Related papers: On the Expansions in Spin Foam Cosmology
General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.
The Christensen-Egan algorithm is extended and generalized to efficiently evaluate new spin foam vertex amplitudes proposed by Engle, Pereira & Rovelli and Freidel & Krasnov, with or without (factored) boundary states. A concrete pragmatic…
It is shown that a spin system with long range interactions can be converted into a chaotic dynamical system that is differentiable and low-dimensional. The thermodynamic limit of the spin system is then equivalent to studying the long term…
We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension…
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding…
We establish the conditions under which scalable spin squeezing can be achieved in interacting spin ensembles embedded in arbitrary, inhomogeneous graph geometries. We identify two different forms of squeezing: OAT-like scalable squeezing…
The stochastic properties of cosmological perturbations are best defined through the Fourier expansion in a finite box. I discuss the reasons for that with reference the curvature perturbation, and explore some issues arising from it.
We modify and extend an earlier proposal by Brown and Teitelboim to relax the effective cosmological term by nucleation of branes coupled to a three-index gauge potential. Microscopic considerations from string/M theory suggest two major…
In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to…
In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…
A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical…
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in…
Investigations of the dynamic modes of the Poincare gauge theory of gravity found only two good propagating torsion modes; they are effectively a scalar and a pseudoscalar. Cosmology affords a natural situation where one might see…
Five dimensional gravity coupled, both in the bulk and on a brane, to a scalar Liouville field yields a geometry confined to a strip around the brane and with time dependent scale factors for the four geometry. In various limits known…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary…
Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of compact spaces is considered. It is shown that equations of motion can be solved exactly…
We examine the issue of the cosmological constant in the $many$ $inflating$ branes scenario, extending on two recent models by I.Oda and Randall-Sundrum. The exact solution in a closed form is found in the slow roll approximation of the…