Quiet@Block[{Print},
<<xAct`xTras`
]

DefManifold[M,4,IndexRange[a,j]]

DefMetric[-1,metric[-a,-b],CD,PrintAs->"g",CurvatureRelations->True,Torsion->False]

DefTensor[phi[],M,PrintAs->"φ"]

DefTensor[V[],M,PrintAs->"V[ϕ]"]

DefTensor[xi[-a],M,PrintAs->"ξ"]

xi[-a]=CD[-a][phi[]]
xi[-b]=CD[-b][phi[]]
DefTensor[W[],M]

W[]=metric[a ,b]*xi[-a]*xi[-b]//ContractMetric

DefConstantSymbol[om,PrintAs->"ω"]

lag= -phi[]*RicciScalarCD[]+(om/(phi[]))*W[]

eomPhi =VarD[phi[],CD][lag]//ContractMetric//ToCanonical

eomMetric = VarL[metric[-a,-b],CD][lag]//ContractMetric//RicciToEinstein//ToCanonical