In most of the inflationary models, or quintessence models, a scalar field has been used to describe the dynamics. Why is this? I know that some models use vector fields, but if you want to use scalars, what are the arguments behind using it?
Ali,
scalar fields are not located in a particular place, they permeate the universe. In a way they represent a smooth background, which may, however couple to other fields in physically interesting ways. To observe them is a challenge.
Matts,
thanks for the swift reply. But does this mean that vector (or higher rank) fields do not spread all over the place? Is there any argument related to the spin of the field under consideration( for example if we were using a vector field to describe the inflaton, we have to take the polarization vector into account)?
Ali,
The general statement is just that scalar fieds are constant in space,
How to use scalar fields together with higher-rank fields is model dependent.
Is it not to do with the fact that scalars are the most basic fields?
Vectors are gradients of scalars.
So if we want to inflate something, we dump a heap of it on the ground (described as a scalar) and look at the way it disperses(described with vectors; both linear and rotational.
As Mohamed said, it is to do with complexity.
This may be due to a large number of physical quantities like inertial mass, stress energy tensor, potentials are associated with some or another kind of scalar fields.
Einstein’s gravitational theory contains two constants, the gravitational constant G and the cosmological constant Λ. It does not have solutions corresponding to inflationary cosmologies. The Jordan-Brans-Dicke theory arose from the question “what if G were not, in fact, constant?” If it’s not a constant then it is ipso facto a scalar field (more precisely, the reciprocal of a scalar field...). The dynamics of that scalar field contained an adjustable parameter, thus allowing cosmological solutions different from the standard Robertson-Walker solutions of Einstein’s theory. Similarly, we can suppose that the cosmological “constant” Λ might be not a constant but a scalar field. If I’ve understood correctly, this gives us the scope to postulate various kinds of dynamics for that scalar field, and we then have a range of phenomenological cosmological theories in which we can appeal to adjustable parameters (“fudge-factors”) to try to fit the theory to the observations – in particular, to the inflationary scenarios and to account for the mysterious “dark energy”.
The answer to "why scalar fields?" is "because that's the simplest way of attempting to fit the theory to the observations."
Eric,
I did not phrase my answer carefully enough. So let me quote Wikipedia for once.
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 value of the scalar field at the same point in space (or spacetime). Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory.
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