Chaotic dynamics in preheating after inflation

We study chaotic dynamics in preheating after inflation in which an inflaton $\phi$ is coupled to another scalar field $\chi$ through an interaction $(1/2)g^2\phi^2\chi^2$. We first estimate the size of the quasi-homogeneous field $\chi$ at the beginning of reheating for large-field inflaton potentials $V(\phi)=V_0\phi^n$ by evaluating the amplitude of the $\chi$ fluctuations on scales larger than the Hubble radius at the end of inflation. Parametric excitations of the field $\chi$ during preheating can give rise to chaos between two dynamical scalar fields. For the quartic potential ($n=4$, $V_0=\lambda/4$) chaos actually occurs for $g^2/\lambda <{\cal O}(10)$ in a linear regime before which the backreaction of created particles becomes important. This analysis is supported by several different criteria for the existence of chaos. For the quadratic potential ($n=2$) the signature of chaos is not found by the time at which the backreaction begins to work, similar to the case of the quartic potential with $g^2/\lambda \gg 1$.Comment: 12 pages, 10 figures, Version to appear in Classical and Quantum Gravit

Inflation and nonequilibrium renormalization group

We study de spectrum of primordial fluctuations and the scale dependence of the inflaton spectral index due to self-interactions of the field. We compute the spectrum of fluctuations by applying nonequilibrium renormalization group techniques.Comment: 6 pages, 1 figure, submitted to J. Phys.

Testing String Theory with CMB

Future detection/non-detection of tensor modes from inflation in CMB observations presents a unique way to test certain features of string theory. Current limit on the ratio of tensor to scalar perturbations, r=T/S, is r < 0.3, future detection may take place for r > 10^{-2}-10^{-3}. At present all known string theory inflation models predict tensor modes well below the level of detection. Therefore a possible experimental discovery of tensor modes may present a challenge to string cosmology. The strongest bound on r in string inflation follows from the observation that in most of the models based on the KKLT construction, the value of the Hubble constant H during inflation must be smaller than the gravitino mass. For the gravitino mass in the usual range, m_{3/2} < O(1) TeV, this leads to an extremely strong bound r < 10^{-24}. A discovery of tensor perturbations with r > 10^{-3} would imply that the gravitinos in this class of models are superheavy, m_{3/2} > 10^{13} GeV. This would have important implications for particle phenomenology based on string theory.Comment: 13 pages, 2 figure

Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem

This paper extends the recent investigation of the string theory landscape in hep-th/0605266, where it was found that the decay rate of dS vacua to a collapsing space with a negative vacuum energy can be quite large. The parts of space that experience a decay to a collapsing space, or to a Minkowski vacuum, never return back to dS space. The channels of irreversible vacuum decay serve as sinks for the probability flow. The existence of such sinks is a distinguishing feature of the string theory landscape. We describe relations between several different probability measures for eternal inflation taking into account the existence of the sinks. The local (comoving) description of the inflationary multiverse suffers from the so-called Boltzmann brain (BB) problem unless the probability of the decay to the sinks is sufficiently large. We show that some versions of the global (volume-weighted) description do not have this problem even if one ignores the existence of the sinks. We argue that if the number of different vacua in the landscape is large enough, the anthropic solution of the cosmological constant problem in the string landscape scenario should be valid for a broad class of the probability measures which solve the BB problem. If this is correct, the solution of the cosmological constant problem may be essentially measure-independent. Finally, we describe a simplified approach to the calculations of anthropic probabilities in the landscape, which is less ambitious but also less ambiguous than other methods.Comment: 42 pages, 5 figures, the paper is substantially extended, a section on the cosmological constant is addeed; the version published in JCA

Susskind's Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions

Given the observed cosmic acceleration, Leonard Susskind has presented the following argument against the Hartle-Hawking no-boundary proposal for the quantum state of the universe: It should most likely lead to a nearly empty large de Sitter universe, rather than to early rapid inflation. Even if one adds the condition of observers, they are most likely to form by quantum fluctuations in de Sitter and therefore not see the structure that we observe. Here I present my own amplified version of this argument and consider possible resolutions, one of which seems to imply that inflation expands the universe to be larger than 10^{10^{10^{122}}} Mpc.Comment: 24 pages, LaTeX, 8 references added and a distinction between Linde's and Vilenkin's tunneling proposal

Brane inflation and the WMAP data: a Bayesian analysis

The Wilkinson Microwave Anisotropy Probe (WMAP) constraints on string inspired ''brane inflation'' are investigated. Here, the inflaton field is interpreted as the distance between two branes placed in a flux-enriched background geometry and has a Dirac-Born-Infeld (DBI) kinetic term. Our method relies on an exact numerical integration of the inflationary power spectra coupled to a Markov-Chain Monte-Carlo exploration of the parameter space. This analysis is valid for any perturbative value of the string coupling constant and of the string length, and includes a phenomenological modelling of the reheating era to describe the post-inflationary evolution. It is found that the data favour a scenario where inflation stops by violation of the slow-roll conditions well before brane annihilation, rather than by tachyonic instability. Concerning the background geometry, it is established that log(v) > -10 at 95% confidence level (CL), where "v" is the dimensionless ratio of the five-dimensional sub-manifold at the base of the six-dimensional warped conifold geometry to the volume of the unit five-sphere. The reheating energy scale remains poorly constrained, Treh > 20 GeV at 95% CL, for an extreme equation of state (wreh ~ -1/3) only. Assuming the string length is known, the favoured values of the string coupling and of the Ramond-Ramond total background charge appear to be correlated. Finally, the stochastic regime (without and with volume effects) is studied using a perturbative treatment of the Langevin equation. The validity of such an approximate scheme is discussed and shown to be too limited for a full characterisation of the quantum effects.Comment: 65 pages, 15 figures, uses iopart. Shortened version, updated references. Matches publication up to appendix B kept on the arXi