Using the latest CMB data, the Mukhanov parametrization of the inflationary equation of state is viable only for 1.5 < α ≤ 2.2, and non-detection of gravitational waves by future missions would rule it out.
Whereas EoS formalism helps us obtain observational predictions at ease without going into the details of underlying physics
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Returning Back to Mukhanov Parametrization of Inflationary Equation of State
Using the latest CMB data, the Mukhanov parametrization of the inflationary equation of state is viable only for 1.5 < α ≤ 2.2, and non-detection of gravitational waves by future missions would rule it out.