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We study spatially flat bouncing cosmologies and models with the early-timeGenesis epoch in a popular class of generalized Galileon theories. We askwhether there exist solutions of these types which are free of gradient andghost instabilities. We find that irrespectively of the forms of the Lagrangianfunctions, the bouncing models either are plagued with these instabilities orhave singularities. The same result holds for the original Genesis model andits variants in which the scale factor tends to a constant as $t\to -\infty$.The result remains valid in theories with additional matter that obeys the NullEnergy Condition and interacts with the Galileon only gravitationally. Wepropose a modified Genesis model which evades our no-go argument and give anexplicit example of healthy cosmology that connects the modified Genesis epochwith kination (the epoch still driven by the Galileon field, which is aconventional massless scalar field at that stage).

Generalized Galileons: instabilities of bouncing and Genesis cosmologies and modified Genesis