Some basic equations relevant for fully relativistic as well as perturbative cosmological calculations are summarized in this section, including the complete Einstein equations, choices of kinematical conditions, initial data constraints, stress-energy-momentum tensors, dynamical equations for various matter sources, and the Newtonian counterparts on background isotropic models. References to numerical methods are also provided.

6.1 The Einstein equations

6.1.1 ADM formalism

6.1.2 Kinematic conditions

6.1.3 Symplectic formalism

6.1.4 Regge calculus model

6.2 Sources of matter

6.2.1 Cosmological constant

6.2.2 Scalar field

6.2.3 Collisionless dust

6.2.4 Ideal gas

6.2.5 Imperfect fluid

6.3 Constrained nonlinear initial data

6.4 Newtonian limit

6.4.1 Dark and baryonic matter equations

6.4.2 Primordial chemistry

6.4.3 Numerical methods

6.4.4 Linear initial data

6.1.1 ADM formalism

6.1.2 Kinematic conditions

6.1.3 Symplectic formalism

6.1.4 Regge calculus model

6.2 Sources of matter

6.2.1 Cosmological constant

6.2.2 Scalar field

6.2.3 Collisionless dust

6.2.4 Ideal gas

6.2.5 Imperfect fluid

6.3 Constrained nonlinear initial data

6.4 Newtonian limit

6.4.1 Dark and baryonic matter equations

6.4.2 Primordial chemistry

6.4.3 Numerical methods

6.4.4 Linear initial data

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