It is argued that the amplitudes of the production of n soft scalar particles by one or a few energetic ones in theories like λϕ 4 has the exponential form,

We study spatially flat bouncing cosmologies and models with the early-time Genesis epoch in a popular class of generalized Galileon theories. We ask whether there exist solutions of these types which are free of gradient and ghost instabilities. We find that irrespectively of the forms of the Lagrangian functions, the bouncing models either are plagued with these instabilities or have singularities. The same result holds for the original Genesis model and its variants in which the scale factor tends to a constant as t → −∞. The result remains valid in theories with additional matter that obeys the Null Energy Condition and interacts with the Galileon only gravitationally. We propose a modified Genesis model which evades our no-go argument and give an explicit example of healthy cosmology that connects the modified Genesis epoch with kination (the epoch still driven by the Galileon field, which is a conventional massless scalar field at that stage).

We suggest a mechanism explaining the origin of three generations of the Standard Model fermions from one generation in a higher-dimensional theory.Four-dimensional fermions appear as zero modes trapped in the core of a topological defect with topological number three. We discuss hierarchical pattern of masses and mixings which arises in these models.