Common use of Cosmology Clause in Contracts

Cosmology. ‌ I restrict to an isotropic and homogeneous space to find the background cosmological dynamics, following the definitions in section 2.8. Writing the constraint as C = C(a, ψ, R) where R = R(a, ψ, p¯, π), the equations of motion are given by, a˙ = 1 ∂R ∂C , p¯˙ = −1 ( ∂C + ∂R ∂C ) , N 6a ∂p¯ ∂R N 6a ∂a ∂a ∂R ψ˙ = ∂R ∂C , π˙ = − ∂C − ∂R ∂C , N ∂π ∂R N ∂ψ ∂ψ ∂R into which I can substitute ∂C = a3√|β|. When I assume minimal coupling (ωR′ = 0, ωψ′ = 0) and time-symmetry (ξ = 0), the equations of motion become, −3σβp¯2 3 kωR σβπ2 ψ ˙ R → ωRa2 − a2 + 2ω a6 , ωR a˙ = −σβp¯√|β|, ψ = σβ π √|β|, π˙ ∂C = − , (5.61) ωψa3 = p¯˙ −1 ∂C 6a |β| a2 + a2 − 2ω √ ( σβp¯2 kωR R a6