In this work, we show that the zero field excitation spectra in the quantum spin ice candidate pyrochlore compound Yb2Ti2O7 is a continuum characterized by a very broad and almost flat dynamical response which extends up to 1 − 1.5 meV, coexisting or not with a quasi-elastic response depending on the wave-vector. The spectra do not evolve between 50 mK and 2 K, indicating that the spin dynamics is only little affected by the temperature in both the short-range correlated and ordered regimes. Although classical spin dynamics simulations qualitatively capture some of the experimental observations, we show that they fail to reproduce this broad continuum. In particular, the simulations predict an energy scale twice smaller than the experimental observations. This analysis is based on a careful determination of the exchange couplings, able to reproduce both the zero field diffuse scattering and the spin wave spectrum rising in the field polarized state. According to this analysis, Yb2Ti2O7 lies at the border between a ferro and an antiferromagnetic phase. These results suggest that the unconventional ground state of Yb2Ti2O7 is governed by strong quantum fluctuations arising from the competition between those phases. The observed spectra may correspond to a continuum of deconfined spinons as expected in quantum spin liquids. arXiv:1506.01729v1 [cond-mat.str-el]