Adapted from P. Coles, 1999, *The Routledge Critical
Dictionary of the New Cosmology*, Routledge Inc., New York. Reprinted
with the author's permission. To order this book click here:
http://www.routledge-ny.com/books.cfm?isbn=0415923549

In the standard **Friedmann models** on which the **Big Bang
theory** is based, the material components of the Universe are generally
described as if they were perfect classical fluids with a well-defined
density and pressure
*p*. Models of such perfect fluids can describe
most of the **thermal history of the Universe** quite adequately, but for
the very early Universe they are expected to break down. At very high
temperatures it is necessary to describe matter using **quantum field
theory** rather than fluid mechanics, and this requires some alterations
to be made to the relevant **cosmological models**.

One idea which emerges from these considerations, and which is now
ubiquitous in modern cosmology, is the idea that the dynamical
behaviour of the early Universe might be dominated by a variety of
quantum field called a *scalar field*. A scalar field is characterised
by some numerical value, which we shall call
. It can be a function
of spatial position, but for the purposes of illustration we take it
to be a constant. (A *vector field* would be characterised by a set of
numbers for each spatial position, like the different components of
spin, for example.) We can discuss many aspects of this kind of entity
without having to use detailed **quantum theory** by introducing the
concept of a *Lagrangian action* to describe its interactions. The
Lagrangian for a scalar field can be written in the form

*L*() = 1/2 (d / d*t*)^{2} -
*V*()

The first of these terms is usually called the *kinetic term* (it looks
like the square of a velocity), while the second is the *potential term*
(*V* is a function that describes the interactions of the field). The
Lagrangian action is used to derive the equations that show how
varies with time, but we do not need them for this discussion. The
appropriate energy-momentum **tensor** to describe such a field in the
framework of **general relativity** can be written in the form

*T _{ij}* =

where *g _{ij}* is the metric, and

*t*)^{2} +
*V*()

and

*p* = 1/2 (d /
d*t*)^{2} - *V*()

If the kinetic term is negligible with respect to the potential term,
the effective equation of state for the field becomes *p* = -. This
is what happens during the **phase transitions** that are thought the
drive the **inflationary Universe** model. Under these conditions the
field behaves in exactly the same way as an effective **cosmological
constant** with

*G* /
*c*^{2}

where we have replaced the required factor of *c*^{2} in
this expression.

Despite the fact that the scalar field can behave as a fluid in certain situations, it is important to realise that it is not like a fluid in general. If is oscillating, for example, there is no definite relationship between the effective pressure and the effective energy density.

FURTHER READING: Kolb, F.W. and Turner, M.S., *The Early Universe*
(Addison-Wesley, Redwood City, CA, 1990).