Aspects of the Bosonic Spectral Action: Successes and Challenges

A short introduction on elements of noncommutative geometry, which offers a purely geometric interpretation of the Standard Model and implies a higher derivative gravitational theory, is presented. Physical consequences of almost commutative manifolds are briefly discussed and cosmological consequences of the gravitational sector, which is shown not to be plagued by linear instability, are highlighted. Successes and challenges are discussed. A novel spectral action proposal based on zeta function regularisation is briefly presented.Comment: 10 pages. Invited talk to appear in the Proceedings of the Corfu Summer Institute 2015 "School and Workshops on Elementary Particle Physics and Gravity", 1-27 September 2015, Corfu, Greec

Noncommutative Spectral Geometry: A Short Review

We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong interactions. Despite the phenomenological successes of the model, the discrepancy between the predicted Higgs mass and the current experimental data indicate that one may have to go beyond the simple model considered at first. We review the current status of the phenomenological consequences and their implications. Since this model lives by construction at high energy scales, namely at the Grand Unified Theories scale, it provides a natural framework to investigate early universe cosmology. We briefly review some of its cosmological consequences.Comment: 11 pages. Invited talk in the Sixth International Workshop DICE2012, Castello Pasquini/Castiglioncello (Tuscany), September 17-21, 201

The role of topologigal defects in cosmology

Topological defects are involved in a plethora of physical and astrophysical phenomena. In these lectures, I will review the r\^ ole they could play in the large-scale structure formation and the anisotropies of the cosmic microwave background, as well as in various high energy phenomena, including baryon number asymmetry, ultra-high energy cosmic rays, and gamma ray bursts. I will then summarize the gravitational effects of cosmic strings. Finally, I will briefly discuss the r\^ ole of topological defects in brane world cosmology.Comment: Invited lectures in the NATO ASI / COSLAB (ESF) School ``Patterns of symmetry breaking'', September 2002 (Cracow). 28 page

Inflation and cosmic (super)strings: implications of their intimate relation revisited

We briefly discuss constraints on supersymmetric hybrid inflation models and examine the consistency of brane inflation models. We then address the implications for inflationary scenarios resulting from the strong constraints on the cosmic (super)string tension imposed from the most recent cosmic microwave background temperature anisotropies data.Comment: 9 pages; Invited talk in the "Quantized Flux in Tightly Knotted and Linked Systems" workshop in association with the Newton Institute programme "Topological Dynamics in the Physical and Biological Sciences" -- Isaac Newton Institute for Mathematical Sciences, Cambridge 3 - 7 December 201

Space-time dimensionality from brane collisions

Collisions and subsequent decays of higher dimensional branes leave behind three-dimensional branes and anti-branes, one of which could play the role of our universe. This process also leads to the production of one-dimensional branes and anti-branes, however their number is expected to be suppressed. Brane collisions may also lead to the formation of bound states of branes. Their existence does not alter this result, it just allows for the existence of one-dimensional branes captured within the three-dimensional ones.Comment: 4 pages, one minor modification to match version to appear in Phys. Let.

Formation & evolution of cosmic superstrings: a short review

I will briefly review the formation and evolution of cosmic superstrings, in the context of brane-world cosmological models within M-theory. These objects can play the role of cosmic strings, offering a variety of astrophysical consequences, which I will briefly discuss.Comment: 4 pages; invited talk in the workshop on Cosmology-Strings: Theory-Cosmology-Phenomenology, Corfu (Greece), Sept. 200