Physical Foundations of Cosmology

5.6 “Menu” of scenarios 259

is inflation not satisfactory ifpdepends only onX? Consider a generalp(X,φ)

without an explicit potential term, that is,p→0 whenX→0. Formulate the

conditions which this function must satisfy to provide us with a slow-roll infla-

tionary stage and a graceful exit. The inflationary scenario based on the nontrivial

dependence of the Lagrangian on the kinetic term is calledkinflation.

ScenariosThe simplest inflationary scenarios can be subdivided into three classes.

They correspond to the usual scalar field with a potential, higher-derivative gravity

andkinflation. The cosmological consequences of scenarios from the different

classes are almost indistinguishable−they can exactly imitate each other. Within

each class, however, we can try to make further distinctions by addressing the

questions: (a) what was before inflation and (b) how does a graceful exit to a

Friedmann stage occur? For our purpose it will be sufficient to consider only the

simplest case of a scalar field with canonical kinetic energy. The potential can have

different shapes, as shown in Figure 5.7. The three cases presented correspond to

the so-called old, new and chaotic inflationary scenarios. The first two names refer

to their historical origins.

Old inflation(see Figure 5.7(a)) assumes that the scalar field arrives at the local

minimum of the potential atφ=0 as a result of a supercooling of the initially

hot universe. After that the universe undergoes a stage of accelerated expansion

with a subsequent graceful exit via bubble nucleation. It was clear from the very

beginning that this scenario could not provide a successful graceful exit because

all the energy released in a bubble is concentrated in its wall and the bubbles have

no chance to collide. This difficulty was avoided in the new inflationary scenario,

a scenario similar to a successful model in higher-derivative gravity which had

previously been invented.

New inflationis based on a Coleman–Weinberg type potential (Figure 5.7(b)).

Because the potential is very flat and has a maximum atφ=0, the scalar field

VV V

φφ φ

(a) (b) (c)

Fig. 5.7.