The simplest possible classical model leading to a cosmological bounce is examined in the light of the non-Gaussianities it can generate. Concentrating solely on the transition between contraction and expansion, and assuming initially purely Gaussian
perturbations at the end of the contracting phase, we find that the bounce acts as a source such that the resulting value for the post-bounce $f_{mathrm{NL}}$ may largely exceed all current limits, to the point of potentially casting doubts on the validity of the perturbative expansion. We conjecture that if one can assume that the non-Gaussianity production depends only on the bouncing behavior of the scale factor and not on the specifics of the model examined, then many realistic models in which a nonsingular classical bounce takes place could exhibit a generic non-Gaussianity excess problem that would need to be addressed for each case.
We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic
term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussianities are generically produced at the bounce itself and also discuss which shapes of non-gaussianities are mostly likely to be produced.
We calculate a two-pion wave function for the I=2 $S$-wave two-pion system with a finite scattering momentum and estimate the interaction range between two pions, which allows us to examine the validity of a necessary condition for the finite size fo
rmula presented by Rummukainen and Gottlieb. We work in the quenched approximation employing the plaquette gauge action for gluons and the improved Wilson action for quarks at $1/a=1.63 {rm GeV}$ on $32^3times 120$ lattice. The quark masses are chosen to give $m_pi = 0.420$, 0.488 and $0.587 {rm GeV}$. We find that the energy dependence of the interaction range is small and the necessary condition is satisfied for our range of the quark mass and the scattering momentum, $k le 0.16 {rm GeV}$. We also find that the scattering phase shift can be obtained with a smaller statistical error from the two-pion wave function than from the two-pion time correlator.
