The Spectral Action and Cosmic Topology

The Coupling of Topology and Inflation in Noncommutative Cosmology

We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slowroll inflation potentials obtained in the model from the nonperturbative form of the spectral action are sensitive not only to the geometry (flat or positively curved) of the universe, but also...

Temperature Correlations in a Finite Universe

We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all possible finite flat models. We examine the angular correlation function itself, pointing out visible and discrete features that arise from topology. While observations of the power spectrum on large...

On two problems concerning the Zariski topology of modules

Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...

A NEW MEMETIC SWARM OPTIMIZATION FOR SPECTRAL LAYOUT DESIGN OF BRACED FRAMES

For most practical purposes, true topology optimization of a braced frame should be synchronized with its sizing. An integrated layout optimization is formulated here to simultaneously account for both member sizing and bracings’ topology in such a problem. Code-specific seismic design spectrum is applied to unify the earthquake excitation. The problem is solved for minimal structural weight un...

Zariski-Like Topology on the Classical Prime Spectrum of a Modules