Tables of integrals

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

/pdf/cosmology-and-fundamental-physics-with-the-euclid-satellite-1pi37a138r.pdf

Cosmology and Fundamental Physics with the Euclid Satellite

Euclid is a European Space Agency medium class mission selected for launch in 2019 within the Cosmic Vision 2015-2025 programme. The main goal of Euclid is to understand the origin of the accelerated expansion of the Universe. Euclid will explore the expansion history of the Universe and the evolution of cosmic structures by measuring shapes and redshifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

/pdf/cosmology-and-fundamental-physics-with-the-euclid-satellite-1fwy2a9zjk.pdf

Cosmology and fundamental physics with the Euclid satellite

http://cds.cern.ch/record/570429/files/0207130.pdf

The pre-big bang scenario in string cosmology

The recent 3 yr Wilkinson Microwave Anisotropy Probe data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit Lambda-cold dark matter prediction. We show that by allowing the large-scale spatial geometry of our universe to be plane symmetric with eccentricity at decoupling or order 10(-2), the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.

Ellipsoidal universe can solve the cosmic microwave background quadrupole problem.

Recent Wilkinson Microwave Anisotropy Probe (WMAP) data confirm the cosmic microwave background (CMB) quadrupole anomaly. We further elaborate our previous proposal that the quadrupole power can be naturally suppressed in axis-symmetric universes. In particular, we discuss in greater detail the CMB quadrupole anisotropy and considerably improve our analysis. As a result, we obtain tighter constraints on the direction of the axis of symmetry as well as on the eccentricity at decoupling. We find that the quadrupole amplitude can be brought in accordance with observations with an eccentricity at decoupling of about 0.64x10{sup -2}. Moreover, our determination of the direction of the symmetry axis is in reasonable agreement with recent statistical analyses of cleaned CMB temperature fluctuation maps obtained by means of improved internal linear combination methods as galactic foreground subtraction technique.

Cosmic Microwave Background Quadrupole and Ellipsoidal Universe

The recent three-year WMAP data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit \Lambda CDM prediction. We show that, allowing the large-scale spatial geometry of our universe to be plane-symmetric with eccentricity at decoupling or order 10^{-2}, the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.

Ellipsoidal Universe Can Solve The CMB Quadrupole Problem

We study the generation of primeval magnetic fields during inflation era in nonlinear theories of electrodynamics. Although the intensity of the produced fields strongly depends on characteristics of inflation and on the form of electromagnetic Lagrangian, our results do not exclude the possibility that these fields could be astrophysically interesting.

Inflation-produced magnetic fields in nonlinear electrodynamics

We reanalyze the production of seed magnetic fields during inflation in $(R/{m}^{2}{)}^{n}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$ and $I{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$ models, where $n$ is a positive integer, $R$ the Ricci scalar, $m$ a mass parameter, and $I\ensuremath{\propto}{\ensuremath{\eta}}^{\ensuremath{\alpha}}$ a power-law function of the conformal time $\ensuremath{\eta}$, with $\ensuremath{\alpha}$ a positive real number. If $m$ is the electron mass, the produced fields are uninterestingly small for all $n$. Taking $m$ as a free parameter, we find that, for $n\ensuremath{\ge}2$, the produced magnetic fields can be sufficiently strong in order to seed the dynamo mechanism and then to explain galactic magnetism. For $\ensuremath{\alpha}\ensuremath{\gtrsim}2$, there is always a window in the parameters defining inflation such that the generated magnetic fields are astrophysically interesting. Moreover, if inflation is (almost) de Sitter and the produced fields almost scale invariant ($\ensuremath{\alpha}\ensuremath{\simeq}4$), their intensity can be strong enough to directly explain the presence of microgauss galactic magnetic fields.

Luigi Tedesco

Papers

Ellipsoidal universe can solve the cosmic microwave background quadrupole problem.

Cosmic Microwave Background Quadrupole and Ellipsoidal Universe

Ellipsoidal Universe Can Solve The CMB Quadrupole Problem

Inflation-produced magnetic fields in nonlinear electrodynamics

Inflation-produced magnetic fields in R n F 2 and I F 2 models