Resolving the Inflationary Power Spectrum

Recently there have been differing viewpoints on how to evaluate the curvature power spectrum generated during inflation. In a series of papers by some authors it has been argued that the renormalization scheme adopted for the inflaton field phi(x) to make finite should also be applied to |phi_k|^2. But this then modifies the curvature power spectrum in a non-trivial way. On the other hand, others have criticized this approach and suggested alternatives, which have been further countered by the original authors. We discuss these differing viewpoints and indicate inconsistencies in both approaches. We then resolve the issue by showing why the standard expression, without any non-trivial regularization, is still valid.Comment: To appear in the proceedings of The 10th International Symposium on Cosmology and Particle Astrophysics (CosPA2013

Current Status of Warm Inflation

Warm inflation is an inflationary scenario in which a thermal bath coexists with the inflaton during inflation. This is unlike standard cold inflation in which the Universe is effectively devoid of particles during inflation. The thermal bath in warm inflation is maintained by the dissipation of the inflaton's energy through its couplings to other fields. Many models of warm inflation have been proposed and their predictions have been compared with cosmological data. Certain models of inflation that are disallowed in the context of cold inflation by the data are allowed in the warm inflationary scenario, and vice versa.Comment: 9 pages, 3 figures; Slightly longer version of a brief review talk at the 18th Lomonosov Conference on Elementary Particle Physics at Moscow State University, August 24-30, 201

On weakly tight families

Using ideas from Shelah's recent proof that a completely separable maximal almost disjoint family exists when $\c < {\aleph}_{\omega}$, we construct a weakly tight family under the hypothesis \s \leq \b < {\aleph}_{\omega}. The case when \s < \b is handled in \ZFC and does not require \b < {\aleph}_{\omega}, while an additional PCF type hypothesis, which holds when \b < {\aleph}_{\omega} is used to treat the case \s = \b. The notion of a weakly tight family is a natural weakening of the well studied notion of a Cohen indestructible maximal almost disjoint family. It was introduced by Hru{\v{s}}{\'a}k and Garc{\'{\i}}a Ferreira \cite{Hr1}, who applied it to the Kat\'etov order on almost disjoint families