Different approaches to the second order Klein-Gordon equation

Abstract

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 equations, 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.

9 pages, revtex4

References in corpus (7)

• The cosmological gravitational wave background from primordial density perturbations
• A Microscopic Limit on Gravitational Waves from D-brane Inflation
• Non-gaussianity from the second-order cosmological perturbation
• Phenomenology of D-Brane Inflation with General Speed of Sound
• Comparing Infrared Dirac-Born-Infeld Brane Inflation to Observations
• Vector modes generated by primordial density fluctuations
• Non-linear vector perturbations in a contracting universe