In either case the Friedman equation thus takes the form:įriedman’s solutions suggest that there is a critical density at which the universe must be flat, where the ratio of the total mass-energy density to the critical density is known as the density parameter Note, this result can also be found by assuming a static universe (i.e. dark energy), which is the current consensus in both cosmology and particle physics then the cosmological constant can be interpreted as an energy density and given in terms of the dark energy density, If we then take the assumption that the universe is pervaded by a form of energy (i.e. The Friedman equation for a flat universe (i.e. Is the radius of the observable universe (i.e.īased on astronomical observations the current cosmological model states that we live in a flat,ĭominated, homogeneous and isotropic universe, composed of radiation, baryonic matter and non-baryonic dark matter. Where a is the scaling factor, k is the curvature constant and The Robertson-Walker solution, which states that the rest frame of the fluid must be the same as the co-moving observer, reduces the Einstein equations to two Friedman equations:
Is the stress-energy tensor, which is modeled as a perfect fluid such that: Is the metric tensor, r is the scalar curvature and With the inclusion of the cosmological constant, Einstein’s field equations are: de Sitter, steady state and the Lemaitre models, whereĪcts as an additional expanding (dark energy) force. However, since then the universe was found to be accelerating and many cosmological models have been put forward with a nonzeroĮ.g. Originally included to allow for static homogenous solutions to Einstein’s equations, it was subsequently removed when the expansion of the universe was discovered. The Einstein field equations of general relativity include a constant To resolve this discrepancy, we first review the fundamental nature of the vacuum energy density and its relationship to the cosmological constant. It is one of the biggest disagreements between theory, experiment and observation and is known as the vacuum catastrophe. The vacuum energy density predicted by quantum field theory disagrees with cosmological observation by approximately 122 orders of magnitude.
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