Related papers: New Solutions of the Inflationary Flow Equations
We find a simple inflationary solution in an inhomogeneous spacetime with heat flux. The heat flux obeys a causal transport equation, and counteracts the inflationary decrease of energy density. At late times, the heat flux tends to zero…
In this paper, we define a non-iterative transformation method for boundary-layer flows of non-Newtonian fluids past a flat plate. The problem to be solved is an extended Blasius problem depending on a parameter. This method allows us to…
One common approach for cosmic inflation consists in couple Einstein's gravity with a scalar field, often referred to inflaton field. In order to derive analytic simple scenarios, we usually work in the {\it slow-roll} regime. In such an…
The method of extremal flows has presented an alluring alternative approach to numerically solving bootstrap constraints. Here I present the development and adaptation of that approach to a more general class of flows with apparent…
Fundamental formulae representing the density perturbation spectrums generated in inflationary scenarios are rigorously proved. Quantum fluctuations as initial conditions for structure generation in some inflationary era can be calculated…
In this work, we consider the dynamic unsplittable flow problem. This variation of the unsplittable flow problem has received little attention so far. The unsplittable flow problem is an NP-hard extension of the multi-commodity flow problem…
I describe a recently derived stochastic approach to inflaton dynamics which can address some serious problems associated with conventional inflationary theory. Using this theory I derive an exact solution to the stochastic dynamics for the…
A new approach is given for the implementation of boundary conditions used in solving the Mukhanov-Sasaki equation in the context of inflation. The familiar quantization procedure is reviewed, along with a discussion of where one might…
Inflationary models, especially those with plateau-type potentials, are consistent with the cosmological data, but inflation itself does not resolve the initial singularity. This singularity is resolved, for example, by the idea of the…
There are hidden observables for inflation, such as features localized in position space, which do not manifest themselves when only one inflation trajectory is considered. To address this issue, we investigate inflation dynamics in a…
For the inflaton field we determine a new exact solution by using the Lie symmetry analysis. Specifically, we construct a second-order differential master equation for arbitrary scalar field potential by assuming that the spectral index for…
A method to estimate the reliability of a perturbative expansion of the stochastic inflationary Langevin equation is presented and discussed. The method is applied to various inflationary scenarios, as large field, small field and running…
The conventional background solution for the evolution of a single canonical inflaton field performs admirably in extreme scenarios such as the slow-roll phase (where the slow-roll parameter is much less than one) and the deep reheating era…
The main contribution of this paper is twofold: (1) Recently, Iyer, Xu, and Zlato\v{s} studied the dissipation enhancement by cellular flows based on standard advection-diffusion equations via a stochastic method. We generalize their…
A perturbative strategy for inflation described by two-inflaton fields is developed using a mathematical analogy with the renormalization-group. Two small quantities, $\alpha$ and $\lambda$, corresponding to standard slow-roll parameters…
Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…
This paper is devoted to sharp interpolation inequalities on the sphere and their proof using flows. The method explains some rigidity results and proves uniqueness in related semilinear elliptic equations. Nonlinear flows allow to cover…
We provide a mean curvature flow method for numerical cosmology and test it on cases of inhomogenous inflation. The results show (in a proof of concept way) that the method can handle even large inhomogeneities that result from different…
We examine the solutions of the equations of motion for an expanding Universe, taking into account the radiation of the inflaton field energy. We then analyze the question of the generality of inflationary solutions in this more general…
Under general assumptions on the velocity field, it is possible to construct a flow that is forward untangled. Once such a flow has been selected, the associated transport problem is well-posed.