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 [8], 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.