Related papers: New Solutions of the Inflationary Flow Equations
The flow equation approach investigated by Wegner et al. is applied to an unbounded Hamiltonian system with a generalization. We show that a well-known quantized complex energy eigenvalues which is related to decay widths can be given with…
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary $e$-folds. Solving the resulting partial…
We adapt the precise definition of the flowing effective action in order to obtain a functional flow equation with simple properties close to physical intuition. The simplified flow equation is invariant under local gauge transformations…
I generalize the inflationary flow equations of Hoffman and Turner to arbitrary order in slow roll. This makes it possible to study the predictions of slow roll inflation in the full observable parameter space of tensor/scalar ratio $r$,…
We propose a new parametrization of the background equations of motion corresponding to (canonical) single-field models of inflation, which allows a better understanding of the general properties of the solutions and of the corresponding…
In this paper we show that the dynamics associated with slow-roll models of inflation can be investigated through a method called deformation procedure. Using the latter, we explicitly derive an expression linking two slow-roll inflationary…
The solution space of any set of power flow equations may contain different number of real-valued solutions. The boundaries that separate these regions are referred to as power flow solution space boundaries. Knowledge of these boundaries…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
The stochastic formalism of inflation allows us to describe the scalar-field dynamics in a non-perturbative way. The correspondence between the diffusion and Schr\"{o}dinger equations makes it possible to exhaustively construct analytical…
We study analytically and numerically the inflationary solutions for various type scalar potentials in the nonminimally coupled scalar field theory. The Hamilton-Jacobi equation is used to deal with nonlinear evolutions of inhomogeneous…
We propose a new class of inflationary solutions to the standard cosmological problems (horizon, flatness, monopole,...), based on a modification of old inflation. These models do not require a potential which satisfies the normal…
In this talk we discuss three different issues. First of all, there exist several proposals how to solve cosmological problems by adiabatic expansion of the Universe, without any use of inflation. We explain why these models do not solve…
We investigate the ability of current CMB data to reliably constrain the form of the primordial power spectrum generated during inflation. We attempt to identify more exotic power spectra that yield equally good fits to the data as simple…
First we give an introduction to the method of diagonalizing or block-diagonalizing continuously a Hamiltonian and explain how this procedure can be used to analyze the two-dimensional Hubbard model. Then we give a short survey on…
We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving…
A simple algebraic method to obtain exact solutions to the scalar field equations in spatially flat FRW cosmology is derived. The field potential fuction is reduced to two terms which can be used to determine some characteristic…
We present a method for solving loop integrals in dimensional regularization that is particularly useful in the context of inflation. We apply this method to the calculation of the tensor power spectrum induced by scalar fluctuations in…
We introduce new families of combinatorial objects whose enumeration computes volumes of flow polytopes. These objects provide an interpretation, based on parking functions, of Baldoni and Vergne's generalization of a volume formula…
We reexamine inflation due to a constrained inflaton in the model of a complex scalar. Inflaton evolves along a spiral-like valley of special scalar potential in the scalar field space just like single field inflation. Sub-Planckian…
In this work we present an inflationary mechanism based on fluid dynamics. Starting with the action for a single barotropic perfect fluid, we outline the procedure to calculate the power spectrum and the bispectrum of the curvature…