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We analyze the flow into inflation for generic "single-clock" systems, by combining an effective field theory approach with a dynamical-systems analysis. In this approach, we construct an expansion for the potential-like term in the…
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a…
We study models in which the inflaton is coupled to two otherwise decoupled sectors, and the effect of preheating and related processes on their energy densities during the evolution of the universe. Over most of parameter space, preheating…
Constraining the inflationary epoch is one of the aims of modern cosmology. In order to fully exploit current and future small-scale observations, it is necessary to devise tools to directly relate them to the early universes dynamics. We…
This paper is a major revision of our previous work on the HST model of inflation. We identify the local fluctuations of the metric with fluctuations of the mass and angular momentum of black holes, and show that the consistency conditions…
A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex…
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…
Several methods have been proposed to estimate the number of clusters in a dataset; the basic ideal behind all of them has been to study an index that measures inter-cluster separation and intra-cluster cohesion over a range of cluster…
Obtaining a potential flat enough to provide slow roll inflation is often difficult when gravitational effects are included. Non-abelian discrete gauge symmetries can guarantee the flatness of the inflaton potential in this case, and also…
Correlation clustering is a flexible framework for partitioning data based solely on pairwise similarity or dissimilarity information, without requiring the number of clusters as input. However, in many practical scenarios, these pairwise…
We examine the hypothesis that inflation is primarily driven by vacuum energy at a scale indicated by gauge coupling unification. Concretely, we consider a class of hybrid inflation models wherein the vacuum energy associated with a grand…
In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…
Any one-field inflation is actually realized in a multifield configuration because the inflaton must have couplings with other fields to reheat the universe and is coupled to all other fields at least gravitationally. In all single inflaton…
Computing market equilibria is an important practical problem for market design, for example in fair division of items. However, computing equilibria requires large amounts of information (typically the valuation of every buyer for every…
We investigate the emergence of large, localized, pseudo-stable configurations (oscillons) from inflaton fragmentation at the end of inflation. We predict the number density of large oscillons, and the conditions necessary for their…
The dilaton is a possible inflaton candidate following recent CMB data allowing a non-minimal coupling to the Ricci curvature scalar in the early Universe. In this paper, we introduce an approach that has seldom been used in the literature,…
We consider a cluster of Primordial Black Holes which is decoupled from the cosmological expansion (Hubble flow) and this region is heated as compared to the surrounding matter. The increased temperature inside the region can be explained…
We discuss various models of inflationary universe with $\Omega \not = 1$. A homogeneous universe with $\Omega > 1$ may appear due to creation of the universe "from nothing" in the theories where the effective potential becomes very steep…
We present a sufficient criterion for the emergence of cluster phases in an ensemble of interacting classical particles with repulsive two-body interactions. Through a zero-temperature analysis in the low density region we determine the…
Cosmological inflation provides the simplest and most promising mechanism for generating fluctuations for structure formation. Using powerful Hamilton-Jacobi methods, I will describe (1) how to compute density fluctuations and cosmic…