Scalar field dynamics Sample Clauses

Scalar field dynamics. ‌ The scalar field that is going to drive inflation is called the inflaton (φ), with action Sφ = ∫ d4x√−gLφ ; Lφ = 1 gµν∂ 2 µ φ − V (φ) , (1.19) where V (φ) is the inflaton potential and g the determinant of the metric gµν. The equation of motion for the inflaton is obtained by varying the action with respect to φ. For a FRW metric we get ∇2φ ˙ dV φ − a2 + 3Hφ + = 0 , (1.20) where ∇2 is the Laplacian. For consistency with the FRW symmetries we impose a homogeneous field distribution throughout the universe at the background level φ(t, x) = φ(t), then ∇2φ = 0. To recover the Einstein equations of motion, the stress energy density is Tµν = 2 ∂Lφ ∂gµν + gµνLφ