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We introduce a new set of flow parameters to describe the time dependence ofthe equation of state and the speed of sound in single field cosmologicalmodels. A scale invariant power spectrum is produced if these flow parameterssatisfy specific dynamical equations. We analyze the flow of these parametersand find four types of fixed points that encompass all known single fieldmodels. Moreover, near each fixed point we uncover new models where the scaleinvariance of the power spectrum relies on having simultaneously time varyingspeed of sound and equation of state. We describe several distinctive newmodels and discuss constraints from strong coupling and superluminality.

The four fixed points of scale invariant single field cosmological models