Related papers: Operator Method and Recursion Relations for Inflat…
We describe a new framework for causal inference and its application to return time series. In this system, causal relationships are represented as logical formulas, allowing us to test arbitrarily complex hypotheses in a computationally…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
We explore the correlations between correlation functions of the primordial curvature perturbation produced during inflation. We find that for general single field inflation, other than the source terms which depend on the model details,…
We reconstruct the potential of minimally coupling inflation model which produces small value of the tensor-scalar ratio. In these inflation models, tensor-scalar ratio is proportional to 1/N^2 scalar spectral index is in good agreement…
We discuss the application of Minkowski functionals to galaxy catalogues with emphasis on the boundary corrections and point out the relevance for other statistical methods. The analysis of a cubic subsample of the CfA--1 data serves as an…
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…
Recent advances are being discussed on the calculation, within the conformal field theory approach, of the correlation functions for local operators in the theory of 2D gravity coupled to the minimal models of matter.
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…
The exponential rate of convergence for some Markov operators is established. The operators correspond to continuous iterated function systems which are a very useful tool in some cell cycle models.
The purpose of this short note, is to rewrite Morozov's formula for correlation functions over the unitary group, in a much simpler form, involving the computation of a single determinant.
In construction of an inflationary model, one usually assumes that the matter sector of the gravitational action is minimally coupled to the background. It means that the matter (inflaton) part of the action is coupled with the same metric…
In this paper, we introduce operator geodesically convex and operator convex-log functions and characterize some properties of them. Then apply these classes of functions to present several operator Azc\'{e}l and Minkowski type inequalities…
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…
We establish an explicit formula for the n-point correlation functions in the sense of Bloch-Okounkov for the irreducible representations of $\hat{gl}_\infty$ and $W_{1+\infty}$ of arbitrary positive integral levels.
Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and particle content. In this paper, we develop an understanding of…
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…
Correlation functions of primordial density fluctuations provide an exciting probe of the physics governing the earliest moments of our Universe. However, the standard approach to compute them is technically challenging. Theoretical…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We derive the recurrence relation of irreducible tensor operator for O(4) in using the Wigner-Eckart theorem. The physical process like radiative transitions in atomic physics, nuclear transitions between excited nuclear states can be…
In this paper, we analyze a simple class of Horndeski scalar-tensor theory. We investigate several cosmological solutions for inflation, bounce scenario and finite future-time singuarities. Perturbations respect to…