Cosmology, Relativity, and Gravity Commons^™

Rationality Of The Spectral Action For Robertson-Walker Metrics And The Geometry Of The Determinant Line Bundle For The Noncommutative Two Torus, Asghar Ghorbanpour

Electronic Thesis and Dissertation Repository

In noncommutative geometry, the geometry of a space is given via a spectral triple $(\mathcal{A,H},D)$. Geometric information, in this approach, is encoded in the spectrum of $D$ and to extract them, one should study spectral functions such as the heat trace $\Tr (e^{-tD^2})$, the spectral zeta function $\Tr(|D|^{-s})$ and the spectral action functional, $\Tr f(D/\Lambda)$.

The main focus of this thesis is on the methods and tools that can be used to extract the spectral information. Applying the pseudodifferential calculus and the heat trace techniques, in addition to computing the newer terms, we prove the rationality of the spectral action …