Related papers: Functional Approach to Stochastic Inflation
Scalar field cosmological inflation has a first integral relating the Hubble function and the lagrangian of the scalar field(s), which is known under the names of "Hamilton-Jacobi approach" or "superpotential equation". Here we exploit the…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We investigate a method to extract response functions (dynamical polarisabilities) directly from a bound-state approach applied to calculations of perturbation-induced reactions. The use of a square-integrable basis leads to a response in…
The methods of effective field theory are used to study generic theories of inflation with a single inflaton field. For scalar modes, the leading corrections to the ${\cal R}$ correlation function are found to be purely of the $k$-inflation…
We explore inflationary cosmology in a theory where there are two scalar fields which non-minimally couple to the Ricci scalar and an additional $R^2$ term, which breaks the conformal invariance. Particularly, we investigate the slow-roll…
We investigate multi-field inflationary scenarios with fields that drop out of the model in a staggered fashion. This feature is natural in certain multi-field inflationary setups within string theory; for instance, it can manifest itself…
We introduce a frame-covariant formalism for inflation of scalar-curvature theories by adopting a differential geometric approach which treats the scalar fields as coordinates living on a field-space manifold. This ensures that our…
In this work, we systematically present a new dynamical systems approach to standard inflationary processes and their variants as constant-roll inflation. Using the techniques presented in our work one can in general investigate the…
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution…
The inflationary flow equations are a frequently used method of surveying the space of inflationary models. In these applications the infinite hierarchy of differential equations is truncated in a way which has been shown to be equivalent…
Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in (\frac13, \frac12)$ and $f$ is a continuously…
I explore properties of the inflationary flow equations. I show that the flow equations do not correspond directly to inflationary dynamics. Nevertheless, they can be used as a rather complicated algorithm for generating inflationary…
A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields -…
We propose a new approach to investigate inflation in a model-independent way, and in particular to elaborate the involved observables, through the introduction of the "scale factor potential". Through its use one can immediately determine…
Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the…
We develop a general formalism for analyzing linear perturbations in multiple-field cosmological inflation based on the gauge-ready approach. Our inflationary model consists of an arbitrary number of scalar fields with non-minimal kinetic…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
In this paper we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of…
In this work, we solved the scalar and tensor perturbation equations numerically and using the improved uniform approximation method together with the third-order phase-integral method, for the $\alpha$-attractor inflationary model. This…
In this paper we study the inflation model driven by the phantom field. We propose a possible exit from phantom inflation to our observational cosmology by introducing an additional normal scalar field, similar to hybrid inflation model.…