2,115 research outputs found
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, , where
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 . 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
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