In general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, Newtonian gauge is a perturbed form of the Friedmann-Lemaitre-Robertson-Walker line element. The gauge freedom

Gauge theory

In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...

 of general relativity is used to eliminate two scalar degrees of freedom of the metric, so that it can be written as
where the Latin indices a and b are summed over the spatial directions and is the Kronecker delta. Conformal Newtonian gauge is the closely related gauge in which
which is related by the simple transformation . These metrics are perturbed forms of the Friedmann-Lemaitre-Robertson-Walker metric. They are called Newtonian gauge because is the Newtonian gravitational potential of classical Newtonian gravity, which satisfies the Poisson equation  for non-relativistic matter and on scales where the expansion of the universe may be neglected. It includes only scalar

Scalar field

In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...

 perturbations of the metric: by the scalar-vector-tensor decomposition

Scalar-vector-tensor decomposition

In cosmological perturbation theory, the scalar-vector-tensor decomposition is a decomposition of the most general linearized perturbations of the Friedmann-Lemaitre-Robertson-Walker metric into components according to their transformations under spatial rotations. It was first discovered by E. M....

 these evolve independently of the vector and tensor

Tensor

Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

 perturbations and are the predominant ones affecting the growth of structure in the universe in cosmological perturbation theory

Cosmological perturbation theory

In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the big bang model. It uses general relativity to compute the gravitational forces causing small perturbations to grow and eventually seed the formation of stars, quasars,...

. The vector perturbations vanish in cosmic inflation

Cosmic inflation

In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...

 and the tensor perturbations are gravitational waves, which have a negligible effect on physics except for the so-called B-modes of the cosmic microwave background polarization. The tensor perturbation is truly gauge independent, since it is the same in all gauges.

In a universe without anisotropic stress (that is, where the stress-energy tensor

Stress-energy tensor

The stress–energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields...

 is invariant under spatial rotations, or the three principal pressures are identical) the Einstein equation sets .