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We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of D3 branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological timescale of 10 10 years. We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

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Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we briefly describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance, which we called preheating. It may occur in an expanding universe if the initial amplitude of oscillations of the inflaton field is large enough. We investigate a simple model of a massive inflaton field φ coupled to another scalar field χ with the interaction term g 2 φ 2 χ 2 . Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is quite different from parametric resonance in the case when the expansion of the universe is neglected. Quantum fields interacting with the oscillating inflaton field experience a series of kicks which, because of the rapid expansion of the universe, occur with phases uncorrelated to each other. Despite the stochastic nature of the process, it leads to exponential growth of fluctuations of the field χ. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and backreaction of produced particles, including the effects of rescattering. This investigation extends our previous study of reheating after inflation [1]. We show that the contribution of the produced particles to the effective potential V (φ) is proportional not to φ 2 , as is usually the case, but to |φ|. The process of preheating can be divided into several distinct stages. In the first stage the backreaction of created particles is not important. In the second stage backreaction increases the frequency of oscillations of the inflaton field, which makes the process even more efficient than before. Then the effects related to scattering of χ-particles on the oscillating inflaton field terminate the resonance. We calculate the number density of particles nχ produced during preheating and their quantum fluctuations χ 2 with all backreaction effects taken into account. This allows us to find the range of masses and coupling constants for which one can have efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field. PACS: 98.80.CqIfA-97-28 SU-ITP-97-18 hep-ph/9704452

The theory of reheating of the Universe after inflation is developed. We have found that typically at the first stage of reheating the classical inflaton field φ rapidly decays into φ-particles or into other bosons due to a broad parametric resonance. Then these bosons decay into other particles, which eventually become thermalized. Complete reheating is possible only in those theories where a single particle φ can decay into other particles. This imposes strong constraints on the structure of inflationary models, and implies that the inflaton field can be a dark matter candidate.

We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well known difficulty of brane–antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.

This is the LaTeX version of my book "Particle Physics and Inflationary Cosmology" (Harwood, Chur, Switzerland, 1990). I decided to put it to hep-th, to make it easily available. Many things happened during the 15 years since the time when it was written. In particular, we have learned a lot about the high temperature behavior in the electroweak theory and about baryogenesis. A discovery of the acceleration of the universe has changed the way we are thinking about the problem of the vacuum energy: Instead of trying to explain why it is zero, we are trying to understand why it is anomalously small. Recent cosmological observations have shown that the universe is flat, or almost exactly flat, and confirmed many other predictions of inflationary theory. Many new versions of this theory have been developed, including hybrid inflation and inflationary models based on string theory. There was a substantial progress in the theory of reheating of the universe after inflation, and in the theory of eternal inflation.It s clear, therefore, that some parts of the book should be updated, which I might do sometimes in the future. I hope, however, that this book may be of some interest even in its original form. I am using it in my lectures on inflationary cosmology at Stanford, supplementing it with the discussion of the subjects mentioned above. I would suggest to read this book in parallel with the book by Liddle and Lyth "Cosmological Inflation and Large Scale Structure," with the book by Mukhanov "Physical Foundations of Cosmology," which is to be published soon, and with my review article hep-th/0503195, which contains a discussion of some (but certainly not all) of the recent developments in inflationary theory.

Usually inflation ends either by a slow rolling of the inflaton field, which gradually becomes faster and faster, or by a first-order phase transition. We describe a model where inflation ends in a different way, due to a very rapid rolling ('waterfall') of a scalar field σ triggered by another scalar field φ. This model looks as a hybrid of chaotic inflation with V (φ) = m 2 φ 2 2 PACS number 98.80.Cq 1 On leave from: Lebedev Physical Institute,