International Journal of Modern Physics D

Electrodynamics is the most tested fundamental physical theory. Relativity arose from the completion of Maxwell–Lorentz electrodynamics. Introducing the metric $g_{ij}$ as gravitational potential in 1913, versed in general (coordinate-)covariant formalism in 1914 and shortly after the completion of general relativity, Einstein put the Maxwell equations in general covariant form with only the constitutive relation between the excitation and the field dependent on and connected by the metric in 1916. Further clarification and developments by Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923 together with the corresponding developments in electrodynamics of continuous media by Bateman in 1910, Tamm in 1924, Laue in 1952 and Post in 1962 established the premetric formalism of electrodynamics. Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle I (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom — the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the ultrahigh precision empirical tests of nonbirefringence together with present status of tests of cosmic Abelian axion and dilaton. If the stronger version of WEP is assumed, i.e. WEP II for photons (wave packets of light) which states in addition to WEP I also that the polarization state of the light would not change (e.g. no polarization rotation for linear polarized light) and no amplification/attenuation of light, then no Abelian (EM) axion and no dilaton, and we have a pure metric theory.

In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton’s gravitostatics and to Maxwell’s electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler’s program succeeds here without provisos. In Kottler’s approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way.

A nonmetric theory of gravity is presented, which agrees with all experiments to date. It possesses a Lagrangian-based nonmetric (i.e. nonminimum) coupling between electromagnetism and gravity which has complete continuous-coordinate-transformation symmetry but violates parity and time-reversal-invariance. The theory predicts the universality of free fall for test bodies, i.e. it obeys the Weak Equivalence Principle (WEP). But due to the nonmetrical coupling between electromagnetism and gravity, it violates the Einstein Equivalence Principle (EEP). Hence, this theory disproves the conjecture due to Schiff which states that any gravitation theory that obeys the WEP must also, unavoidably, obey the EEP. Further examination of the empirical status implications of the EEP is therefore urged.

We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincaré group, leads to a Weyl–Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density ${\chi }^{ijkl}=-{\chi }^{jikl}=-{\chi }^{ijlk}$ with 36 independent components. This tensor density incorporates the permittivities, permeabilities and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in ${\chi }^{ijkl}$, it can be derived from it.

It is shown that stringy charge leads naturally to an observable magnetic moment of the electron.

A new model of nonlinear electromagnetic fields possessing a dimensional parameter $\beta$ is proposed. Electromagnetic fields are considered as the source of the gravitation field and accelerated expansion of the universe is driven by nonlinear electromagnetic fields. We consider the magnetic universe and the stochastic magnetic field is a source of the universe acceleration. After the universe inflation and the accelerated expansion the universe decelerates. We show the causality of the model and a classical stability at the deceleration phase. The spectral index, the tensor-to-scalar ratio and the running of the spectral index were estimated that approximately fulfil the PLANCK, WMAP and BICEP2 data.

In this paper, we studied how nonlinear vacuum electrodynamics can affect charged collapsar spacetime structure and properties of particles movement in this spacetime. Analysis of uncharged particle orbits stability shows that the main features of this orbit in Reissner–Nordström spacetime remains actual for Einstein–Born–Infeld theory. At the same time, there is a significant quantitative difference between stable orbits parameters in these theories and this fact may influence on accretion rate predictions for charged collapsar.

A new approach to the Kaluza theory and its relation to the gauge theory is presented. Two degenerate metrics on the $4+d$-dimensional total manifold are used, one corresponding to the spacetime metric and giving the fiber of the gauge bundle, and the other one to the metric of the fiber and giving the horizontal bundle of the connection. When combined, the two metrics give the Kaluza metric and its generalization to the non-Abelian case, justifying thus his choice. Considering the two metrics as fundamental rather than the Kaluza metric explains why Kaluza’s theory should not be regarded as five-dimensional (5D) vacuum gravity. This approach suggests that the only evidence of extra dimensions is given by the existence of the gauge forces, explaining thus why other kinds of evidence are not available. In addition, because the degenerate metric corresponding to the spacetime metric vanishes along the extra dimensions, the lengths in the extra dimensions is zero, preventing us to directly probe them. Therefore, this approach suggests that it is not justified to search for experimental evidence of the extra dimensions as if they are merely extra spacetime dimensions. On the other hand, the new approach uses a very general formalism, which can be applied to known and new generalizations of the Kaluza theory aiming to achieve more and make different experimental predictions.

The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor ${\chi }^{\mu }{}_{\nu }$ relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between ${\chi }^{\mu }{}_{\nu }$ and the microscopic conductivity tensor ${\sigma }_{k\ell }$ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohm's law.

A decade ago, the first leptogenesis model based on inflation was proposed, where the complex phase of the inflaton field carries lepton number [S. H. S. Alexander, M. E. Peskin and M. M. Sheikh-Jabbari, Phys. Rev. Lett. 96 (2006) 081301, arXiv:hep-th/0403069]. If the inflaton field is an axion, it can couple to gravitational waves and gauge fields via Chern–Simons invariants. Due to these couplings, birefringent gravitational and gauge primordial perturbations are created during inflation to generate a lepton asymmetry, establishing a possible connection between nonvanishing TB-parity-violating polarization cross-correlations and leptogenesis. We also discuss the prospect for a subset of these models which can directly source circular (V-mode) polarization in the CMB.

A flavor-space locked gauge field is shown to behave like a birefringent medium, imparting a preferred left- or right-circular polarization onto gravitational waves. In a cosmological scenario, such a gauge field can cause a primordial spectrum of gravitational waves to develop a net handedness. The degree of chiral asymmetry depends on the wavelength, the abundance of the gauge field, and the strength of the gauge coupling. An asymmetry in the gravitational wave spectrum would be imprinted on the photon polarization pattern of the cosmic microwave background at last scattering. In this scenario, cosmic parity violation is written on the sky, as we predict nonzero correlation of the curl polarization with the temperature, as well as curl with gradient polarization. We compare this phenomena with parity violation in models of chiral gravity, in which the chiral asymmetry is primordial, and with models of quintessence cosmic birefringence, in which parity-violating correlations are induced along the line of sight.

The search for possible effects of parity violations in the electromagnetic sector has achieved great accuracy with the latest cosmic microwave background (CMB) observations. The sensitivity of current and future experiments is such that the need to understand the interaction of parity violations with several competing effects is now crucial in order to improve current constraining power. It also allows to not only put constraints on the most generic features of parity violations but also for distinguishing between several production mechanisms, if any effect is ever observed. The results here reported were presented at the Cosmic Polarization Rotation workshop held in Florence on 7–8 September 2015.

The Planck 2015 cosmic microwave background (CMB) likelihood is employed to constrain the cosmological birefringence angle, i.e. the in vacuo rotation of the linear polarization that CMB photons would experience during propagation in case of parity violating coupling within the electromagnetic sector of the Standard Model of particle physics. We find $\alpha =0.0^{\circ }\pm 1.3^{\circ }\mathrm{\text{(stat)}}\pm 1^{\circ }\mathrm{\text{(sys)}}$ which is well compatible with no parity violation mechanism in action from recombination epoch to present.

We introduce a method to isolate the contribution of parity-violating modes to the peak constrained correlation function. This method can be used as a local estimate of polarization rotation. We test this method using simulations and by applying it to Planck maps [P. A. R. Ade et al., arXiv:1502.01589 astro.ph.co]. We obtain a constraint on the monopole of the polarization rotation angle $\alpha =0.31\pm 0.23$.

The polarization properties of extragalactic radio sources at frequencies higher than $20$GHz are still poorly constrained. However, their characterization would provide invaluable information about the physics of the emission processes and is crucial to estimate their contamination as foregrounds of the polarized Cosmic Microwave Background (CMB) angular power spectrum on scales $\lesssim 30$arcmin. In this contribution, after summarizing the state-of-the-art of polarimetric observations in the millimetric wavelength bands, we present our observations of a complete sample of 53 sources with $S_{20\mathrm{\text{GHz}}}>200$mJy carried out with the Australia Telescope Compact Array (ACTA) between $5.5$ and $38$GHz. The analysis clearly shows that polarization properties cannot be simply inferred from total intensity ones, as the spectral behaviors of the two signals are typically different.

Radio source observations play important roles in polarimetric cosmological studies. On the one hand, they constitute the main foregrounds for cosmic microwave background (CMB) radiation on scales smaller than 30 arcmin up to 100 GHz, on the other they can be used as targets for validation of products of polarimetric experiments dedicated to cosmology. Furthermore, extragalactic high-redshift sources have been used for cosmic polarization rotation (CPR) investigation. In this paper, we will discuss the support to cosmological studies from ground-based polarimetric observations in the radio and millimetric wavelength bands. Most of the limits to accuracy improvements arise from systematic effects and low calibration quality. We will discuss some details of interferometric calibration procedures and show some of the perspectives that the Atacama large millimeter array (ALMA) could offer for CPR studies.

The polarization of the cosmic microwave background (CMB) provides a plethora of information about the early universe. Most notably, gravitational waves from the Inflationary epoch (the leading explanation of the origin of the universe) create a unique CMB polarization $B$-mode signal. An unambiguous detection of the Inflationary $B$-mode signal would be a window into the physics of the universe as it was $10^{-36}$s after the Big Bang, at energy scales many orders of magnitude larger than what the LHC can produce. However, there are several instrumental and astrophysical sources that can obfuscate the Inflationary $B$-mode signal. One of the most difficult parameters to calibrate for CMB telescopes is the absolute orientation of the antenna’s polarization sensitive axis. A miscalibration of the polarization orientation rotates the much brighter $E$-mode signal, producing a false $B$-mode signal. The current best uncertainty on polarization orientation in the CMB community is $0.5^{\circ }$, set from extrapolating IRAM measurements of the Crab Nebula supernova remnant at 90 GHz to 150 GHz, where the CMB signals peak. This accuracy is not sufficient to convincingly detect $B$-modes predicted by currently allowable models of Inflation. We suggest to precisely measure the Crab Nebula’s polarization, which can be calibrated absolutely to $0.1^{\circ }$ from measurements of the polarized emission of Mars, and use these data to calibrate current and upcoming CMB experiments. In addition to Inflationary $B$-modes, more precise calibration will allow us to better constrain the sum of the neutrino masses and set limits on exotic physics such as parity violation through cosmic polarization rotation.

In this note, we discuss the prospect of accurate measurements of cosmic microwave background (CMB) polarization rotation with future surveys. We focus on instrumental issues, analyzing the required improvements in detection methods and calibration procedures, and discuss the impact of these requirements in the design and optimization of forthcoming CMB polarimeters.