2,292 research outputs found
Gauge-Invariant Temperature Anisotropies and Primordial Non-Gaussianity
We provide the gauge-invariant expression for large-scale cosmic microwave
background temperature fluctuations at second-order in perturbation theory. It
enables to unambiguously define the nonlinearity parameter f_NL which is used
by experimental collaborations to pin down the level of Non-Gaussianity in the
temperature fluctuations. Furthermore, it contains a primordial term encoding
all the information about the Non-Gaussianity generated at primordial epochs
and about the mechanism which gave rise to cosmological perturbations, thus
neatly disentangling the primordial contribution to Non-Gaussianity from the
one caused by the post-inflationary evolution.Comment: 4 pages, LaTeX file. Revised to match the version to appear in Phys.
Rev. Let
Depth of cohomology support loci for quasi-projective varieties via orbifold pencils
The present paper describes a relation between the quotient of the
fundamental group of a smooth quasi-projective variety by its second commutator
and the existence of maps to orbifold curves. It extends previously studied
cases when the target was a smooth curve. In the case when the quasi-projective
variety is a complement to a plane algebraic curve this provides new relations
between the fundamental group, the equation of the curve, and the existence of
polynomial solutions to certain equations generalizing Pell's equation. These
relations are formulated in terms of the depth which is an invariant of the
characters of the fundamental group discussed in detail here.Comment: 22 page
Characteristic varieties of graph manifolds and quasi-projectivity of fundamental groups of algebraic links
The present paper studies the structure of characteristic varieties of
fundamental groups of graph manifolds. As a consequence, a simple proof of
Papadima's question is provided on the characterization of algebraic links that
have quasi-projective fundamental groups. The type of quasi-projective
obstructions used here are in the spirit of Papadima's original work.Comment: 22 pages, 6 figures, to appear in European Journal of Mathematic
- …