be , according to results published by the Planck Collaboration in 2018. In a flat universe, is the fraction of the energy of the universe due to the cosmological constant, i.e., what we would intuitively call the fraction of the universe that is made up of dark energy. Note that this value changes over time: The critical density changes with cosmological time but the energy density due to the cosmological constant remains unchanged throughout the history of the universe, because the amount of dark energy increases as the universe grows but the amount of matter does not. Equation of state Another ratio that is used by scientists is the equation of state, usually denoted , which is the ratio of pressure that dark energy puts on the universe to the energy per unit volume. This ratio is for the cosmological constant used in the Einstein equations; alternative time-varying forms of vacuum energy such as quintessence generally use a different value. The value = , measured by the Planck Collaboration (2018) is consistent with , assuming does not change over cosmic time. Positive value Observations announced in 1998 of distance–redshift relation for Type Ia supernovae indicated that the expansion of the universe is accelerating, if one assumes the cosmological principle. When combined with measurements of the cosmic microwave background radiation these implied a value of ≈ 0.7, a result which has been supported and refined by more recent measurements (as well as previous works). If one assumes the cosmological principle, as in the case for all models that use the Friedmann–Lemaître–Robertson–Walker metric, while there are other possible causes of an accelerating universe, such as quintessence, the cosmological constant is in most respects the simplest solution. Thus, the Lambda-CDM model, the current standard model of cosmology which uses the FLRW metric, includes the cosmological constant, which is measured to be on the order of . It may be expressed as (by multiplication with , i.e. ≈) or as 10−122 ℓ−2 (where ℓ is the Planck length). The value is based on recent measurements of vacuum energy density, = ≘ = . However, due to the Hubble tension and the CMB dipole, recently it has been proposed that the cosmological principle is no longer true in the late universe and that the FLRW metric breaks down, so it is possible that observations usually attributed to an accelerating universe are simply a result of