Beta-function formalism for k-essence constant-roll inflation

Understand

The beta function formalism is being used to study the constant-roll inflation in the k-essence model.

• Assuming the second slow-roll parameter as a constant leads to a first-order differential equation for $\beta$-function which is much easier to solve and find a solution than the second (non-linear) order equation that we have in corresponding standard constant-roll inflation.
• Many cosmological models are known as a subclass of k-essence, so we will try to consider the model as general as possible.
• It is determined that the second slow-roll parameter should be positive to produce a small value for the first slow-roll parameter.