Related papers: Generalized $\alpha$-attractor models from element…
We study generalized two-field $\alpha$-attractor models whose rescaled scalar manifold is the triply-punctured sphere endowed with its complete hyperbolic metric, whose underlying complex manifold is the modular curve $Y(2)$. Using an…
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…
Cosmological alpha-attractors give a natural explanation for the spectral index n_s of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more…
The cosmological models called $\alpha$-attractors provide an excellent fit to the latest observational data. Their predictions $n_{s} = 1-2/N$ and $r = 12\alpha/N^{2}$ are very robust with respect to the modifications of the inflaton…
A class of positive curvature spatially homogeneous but anisotropic cosmological models within an Einstein-aether gravitational framework are investigated. The matter source is assumed to be a scalar field which is coupled to the expansion…
$\alpha$-attractor models naturally appear in supergravity with hyperbolic geometry. The simplest versions of $\alpha$-attractors, T- and E-models, originate from theories with non-singular potentials. In canonical variables, these…
Cosmological models arising from a generalized compactification of Einstein gravity are derived. It is shown that a redefinition of the moduli fields reduces the system to a set of massless fields and a single field with a single…
We propose a class of two-field cosmological models derived from gravity coupled to non-linear sigma models whose target space is a non-compact and geometrically-finite hyperbolic surface, which provide a wide generalization of so-called…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet…
Cosmological alpha-attractor models in \cN=1 supergravity are based on hyperbolic geometry of a Poincar\'e disk with the radius square {\cal R}^2=3\alpha. The predictions for the B-modes, r\approx 3\alpha {4\over N^2}, depend on moduli…
We investigate the global structure of the recently discovered family of $SL(2,\mathbb{Z})$-invariant potentials describing inflationary $\alpha$-attractors. These potentials have an inflationary plateau consisting of the fundamental domain…
Inflationary $\alpha$-attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincare disk hyperbolic geometry. We refine these models by constructing Kahler potentials with…
Results of a general study on the dynamics of cosmological scalar fields with arbitrary potentials are presented. Exact and approximate attractor solutions are found, with applications to quintessence, moduli stabilization and inflation.
We study $\alpha$-attractor models with both E-model and T-model potential in an extended Non-Minimal Derivative (NMD) inflation where a canonical scalar field and its derivatives are non-minimally coupled to gravity. We calculate the…
Consider the Poincare disc model for hyperbolic geometry. In this paper, a convenient computational formula is developed along with an aesthetic geometric interpretation. Two proofs, one geometric and one analytical, of each result are…
A generalization of inflationary $\alpha$-attractor models (``polynomial $\alpha$-attractor'') was recently proposed by Kallosh and Linde, in which the potential involves logarithmic functions of the inflaton so that the derivative of the…
In this paper, we introduce a birationally admissible stratification on the Deligne-Mumford stack of stable minimal models (e.g., the KSBA moduli stack), such that the universal family over each stratum admits a simple normal crossing log…
We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…
We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…