By Mukhanov V.

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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 (see “Bibliography”). Old inflation (see Fig. 7a) assumes that the scalar field arrives at the local minimum of the potential at ϕ = 0 as a result of a supercooling of the initially hot universe. After that the universe undergoes a stage of accelerated expansion with 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.

By solving these extra problems, inflation opens the door to theories that would otherwise be prohibited by cosmology. Depending on one’s attitude, this is either a useful or damning achievement of inflation. De Sitter solution and inflation. The last point we would like to make concerns the role of a cosmological constant and a pure de Sitter solution for inflation. We have already said that the pure de Sitter solution cannot provide us with a model with a graceful exit. Even the notion of expansion is not unambiguously defined in de Sitter space.

This can easily be understood. Einstein gravity is the only metric theory in four dimensions where the equations of motion are second order. Any modification of the Einstein action introduces higher derivative terms. This means that, in addition to the gravitational waves, the gravitational field has extra degrees of freedom including, generically, a spin zero field. Problem 15. Consider a gravity theory with metric gµν and action S= √ f (R) −gdx, 1 16π (108) where f (R) is an arbitrary function of the scalar curvature R.

### Inflation Homogeneous Limit by Mukhanov V.

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