Here the scalar field
[phi], the metric 00-and 11-components [e.
So, in general terms the limit V [right arrow] [infinity] renders the system singular, and also 2[omega] + 3 [right] 0 implies [absolute value of H] [right arrow] [infinity] with the same conclusion that passing through [omega]([PSI]) = - 3/2 (corresponding to the change of the sign of the scalar field
kinetic term in the Einstein frame action) would entail a space-time singularity and is impossible.
The procedures that the above four models commonly follow in the explanation of the SNeIa measurements include the following four steps: (1) Modifying the FE with an appropriate input of [LAMBDA], scalar field
, perturbation, or external energy; (2) Determining the expansion rates (Hubble parameter) of the universe according to their modified FEs; (3) Submitting their expansion rates into the [D.
The material time derivative of the scalar field
f (r,t) [member of] R is its substantial derivative
The scalar field
that was introduced to the cosmology in various models has also been considered as a candidate of dark energy for the acceleration of the universe.
Can Brans-Dicke Scalar Field
Account for Dark Energy and Dark Matter?
Van Vlaenderen obtained a scalar field
for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For instance one can begin with the inhomogeneous scalar field
cosmologies with exponential potential , where the scalar field
component of Einstein-Klein-Gordon equation can be represented in terms of:
Finite element formulation for scalar field
problems in multidimensions
These spaces have a single scalar field
for which the field equation was written and the particular solutions were found for the spherical symmetry and for the rhombododecaedron symmetry of the space.
ij] on the boundary, needed to cancel the second derivatives in R(4) when the action is varied with the metric and scalar field
, but not their normal derivatives, fixed on the boundary.
The degeneration of some parts of the flow into circles (topological features) results in in-homogeneities and gives rise to a scalar field
, analogous to the gravitational field.