Related papers: The harmonic oscillator, dimensional analysis and …
Motivated by the prospect of testing inflation from precision cosmic microwave background observations, we present analytic results for scalar and tensor perturbations in single-field inflation models based on the application of uniform…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
We consider an inflationary scenario where the energy scale of inflation stems from gauge theory dynamics. We point out its generic implications on vacuum selection of our universe, in particular, on determination of spacetime symmetries…
We study the presence of chaotic behavior in phase space in the pre-inflationary stage of hybrid inflation models. This is closely related to the problem of initial conditions associated to these inflationary type of models. We then show…
New inflationary solutions to the Einstein equation are explicitly constructed in a simple five-dimensional model with an orbifold extra dimension $S^1/Z_2$. We consider inflation caused by cosmological constants for the five-dimensional…
While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by…
We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point…
We consider higher-dimensional uniform inflation, in which the extra dimensions expand at the same rate as three-dimensional non-compact space during inflation. We compute the cosmological perturbation in $D+4$ dimensions and derive the…
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the…
We present a new approximation scheme that allows us to increase the accuracy of analytical predictions of the power spectra of inflationary perturbations for two specific classes of inflationary models. Among these models are chaotic…
In this paper we investigate the general features of "Oscillatory Inflation". In adiabatic approximation, we derive a general formula for the number of e-foldings $\tilde{N}$ which reduces to the standard expression in case of the slow role…
We discuss an inflationary scenario based on Lovelock terms. These higher order curvature terms can lead to inflation when there are more than three spatial dimensions. Inflation will end if the extra dimensions are stabilised, so that at…
Within the framework of geometric inflation, where the Friedmann equation is modified to incorporate an infinite series of higher curvature corrections, we describe the emergence of a de Sitter inflationary phase near the poles of an…
Numerical simulations of the inflationary dynamics are presented here for a single canonical scalar field minimally coupled to gravity. We spell out the basic equations governing the inflationary dynamics in terms of cosmic time $t$ and…
We present a new, exact scalar field cosmology for which the spectrum of scalar (density) perturbations can be calculated exactly. We use this exact result to the probe the accuracy of approximate calculations of the perturbation spectrum.
In this paper, an elegant mathematical approach is introduced to solve the equations of warm inflationary model without using extra approximations other than slow-roll. This important inflationary method known as Hamilton-Jacobian…
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 investigate the dynamics of homogeneous phase space for single-field models of inflation. Inflationary trajectories are formally attractors in phase space, but since in practice not all initial conditions lead to them, some degree of…
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…
In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of…