Related papers: New Solutions of the Inflationary Flow Equations

The exact solutions in the standard inflationary model based on the self-interacting scalar field minimally coupled to gravity are considered. The shape's freedom of the self-interacting potential $V(\phi)$ is postulated to obtain a new set…

Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…

In our previous paper, we have proposed a new algorithm to calculate the power spectrum of the curvature perturbations generated in inflationary universe with use of the stochastic approach. Since this algorithm does not need the…

New exact inflationary solutions are presented in the scalar field theory, minimally coupled to gravity, with a potential term. No use is made of the slow rollover approximation. The scale factors are completely nonsingular and the…

A new family of inflationary models is introduced and analysed. The behaviour of the parameters characterising the models suggest preferred values, which generate the most interesting testable predictions. Results are further improved if…

In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…

A scalar field with an exponential potential has been proposed as a model of inflation (called power-law inflation). Although it admits an exact solution, the integrability of the system has not been shown.We uncover the hidden symmetries…

We develop a technique to construct analytical solutions of the linear perturbations of inflation with a nonlinear dispersion relation, due to quantum effects of the early universe. Error bounds are given and studied in detail. The…

The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…

Inflationary solutions are constructed in a specific five-dimensional model with boundaries motivated by heterotic M-theory. We concentrate on the case where the vacuum energy is provided by potentials on those boundaries. It is pointed out…

We use the flow equations to determine the different hierarchy Hubble parameters as a function of the number of e-folds for intermediate models in single-field inflation. The obtained expressions allow us to determine at second order in the…

We derive a reduced-order model describing the inflation and deflation dynamics of a liquid-filled hyperelastic balloon, focusing on inviscid laminar flow and the extensional motion of the balloon. We initially study the flow and pressure…

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for "intermediate" potentials…

A new closed-form inflationary solution is given for a hyperbolic interaction potential. The method used to arrive at this solution is outlined as it appears possible to generate additional sets of equations which satisfy the model. In…

We investigate the dynamics of the recently proposed model of assisted inflation. In this model an arbitrary number of scalar fields with exponential potentials evolve towards an inflationary scaling solution, even if each of the individual…

We propose a new approach for calculating the curvature perturbations produced during inflation in the stochastic formalism. In our formalism, the fluctuations of the e-foldings are directly calculated without perturbatively expanding the…

We study an inflationary scenario where thermal inflation is followed by fast-roll inflation. This is a rather generic possibility based on the effective potentials of spontaneous symmetry breaking in the context of particle physics models.…

We summarize our work on constant roll inflationary models. It was understood recently that constant roll inflation, in a regime beyond the slow roll approximation, can give models that are in agreement with the observational constraints.…

In inflationary scenarios with more than one scalar field, inflation may proceed even if each of the individual fields has a potential too steep for that field to sustain inflation on its own. We show that scalar fields with exponential…

Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar…