- Specify a space-time.
- Specify a set of gauge fields.
- Specify a set of elementary particles, and partition them into a finite number of generations.
- Specify the strengths of the gauge fields.
- Specify the couplings between the gauge fields and the elementary particles.
- Specify the direct ('Yukawa') couplings between elementary particles.
- Specify the 'mixing' between the elementary particles in different generations.
- Specify cosmological parameters corresponding to the initial conditions for the universe.
This list is based upon the understanding gleaned from general relativistic cosmology and the standard model of particle physics, the latter being an application of quantum field theory. Both these theories are empirically verified. I do not intend to consider how one might define a physical universe according to speculative theories such as string theory or supersymmetry.
Our own physical universe is specified as follows:
- Space-time is a 4-dimensional pseudo-Riemannian manifold with three spatial dimensions and one time dimension.
- There are three force fields: the strong nuclear force, the weak nuclear force, and the electromagnetic force. The weak and electromagnetic fields are unified in the electroweak gauge field.
- The elementary particles consist of quarks, leptons and gauge bosons. Elementary particles are divided into fermions and bosons according to the value they possess of a property called 'intrinsic spin'. If a particle possesses a non-integral value of intrinsic spin, it is referred to as a fermion, whilst if it possesses an integral value, it is referred to as a boson. The particles of the elementary matter fields are fermions and the interaction carriers of the gauge force fields are bosons. The elementary fermions come in two types: leptons and quarks. Whilst quarks interact via both the strong and electroweak forces, leptons interact via the electroweak force only. There are three generations of elementary fermions in our universe.
- The strength of each gauge field is specified by what physicists call the 'coupling constants' of the gauge field.
- To specify the couplings between the gauge fields and the elementary particles, the values of the 'charges' possessed by elementary particles are specified. For example, in the case of couplings between particles and the electromagnetic force, the strength of the coupling is determined by the electromagnetic charge of the particle.
- Our universe appears to be subject to spontaneous symmetry breaking caused by Higgs fields, in which case the values of coefficients in the Yukawa matrices specify the direct interactions between the Higgs bosons and the elementary fermions.
- The mixing between the quarks in different generations is specified by the Cabibbo-Kobayashi-Maskawa (CKM) matrix. If, as current evidence indicates, the neutrinos possess mass, then there is a corresponding notion of lepton mixing, and the CKM matrix has a lepton counterpart called the Maki-Nakagawa-Sakata matrix.
- Our universe is taken to be spatially homogeneous, and to specify cosmological parameters corresponding to the initial conditions for such a universe, the global symmetry group (or Killing Lie algebra) of the homogeneous 3-dimensional space is specified, along with the dynamical parameters which determine the time evolution of the 3-dimensional geometry, such as the Hubble parameter, and the density parameter, Omega.