Different approaches to the second-order Klein-Gordon equation
journal contribution
posted on 2023-06-07, 22:41authored byKarim A Malik, David SeeryDavid Seery, Kishore N Ananda
We derive the Klein-Gordon equation for a single scalar field coupled to gravity at second order in perturbation theory and leading order in slow-roll. This is done in two ways: we derive the Klein-Gordon equation first using the Einstein field equation and then directly from the action after integrating out the constraint equations. We also point out an unexpected result regarding the treatment of the field equations