CMB Anisotropies at Second Order I

We present the computation of the full system of Boltzmann equations at second-order describing the evolution of the photon, baryon and cold dark matter fluids. These equations allow to follow the time evolution of the Cosmic Microwave Background (CMB) anisotropies at second-order at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present through the recombination era. This paper sets the stage for the computation of the full second-order radiation transfer function at all scales and for a a generic set of initial conditions specifying the level of primordial non-Gaussianity. In a companion paper, we will present the computation of the three-point correlation function at recombination which is so relevant for the issue of non-Gaussianity in the CMB anisotropies.Comment: 26 pages, LaTeX file, typos correcte

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

Microstructured superhydrorepellent surfaces: Effect of drop pressure on fakir-state stability and apparent contact angles

In this paper we present a generalized Cassi-Baxter equation to take into account the effect of drop pressure on the apparent contact angle theta_{app}. Also we determine the limiting pressure p_{W} which causes the impalement transition to the Wenzel state and the pull-off pressure p_{out} at which the drop detaches from the substrate. The calculations have been carried out for axial-symmetric pillars of three different shapes: conical, hemispherical topped and flat topped cylindrical pillars. Calculations show that, assuming the same pillar spacing, conical pillars may be more incline to undergo an impalement transition to the Wenzel state, but, on the other hand, they are characterized by a vanishing pull-off pressure which causes the drop not to adhere to the substrate and therefore to detach very easily. We infer that this property should strongly reduce the contact angle hysteresis as experimentally osberved in Ref. \cite{Martines-Conical-Shape}. It is possible to combine large resistance to impalement transition (i.e. large value of p_{W}) and small (or even vanishing) detaching pressure p_{out} by employing cylindrical pillars with conical tips. We also show that depending on the particular pillar geometry, the effect of drop pressure on the apparent contact angle theta_{app} may be more or less significant. In particular we show that in case of conical pillars increasing the drop pressure causes a significant decrease of theta_{app} in agreement with some experimental investigations \cite{LafunaTransitio}, whereas theta_{app} slightly increases for hemispherical or flat topped cylindrical pillars.Comment: 21 pages, 13 figure

No many-scallop theorem: Collective locomotion of reciprocal swimmers

To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. We show here that there is no many-scallop theorem. We demonstrate that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions. These results are derived for a minimal dimers model, and generalized to more complex geometries on the basis of symmetry and scaling arguments. We explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field

Loop Representations for 2+1 Gravity on a Torus

We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this system. In particular, we look at the loop transform in the part of the phase space where the holonomies are boosts and study its kernel. This kernel is dense in the connection representation and the transform is not continuous with respect to the natural topologies, even in its domain of definition. Nonetheless, loop representations isomorphic to the connection representation corresponding to this part of the phase space can still be constructed if due care is taken. We present this construction but note that certain ambiguities remain; in particular, functions of loops cannot be uniquely associated with functions of connections.Comment: 24 journal or 52 preprint pages, revtex, SU-GP-93/3-

On the non-Gaussianity from Recombination

The non-linear effects operating at the recombination epoch generate a non-Gaussian signal in the CMB anisotropies. Such a contribution is relevant because it represents a major part of the second-order radiation transfer function which must be determined in order to have a complete control of both the primordial and non-primordial part of non-Gaussianity in the CMB anisotropies. We provide an estimate of the level of non-Gaussianity in the CMB arising from the recombination epoch which shows up mainly in the equilateral configuration. We find that it causes a contamination to the possible measurement of the equilateral primordial bispectrum shifting the minimum detectable value of the non-Gaussian parameter f^equil_NL by Delta f^equil_NL= O(10) for an experiment like Planck.Comment: LaTeX file; 11 pages. v2: Typos corrected; references added; comments about the effective non-linearity parameter added in Sec. IV; comments added in the conclusions of Sec. IV. v3: References added; some clarifications added as footnotes 4 and 6, and in Sec. 3. Matches version accepted for publication in JCA

Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit

We estimate analytically the second-order cosmic microwave background temperature anisotropies at the recombination epoch in the squeezed limit and we deduce the contamination to the primordial local non-Gaussianity. We find that the level of contamination corresponds to f_NL^{con}=O(1) which is below the sensitivity of present experiments and smaller than the value O(5) recently claimed in the literature.Comment: LaTeX file; 15 pages. Slightly revised version. Main result unchange

The Extended Loop Representation of Quantum Gravity

A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum Gravity can be realized on the state space of extended loop dependent wavefunctions. The extended representation generalizes the loop representation and contains this representation as a particular case. The resulting diffeomorphism and hamiltonian constraints take a very simple form and allow to apply functional methods and simplify the loop calculus. In particular we show that the constraints are linear in the momenta. The nondegenerate solutions known in the loop representation are also solutions of the constraints in the new representation. The practical calculation advantages allows to find a new solution to the Wheeler-DeWitt equation. Moreover, the extended representation puts in a precise framework some of the regularization problems of the loop representation. We show that the solutions are generalized knot invariants, smooth in the extended variables, and any framing is unnecessary.Comment: 27 pages, report IFFC/94-1

O-V-S-Z and friends: Non-Gaussianity from inhomogeneous reionization

We calculate the cosmic microwave background (CMB) bispectrum due to inhomogeneous reionization. We calculate all the terms that can contribute to the bispectrum that are products of first order terms on all scales in conformal Newtonian gauge. We also correctly account for the de-correlation between the matter density and initial conditions using perturbation theory up to third order. We find that the bispectrum is of local type as expected. For a reasonable model of reionization, in which the Universe is completely ionized by redshift z_{ri} ~ 8 with optical depth to the last scattering surface \tau_0=0.087 the signal to noise for detection of the CMB temperature bispectrum is S/N ~ 0.1 and confusion in the estimation of primordial non-Gaussianity is f_{NL} ~ -0.1. For an extreme model with z_{ri} ~ 12.5, \tau_0=0.14 we get S/N ~ 0.5 and f_{NL} ~ -0.2.Comment: Published versio

Testing Primordial Black Holes as Dark Matter through LISA

The idea that primordial black holes (PBHs) can comprise most of the dark matter of the universe has recently reacquired a lot of momentum. Observational constraints, however, rule out this possibility for most of the PBH masses, with a notable exception around $10^{-12} M_\odot$. These light PBHs may be originated when a sizeable comoving curvature perturbation generated during inflation re-enters the horizon during the radiation phase. During such a stage, it is unavoidable that gravitational waves (GWs) are generated. Since their source is quadratic in the curvature perturbations, these GWs are generated fully non-Gaussian. Their frequency today is about the mHz, which is exactly the range where the LISA mission has the maximum of its sensitivity. This is certainly an impressive coincidence. We show that this scenario of PBHs as dark matter can be tested by LISA by measuring the GW two-point correlator. On the other hand, we show that the short observation time (as compared to the age of the universe) and propagation effects of the GWs across the perturbed universe from the production point to the LISA detector suppress the bispectrum to an unobservable level. This suppression is completely general and not specific to our model.Comment: 22 pages, 12 figures. v3: matching published versio