Enlightening the CSL model landscape in inflation

We propose a novel realization for the natural extrapolation of the continuous spontaneous localization (CSL) model, in order to account for the origin of primordial inhomogeneities during inflation. This particular model is based on three main elements: (i) the semiclassical gravity framework, (ii) a collapse-generating operator associated to a relativistic invariant scalar of the energy-momentum tensor, and (iii) an extension of the CSL parameter(s) as a function of the spacetime curvature. Furthermore, employing standard cosmological perturbation theory at linear order, and for a reasonable range within the parameter space of the model, we obtain a nearly scale invariant power spectrum consistent with recent observational CMB data. This opens a vast landscape of different options for the application of the CSL model to the cosmological context, and possibly sheds light on searches for a full covariant version of the CSL theory.

Shift-symmetric 𝖲𝖮(𝖭) multi-Galileon

A Poincarè invariant, local scalar field theory in which the Lagrangian and the equation of motion contain only up to second-order derivatives of the fields is called generalized Galileon. The covariant version of it in four dimensions is called Horndeski theory, and has been vigorously studied in applications to inflation and dark energy. In this paper, we study a class of multi-field extensions of the generalized Galileon theory. By imposing shift and SO(N) symmetries on all the currently known multi-Galileon terms in general dimensions, we find that the structure of the Lagrangian is uniquely determined and parameterized by a series of coupling constants. We also study tensor perturbation in the shift-symmetric SO(3) multi-Galileon theory in four dimensions. The tensor perturbations can obtain a mass term stemming from the same symmetry breaking pattern as the solid inflation. We also find that the shift-symmetric SO(3) multi-Galileon theory gives rise to new cubic interactions of the tensor modes, suggesting the existence of a new type of tensor primordial non-Gaussianity.

Further useful ideas

The chapter discusses several further aspects of the physics and mathematics that prove very useful in practice. First we define 4-velocity, 4-momentum and 4-acceleration. Then we introduce the tetrad and show how it can be used to relate a given 4-momentum to the energy and momentum observed in a LIF (local inertial frame). Then we define covariant version of the vector operators div, grad, curl, and obtain simplified expressions for the divergence of a vector and an antisymmetric tensor. The generalized Gauss divergence theorem is then presented.

The worldsheet dual of free super Yang-Mills in 4D

The worldsheet string theory dual to free 4d $$ \mathcal{N} $$ N = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 × S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3. As in the case of AdS3, the worldsheet theory contains spectrally flowed representations. We proposed in [1] that in each such sector only a finite set of generalised zero modes (‘wedge modes’) are physical. Here we show that after imposing the appropriate residual gauge conditions, this worldsheet description reproduces precisely the spectrum of the planar gauge theory. Specifically, the states in the sector with w units of spectral flow match with single trace operators built out of w super Yang-Mills fields (‘letters’). The resulting physical picture is a covariant version of the BMN light-cone string, now with a finite number of twistorial string bit constituents of an essentially topological worldsheet.

Analogous Hawking Effect in Dielectric Media and Solitonic Solutions

We review some aspects of our longstanding research concerning the analogous Hawking effect in dispersive dielectric media. We introduce nonlinear contributions in the polarization field in the relativistically covariant version of the Hopfield model and then, in order to provide a simplified description aimed at avoiding some subtleties in the quantization of the original model, we discuss the so-called ϕψ-model. We show that the nonlinearity allows for introducing in a self-consistent way the otherwise phenomenological dependence of the susceptibility and of the resonance frequency ω0 on the spacetime variables, and this is a consequence of the linearization of the model around solitonic solutions representing propagating perturbations of the refractive index, to be then associated with the Hawking effect.

Galilean covariant effective theory for bound states of heavy mesons

In this work we formulate the Galilei-covariant version of an effective theory containing nonrelativistic heavy mesons and pions as degrees of freedom. This manifestly Galilean covariant framework is based on a five-dimensional space–time that has been used in the description of covariant nonrelativistic physics. In this context, effective Lagrangian is introduced without ambiguities, containing kinetic and interaction terms that are naturally Galilean invariant. The leading-order scattering amplitudes and the properties of possible heavy-meson bound states are calculated and discussed.

Anisotropic Jüttner (relativistic Boltzmann) distribution

A rigorous derivation of the Jüttner (covariant Boltzmann) distribution is provided for anisotropic pressure (or temperature) tensors. It was in similar form anticipated first by Gladd (1983). Its manifestly covariant version follows straightforwardly from its scalar property.