Strange nonchaotic attractors in noise driven systems

Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an intermittent way, forms a strange attractor gradually. The existence of SNAs is confirmed by simulation results of various critera both in map and continuous systems. Dimension transition is found and intermittent behavior is studied by peoperties of local Lyapunov exponent. The universality and generalization of this kind of SNAs are discussed and common features are concluded

One-loop Evolution of a Rolling Tachyon

We study the time evolution of the one-loop diagram in Sen's rolling tachyon background. We find that at least in the long cylinder case they grow rapidly at late time, due to the exponential growth of the timelike oscillator terms in the boundary state. This can also be interpreted as the virtual open string pair creation in the decaying brane. This behavior indicates a breakdown of this rolling tachyon solution at some point during the evolution. We also discuss the closed string emission from this one-loop diagram, and the evolution of a one-loop diagram connecting a decaying brane to a stable brane, which is responsible for the physical open string creation on the stable brane.Comment: 21 pages, 2 figures; v2: references added, comments revised in various places; v3: footnotes 7&8 added, revised version to appear in PR

Cosmological Rescaling through Warped Space

We discuss a scenario where at least part of the homogeneity on a brane world can be directly related to the hierarchy problem through warped space. We study the dynamics of an anti-D3-brane moving toward the infrared cut-off of a warped background. After a region described by the DBI action, the self-energy of the anti-D3-brane will dominate over the background. Then the world-volume scale of the anti-D3-brane is no longer comoving with the background geometry. After it settles down in the infrared end, the world-volume inhomogeneity will appear, to a Poincare observer, to be stretched by an exponentially large ratio. This ratio is close to that of the hierarchy problem between the gravitational and electroweak scales.Comment: 12 pages, 2 figures; v2, PRD version, comments and references adde

Inflation from Warped Space

A long period of inflation can be triggered when the inflaton is held up on the top of a steep potential by the infrared end of a warped space. We first study the field theory description of such a model. We then embed it in the flux stabilized string compactification. Some special effects in the throat reheating process by relativistic branes are discussed. We put all these ingredients into a multi-throat brane inflationary scenario. The resulting cosmic string tension and a multi-throat slow-roll model are also discussed.Comment: 39 pages; v4, added reference, to appear in JHE

Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background

Quasi-single field inflation predicts a peculiar momentum dependence in the squeezed limit of the primordial bispectrum which smoothly interpolates between the local and equilateral models. This dependence is directly related to the mass of the isocurvatons in the theory which is determined by the supersymmetry. Therefore, in the event of detection of a non-zero primordial bispectrum, additional constraints on the parameter controlling the momentum-dependence in the squeezed limit becomes an important question. We explore the effects of these non-Gaussian initial conditions on large-scale structure and the cosmic microwave background, with particular attention to the galaxy power spectrum at large scales and scale-dependence corrections to galaxy bias. We determine the simultaneous constraints on the two parameters describing the QSF bispectrum that we can expect from upcoming large-scale structure and cosmic microwave background observations. We find that for relatively large values of the non-Gaussian amplitude parameters, but still well within current uncertainties, galaxy power spectrum measurements will be able to distinguish the QSF scenario from the predictions of the local model. A CMB likelihood analysis, as well as Fisher matrix analysis, shows that there is also a range of parameter values for which Planck data may be able distinguish between QSF models and the related local and equilateral shapes. Given the different observational weightings of the CMB and LSS results, degeneracies can be significantly reduced in a joint analysis.Comment: 27 pages, 14 figure

Observational Signatures and Non-Gaussianities of General Single Field Inflation

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.Comment: 53 pages, 5 figures; v3, minor revision, JCAP version; v4, numerical coefficients corrected in Appendix B, discussion on consistency condition revise

Observational Signatures and Non-Gaussianities of General Single Field Inflation

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.Comment: 53 pages, 5 figures; v3, minor revision, JCAP version; v4, numerical coefficients corrected in Appendix B, discussion on consistency condition revise

Is Brane Inflation Eternal?

In this paper, we show that eternal inflation of the random walk type is generically absent in the brane inflationary scenario. Depending on how the brane inflationary universe originated, eternal inflation of the false vacuum type is still quite possible. Since the inflaton is the position of the D3-brane relative to the anti-D3-brane inside the compactified bulk with finite size, its value is bounded. In DBI inflation, the warped space also restricts the amplitude of the scalar fluctuation. These upper bounds impose strong constraints on the possibility of eternal inflation. We find that eternal inflation due to the random walk of the inflaton field is absent in both the KKLMMT slow roll scenario and the DBI scenario. A more careful analysis for the slow-roll case is also presented using the Langevin equation, which gives very similar results. We discuss possible ways to obtain eternal inflation of the random walk type in brane inflation. In the multi-throat brane inflationary scenario, the branes may be generated by quantum tunneling and roll out the throat. Eternal inflation of the false vacuum type inevitably happens in this scenario due to the tunneling process. Since these scenarios have different cosmological predictions, more data from the cosmic microwave background radiation will hopefully select the specific scenario our universe has gone through.Comment: 32 pages; v2: references and comments adde

Duality Cascade in Brane Inflation

We show that brane inflation is very sensitive to tiny sharp features in extra dimensions, including those in the potential and in the warp factor. This can show up as observational signatures in the power spectrum and/or non-Gaussianities of the cosmic microwave background radiation (CMBR). One general example of such sharp features is a succession of small steps in a warped throat, caused by Seiberg duality cascade using gauge/gravity duality. We study the cosmological observational consequences of these steps in brane inflation. Since the steps come in a series, the prediction of other steps and their properties can be tested by future data and analysis. It is also possible that the steps are too close to be resolved in the power spectrum, in which case they may show up only in the non-Gaussianity of the CMB temperature fluctuations and/or EE polarization. We study two cases. In the slow-roll scenario where steps appear in the inflaton potential, the sensitivity of brane inflation to the height and width of the steps is increased by several orders of magnitude comparing to that in previously studied large field models. In the IR DBI scenario where steps appear in the warp factor, we find that the glitches in the power spectrum caused by these sharp features are generally small or even unobservable, but associated distinctive non-Gaussianity can be large. Together with its large negative running of the power spectrum index, this scenario clearly illustrates how rich and different a brane inflationary scenario can be when compared to generic slow-roll inflation. Such distinctive stringy features may provide a powerful probe of superstring theory.Comment: Corrections in Eq.(5.47), Eq (5.48), Eq(5.49) and Fig