Geometric scalar model‌ Sample Clauses

Geometric scalar model‌. ( ) As demonstrated in the previous chapter, section 2.4.1, the geometric scalar model comes from parameterising F (4)R gravity so that the additional degree of freedom of the scalar curvature is instead embodied in a non-minimally coupled scalar field ψ [77, 80]. Its couplings are given by ωR = ψ and ωψ = 0. This model is a special case of the Xxxxx- Xxxxx model, which has ωψ = ω0/ψ, when the Dicke coupling constant ω0 vanishes. I can add in a minimally coupled scalar field with ωφ = 1 and thereby see the effect of this scalar-tensor gravity on the matter sector. However, I set ωφ = 0 because it does not significantly affect my results. The effective action for this model is given by, β β Lgeo = 1 √q |β| {ψ (R − K ) − νψ v − 2∆ψ} − √q U (ψ) , (3.50a) ( ) U (ψ) = ψ (F ′)−1 (ψ) − 1 F ((F ′)−1 (ψ)) , (3.50b) where F refers to the F (4)R function which has been parameterised. The equations of motion when β → 1 are given by, H (ψH + ψ˙ = 1 U, ) (3.51a) ∂U a 3 ∂ψ a¨ = −H2 + 1 , (3.51b) 3 ∂a ∂ψ ψ¨ = −2ψ˙H + ψH2 + (1 + a ∂ 2 ψ ∂ − ) U, (3.51c) from which I can see that the scalar field has very different dynamics compared to minim- ally coupled scalars. This reflects its origin as a geometric degree of freedom rather than a purely matter field.