31 research outputs found
Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
We construct the gauge invariant free action for cosmological perturbations
for the nonminimally coupled inflaton field in the Jordan frame. For this the
phase space formalism is used, which keeps track of all the dynamical and
constraint fields. We perform explicit conformal transformations to demonstrate
the physical equivalence between the Jordan and Einstein frames at the level of
quadratic perturbations. We show how to generalize the formalism to the case of
a more complicated scalar sector with an internal symmetry, such as Higgs
inflation. This work represents a first step in developing gauge invariant
perturbation theory for nonminimally coupled inflationary models.Comment: 21 pages, references added, typos corrected, extended section IV on
Higgs inflatio
Overview of Parallel Platforms for Common High Performance Computing
The paper deals with various parallel platforms used for high performance computing in the signal processing domain. More precisely, the methods exploiting the multicores central processing units such as message passing interface and OpenMP are taken into account. The properties of the programming methods are experimentally proved in the application of a fast Fourier transform and a discrete cosine transform and they are compared with the possibilities of MATLAB's built-in functions and Texas Instruments digital signal processors with very long instruction word architectures. New FFT and DCT implementations were proposed and tested. The implementation phase was compared with CPU based computing methods and with possibilities of the Texas Instruments digital signal processing library on C6747 floating-point DSPs. The optimal combination of computing methods in the signal processing domain and new, fast routines' implementation is proposed as well
The Gaussian entropy of fermionic systems
We consider the entropy and decoherence in fermionic quantum systems. By
making a Gaussian Ansatz for the density operator of a collection of fermions
we study statistical 2-point correlators and express the entropy of a system
fermion in terms of these correlators. In a simple case when a set of N
thermalised environmental fermionic oscillators interacts bi-linearly with the
system fermion we can study its time dependent entropy, which also represents a
quantitative measure for decoherence. We then consider a relativistic fermionic
quantum field theory and take a mass mixing term as a simple model for the
Yukawa interaction. It turns out that even in this Gaussian approximation, the
fermionic system decoheres quite effectively, such that in a large coupling and
high temperature regime the system field approaches the temperature of the
environmental fields.Comment: 28 pages, 13 figures, updated to match published versio
Staying Thermal with Hartree Ensemble Approximations
We study thermal behavior of a recently introduced Hartree ensemble
approximation, which allows for non-perturbative inhomogeneous field
configurations as well as for approximate thermalization, in the model
in 1+1 dimensions. Using ensembles with a free field thermal distribution as
out-of-equilibrium initial conditions we determine thermalization time scales.
The time scale for which the system stays in approximate quantum thermal
equilibrium is an indication of the time scales for which the approximation
method stays reasonable. This time scale turns out to be two orders of
magnitude larger than the time scale for thermalization, in the range of
couplings and temperatures studied. We also discuss simplifications of our
method which are numerically more efficient and make a comparison with
classical dynamics.Comment: 19 pages latex; extensively rewritten to improve presentation, data
essentially unchanged, analysis sharpened and one table adde
Classical approximation to quantum cosmological correlations
We investigate up to which order quantum effects can be neglected in
calculating cosmological correlation functions after horizon exit. As a toy
model, we study theory on a de Sitter background for a massless
minimally coupled scalar field . We find that for tree level and one loop
contributions in the quantum theory, a good classical approximation can be
constructed, but for higher loop corrections this is in general not expected to
be possible. The reason is that loop corrections get non-negligible
contributions from loop momenta with magnitude up to the Hubble scale H, at
which scale classical physics is not expected to be a good approximation to the
quantum theory. An explicit calculation of the one loop correction to the two
point function, supports the argument that contributions from loop momenta of
scale are not negligible. Generalization of the arguments for the toy model
to derivative interactions and the curvature perturbation leads to the
conclusion that the leading orders of non-Gaussian effects generated after
horizon exit, can be approximated quite well by classical methods. Furthermore
we compare with a theorem by Weinberg. We find that growing loop corrections
after horizon exit are not excluded, even in single field inflation.Comment: 44 pages, 1 figure; v2: corrected errors, added references,
conclusions unchanged; v3: added section in which we compare with stochastic
approach; this version matches published versio
Uniqueness of the gauge invariant action for cosmological perturbations
In second order perturbation theory different definitions are known of gauge
invariant perturbations in single field inflationary models. Consequently the
corresponding gauge invariant cubic actions do not have the same form. Here we
show that the cubic action for one choice of gauge invariant variables is
unique in the following sense: the action for any other, non-linearly related
variable can be brought to the same bulk action, plus additional boundary
terms. These boundary terms correspond to the choice of hypersurface and
generate extra, disconnected contributions to the bispectrum. We also discuss
uniqueness of the action with respect to conformal frames. When expressed in
terms of the gauge invariant curvature perturbation on uniform field
hypersurfaces the action for cosmological perturbations has a unique form,
independent of the original Einstein or Jordan frame. Crucial is that the gauge
invariant comoving curvature perturbation is frame independent, which makes it
extremely helpful in showing the quantum equivalence of the two frames, and
therefore in calculating quantum effects in nonminimally coupled theories such
as Higss inflation.Comment: 27 page