The Role of Longitudinal Polarizations in Horndeski and Macroscopic Gravity: Introducing Gravitational Plasmas

We discuss some general and relevant features of longitudinal gravitational modes in Horndeski gravity and their interaction with matter media. Adopting a gauge-invariant formulation, we clarify how massive scalar and vector fields can induce additional transverse and longitudinal excitations, resulting in breathing, vector, and longitudinal polarizations. We review, then, the interaction of standard gravitational waves with a molecular medium, outlining the emergence of effective massive gravitons, induced by the net quadrupole moment due to molecule deformation. Finally, we investigate the interaction of the massive mode in Horndeski gravity with a noncollisional medium, showing that Landau damping phenomenon can occur in the gravitational sector as well. That allows us to introduce the concept of “gravitational plasma”, where inertial forces associated with the background field play the role of cold ions in electromagnetic plasma.

De Sitter braneworld and gravitational waves

We study the braneworld theory constructed by multi scalar fields. The model contains a smooth and infinitely large extra dimension, allowing the background fields propagating in it. We give a de Sitter solution for the four-dimensional cosmology as a good approximation to the early universe inflation. We show that the graviton has a localizable massless mode, and a series of continuous massive modes, separated by a mass gap. There could be a normalizable massive mode, depending on the background solution. The gravitational waves of massless mode evolve the same as the four dimensional theory, while that of the massive modes evolve greatly different from the massless mode.

The future of gravitational theories in the era of the gravitational wave astronomy

We discuss the future of gravitational theories in the framework of gravitational wave (GW) astronomy after the recent GW detections (the events GW150914, GW151226, GW170104, GW170814, GW170817 and GW170608). In particular, a calculation of the frequency and angular dependent response function that a GW detector would see if massive modes from [Formula: see text] theories or scalar–tensor gravity (STG) were present, allowing for sources incident from any direction on the sky, is shown. In addition, through separate theoretical results which do not involve the recent GW detections, we show that [Formula: see text] theories of gravity having a third massless mode are ultimately ruled out while there is still room for STG having a third (massive or massless) mode and for [Formula: see text] theories of gravity having a third massive mode.

Data analysis of massive gravitational waves from gamma ray bursts

We investigate the detectability of massive mode of polarization of Gravitational Waves (GWs) in [Formula: see text] theory of gravity associated with Gamma Ray Bursts (GRBs) sources. We obtain the beam pattern function of Laser Interferometric Gravitational wave Observatory (LIGO) corresponding to the massive polarization of GWs and perform Bayesian analysis to study this polarization. It is found that the massive polarization component with a mass of [Formula: see text][Formula: see text]eV/c2 is too weak to be detected at LIGO with its current configuration.

LOOP VARIABLES AND GAUGE INVARIANCE IN (OPEN) BOSONIC STRING THEORY

We give a simplified and more complete description of the loop variable approach for writing down gauge-invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite worldsheet cutoff and that in the ir limit, equivalence with the Callan–Symanzik β-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon–photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite worldsheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into the standard form.

THE PROPER TIME FORMALISM, GAUGE INVARIANCE AND THE EFFECTS OF A FINITE WORLD SHEET CUTOFF IN STRING THEORY

We discuss the issue of going off-shell in the proper time formalism. This is done by keeping a finite world sheet cutoff. We construct one example of an off-shell covariant Klein-Gordon type interaction. For a suitable choice of the gauge transformation of the scalar field, gauge invariance is maintained off-mass-shell. However, at the second order in the gauge field interaction, one finds that [U(1)] gauge invariance is violated due to the finite cutoff. Interestingly, we find, to the lowest order, that by adding a massive mode with appropriate gauge transformation laws to the sigma model background, we can restore gauge invariance. The gauge transformation law is found to be consistent, to the order calculated, with what one expects from the interacting equation of motion of the massive field. We also extend some previous discussion on applying the proper time formalism for propagating gauge particles, to the interacting (i.e. Yang-Mills) case.

TWO-DIMENSIONAL CHIRAL GAUGE THEORIES IN THE SCHRÖDINGER REPRESENTATION

We present a quantization, in the Schrödinger representation, of a two-dimensional theory consisting of an Abelian gauge field coupled to an arbitrary number of right- and left-handed fermions. A consistent and unitary quantum theory is obtained. The gauge symmetry is broken but Lorentz invariance survives quantization. The theory contains a series of chiral massless particles and a massive mode, which can be interpreted as collective excitations of the fields that we have in the initial Lagrangian. Our formalism is quite transparent and allows a clear understanding of the consistency of the model.

Structures of conserved currents and mass spectra for scalar fields. II. A covariant formulation of the generalization of the Goldstone theorem

By adding the constraint equation [Formula: see text] on the generator G to our formulation exploited in the previous article under the same title (M. Shintani, Can. J. Phys. 58, 463 (1980)), we present a Lorentz-covariant approach to the generalized Goldstone theorem which applies even when the conserved current involves non-trivial c-number functions. As a result of the constraint equation, we derive a new key equation. By solving a new key equation together with the other key equations already obtained in the first part of this series, we can eliminate the massive mode and extract only the Goldstone modes. It is shown that any generator is either a relevant generator or an irrelevant one.