The spectral action and cosmic topology

Abstract

The spectral action functional, considered as a model of gravity coupled to matter, provides, in its non-perturbative form, a slow-roll potential for inflation, whose form and corresponding slow-roll parameters can be sensitive to the underlying cosmic topology. We explicitly compute the non-perturbative spectral action for some of the main candidates for cosmic topologies, namely the quaternionic space, the Poincare' dodecahedral space, and the flat tori. We compute the corresponding slow-roll parameters and see we check that the resulting inflation model behaves in the same way as for a simply-connected spherical topology in the case of the quaternionic space and the Poincare' homology sphere, while it behaves differently in the case of the flat tori. We add an appendix with a discussion of the case of lens spaces.

55 pages, LaTeX

References in corpus (32)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• A high resolution foreground cleaned CMB map from WMAP
• The significance of the largest scale CMB fluctuations in WMAP
• Cosmic Topology
• Gravity and the standard model with neutrino mixing
• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
• Running Inflation in the Standard Model
• Constraining the Topology of the Universe
• Small-Scale Cosmic Microwave Background Anisotropies as a Probe of the Geometry of the Universe
• WMAP data and the curvature of space
• Cosmic microwave background anisotropies in multi-connected flat spaces
• Topological Lensing in Spherical Spaces
• Eigenmodes of 3-dimensional spherical spaces and their application to cosmology
• The Uncanny Precision of the Spectral Action
• Simulating Cosmic Microwave Background maps in multi-connected spaces
• Natural inflation mechanism in asymptotic noncommutative geometry
• A new analysis of Poincaré dodecahedral space model
• Detecting Topology in a Nearly Flat Spherical Universe
• Cosmic microwave background constraints on multi-connected spherical spaces
• Detectability of Cosmic Topology in Almost Flat Universes
• Imprints of spherical non-trivial topologies on the CMB
• Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes
• CMB Alignment in Multi-Connected Universes
• Prescribing eigenvalues of the Dirac operator
• The residual gravity acceleration effect in the Poincare dodecahedral space
• Spherical Universe topology and the Casimir effect
• Dodecahedral topology fails to explain quadrupole-octupole alignment
• APS Instability and the Topology of the Brane-World
• Dirac eigenvalues for generic metrics on three-manifolds

Cited by in corpus (13)

• Particle Physics from Almost Commutative Spacetimes
• Spectral Action for Robertson-Walker metrics
• Geometry of Spin and Spin^c structures in the M-theory partition function
• The coupling of topology and inflation in Noncommutative Cosmology
• Asymptotic and exact expansions of heat traces
• Heat trace and spectral action on the standard Podles sphere
• What can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe ?
• Rationality of Spectral Action for Robertson-Walker Metrics
• Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology
• Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
• Real Spectral Triples over Noncommutative Bieberbach Manifolds
• Spectral action for a one-parameter family of Dirac-type operators on SU(2) and its inflation model
• Fractality in Cosmic Topology Models with Spectral Action Gravity