwave Background anisotropies, had been detected in the late time clustering of galaxies and are considered as potentially the best probe of Dark Energy. |
