Related papers: Dp-finite fields III: inflators and directories

We propose a new model of the D-term hybrid inflation in the framework of supergravity. Although our model introduces, analogously to the conventional D-term inflation, the inflaton and a pair of scalar fields charged under a $U(1)$ gauge…

Inflationary $\alpha$-attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as $n_s=1-{2/ N_e} $, assuming that the potential in terms of the original…

We extend the theory of cosmological perturbations to the case when the ``matter'' Lagrangian is an arbitrary function of the scalar field and its first derivatives. In particular, this extension provides a unified description of known…

We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…

At the end of inflation, dynamical instability can rapidly deposit the energy of homogeneous cold inflaton into excitations of other fields. This process, known as preheating, is rather violent, inhomogeneous and non-linear, and has to be…

This article is a natural construction of our previous works. In this article, we employ similar ideas due to MacLane to provide an estimate of IC(K(X)|K,v) when (K(X)|K,v) is a valuation algebraic extension. Our central result is an…

We make a more general determination of the inflationary observables in the standard 4-D and 5-D single-field inflationary scenarios, by the exact reconstruction of the dynamics of the inflation potential during the observable inflation…

This is an introduction to the author theory of cyclic p-extensions of an absolutely unramified complete discrete valuation field K with arbitrary residue field of characteristic p. In this theory a homomorphism is constructed from the…

We present the first 3+1-dimensional numerical simulations of scalar fields with non-minimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld (DBI) inflaton coupled to…

Using the formalism of Grothendieck's derivators, we construct `the universal localizing invariant of dg categories'. By this, we mean a morphism U_l from the pointed derivator associated with the Morita homotopy theory of dg categories to…

An inflation model based on dimensional (de)construction of a massive gauge theory is proposed. The inflaton in this model is the "zero-mode" of a component of the massive gauge field in the (de)constructed extra dimensions. The inflaton…

We study the class of 2-dimensional affine k-domains R satisfying ML(R) = k, where k is an arbitrary field of characteristic zero. In particular, we obtain the following result: Let R be a localization of a polynomial ring in finitely many…

Snake graphs are a class of planar graphs that are important in the theory of cluster algebras. Indeed, the Laurent expansions of the cluster variables in cluster algebras from surfaces are given as weight generating functions for 1-dimer…

Let ${\cal D}^k$ be the space of $k$-th order linear differential operators on ${\bf R}$: $A=a_k(x)\frac{d^k}{dx^k}+\cdots+a_0(x)$. We study a natural 1-parameter family of $\Diff(\bf R)$- (and $\Vect(\bf R)$)-modules on ${\cal D}^k$. (To…

Motivated by the theory of locally definable groups, we study the theory of $K$-vector spaces with a predicate for the union $X$ of an infinite family of independent subspaces. We show that if $K$ is infinite then the theory is complete and…

We prove that NIP valued fields of positive characteristic are henselian. Furthermore, we partially generalize the known results on dp-minimal fields to dp-finite fields. We prove a dichotomy: if K is a sufficiently saturated dp-finite…

Let $A$ be an affinoid integral domain over a non-Archimedean field $K$, and let $L$ be its field of fractions. We prove that the normalization of $A$ can be reconstructed from $L$ by taking the intersection of all maximal discrete…

In his unpublished preprint "Definable Valuations" Koenigsmann shows that every field that admits a t-henselian topology is either real closed or separably closed or admits a definable valuation inducing the t-henselian topology. To show…

Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\delta K^\flat =0$ by using the Killing non-linear 1-form $K^\flat$ and the spray operator $\delta$ with the Finsler non-linear…

We show that non-minimal inflation, based on the phi^4 potential, may be rendered unitarity conserving and compatible with the Planck results for 4.6x10^(-3)<~r21=c2R/c1R^2<~1, if we introduce a linear contribution (c1R phi) to the frame…