Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.Comment: More clarifications and references adde

Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.Comment: More clarifications and references adde

Adding a Brane to the Brane-Anti-Brane Action in BSFT

We attempt to generalize the effective action for the D-brane-anti-D-brane system obtained from boundary superstring field theory (BSFT) by adding an extra D-brane to it to obtain a covariantized action for 2 D-branes and 1 anti-D-brane. We discuss the approximations made to obtain the effective action in closed form. Among other properties, this effective action admits solitonic solutions of codimension 2 (vortices) when one of the D-brane is far separated from the brane-anti-brane pair.Comment: 23 pages, 2 figures, minor revision

A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, alpha-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.Comment: LaTeX, 12 pages, corrected typo

Reaction-diffusion systems and nonlinear waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.Comment: LaTeX, 16 pages, corrected typo

Tunneling and propagation of vacuum bubbles on dynamical backgrounds

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.Comment: 29 pages, 8 figures, typos corrected, matches published versio

Spectral flow and boundary string field theory for angled D-branes

D-branes intersecting at an arbitrary fixed angle generically constitute a configuration unstable toward recombination. The reconnection of the branes nucleates at the intersection point and involves a generalization of the process of brane decay of interest to non-perturbative string dynamics as well as cosmology. After reviewing the string spectrum of systems of angled branes, we show that worldsheet twist superfields may be used in the context of Boundary Superstring Field Theory to describe the dynamics. Changing the angle between the branes is seen from the worldsheet as spectral flow with boundary insertions flowing from bosonic to fermionic operators. We calculate the complete tachyon potential and the low energy effective action as a function of angle and find an expression that interpolates between the brane-antibrane and the Dirac-Born-Infeld actions. The potential captures the mechanism of D-brane recombination and provides for interesting new physics for tachyon decay.Comment: 32 pages, 9 figures; v2 references added; v3 discussion clarifie

Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.Comment: LaTeX, 18 pages, corrected typo

Re-Focusing - Building a Future for Entrepreneurial Education & Learning

The field of entrepreneurship has struggled with fundamental questions concerning the subject’s nature and purpose. To whom and to what means are educational and training agendas ultimately directed? Such questions have become of central importance to policy makers, practitioners and academics alike. There are suggestions that university business schools should engage more critically with the lived experiences of practising entrepreneurs through alternative pedagogical approaches and methods, seeking to account for and highlighting the social, political and moral aspects of entrepreneurial practice. In the UK, where funding in higher education has become increasingly dependent on student fees, there are renewed pressures to educate students for entrepreneurial practice as opposed to educating them about the nature and effects of entrepreneurship. Government and EU policies are calling on business schools to develop and enhance entrepreneurial growth and skill sets, to make their education and training programmes more proactive in providing innovative educational practices which help and facilitate life experiences and experiential learning. This paper makes the case for critical frameworks to be applied so that complex social processes become a source of learning for educators and entrepreneurs and so that innovative pedagogical approaches can be developed in terms both of context (curriculum design) and process (delivery methods)

An Improved Brane Anti-Brane Action from Boundary Superstring Field Theory and Multi-Vortex Solutions

We present an improved effective action for the D-brane-anti-D-brane system obtained from boundary superstring field theory. Although the action looks highly non-trivial, it has simple explicit multi-vortex (i.e. codimension-2 multi-BPS D-brane) multi-anti-vortex solutions. The solutions have a curious degeneracy corresponding to different ``magnetic'' fluxes at the core of each vortex. We also generalize the brane anti-brane effective action that is suitable for the study of the inflationary scenario and the production of defects in the early universe. We show that when a brane and anti-brane are distantly separated, although the system is classically stable it can decay via quantum tunneling through the barrier.Comment: 24 pages, 1 figure, JHEP3.cls; v2: references added, tunneling rate discussion expande