International Journal of Modern Physics A

Here, we review the most recent progress in our understanding of quantum mechanical observables in cosmology in the perturbative regime. It relies on an approach that considers them directly as functions of the data at the spacelike boundary at future infinity prescinding from the explicit time evolution. It takes inspiration from the on-shell formulation of perturbative scattering amplitudes developed in the past 20 years: starting with the requirement of consistency with some fundamental principles such as causality, unitarity and locality, it provides different ways of phrasing and extracting predictions. In this review, we aim to provide a pedagogical treatment of the most recent insights about the analytic structure of the perturbative quantum mechanical observables in cosmology, its relation to fundamental principles as well as physical processes, and how such observables and their features emerge from novel well-defined mathematical objects with their own first principle definition. The review is divided into three parts: Part 0 discusses the definition of quantum mechanical observables in cosmology and some general principles; Part I reviews the boundary approach to the analysis and computation of the perturbative wave function of the universe; Part II provides an introduction to the combinatorial-geometrical description of cosmological processes in terms of cosmological polytopes.

Usually considered highly speculative, tachyons can be treated via straightforward Einsteinian dynamics. Kinetic theory and thermodynamics for a gas of “dark” tachyons are readily constructed. Such a gas exhibits density and pressure which, for the dominant constituent of a suitable Friedmann–Robertson–Walker space–time, can drive cosmic evolution with features both similar to and distinct from those of a standard dark-energy/dark-matter model. Hence, tachyons might bear further consideration as a cosmic dark-matter candidate.

The angles and the lengths of the sides of all unitarity triangles of the Cabibbo–Kobayashi–Maskawa (CKM) matrix are determined with very high precision from the experimental data. Our analysis is independent of parameterization of the CKM matrix and it is based on the predictions of the unitarity for the angles and the areas of the unitarity triangles. We note that the lengths of the sides of the three unitarity triangles determined from the experimental data do not form a triangle. We resolve this incompatibility by performing a constrained fit, assuming the equality of the area of the unitarity triangles. We demonstrate that the measured data are compatible with the predictions of the unitarity of the CKM matrix. We show that the angles of the unitarity triangles obtained by the multiplication of the rows of the CKM matrix can be obtained from the angles obtained by the multiplication of the columns. The equality of those two types of angles is a simple, but a very powerful test of the general structure of the Standard Model.

We apply the supervariable approach to derive the proper quantum Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetries for the 1D diffeomorphism invariant model of a free scalar relativistic particle by exploiting the infinitesimal classical reparameterization (i.e. 1D diffeomorphism) symmetry of this theory. We derive the conserved and off-shell nilpotent (anti-)BRST charges and prove their absolute anticommutativity property by using the virtues of Curci–Ferrari (CF)-type restriction of our present theory. We establish the sanctity of the existence of CF-type restriction (i) by considering the (anti-)BRST symmetry transformations of the coupled (but equivalent) Lagrangians and (ii) by proving the symmetry invariance of the Lagrangians within the framework of supervariable approach. We capture the nilpotency and absolute anticommutativity of the conserved (anti-)BRST charges within the framework of (anti-)chiral supervariable approach (ACSA) to BRST formalism. One of the novel observations of our present endeavor is the derivation of CF-type restriction by using the modified Bonora–Tonin (BT) supervariable approach (while deriving the (anti-)BRST symmetries for the target space–time and/or momenta variables) and by symmetry considerations of the Lagrangians of the theory. The rest of the (anti-)BRST symmetries, for the other variables, are derived by using the newly proposed ACSA. We also demonstrate the existence of CF-type restriction in the proof of absolute anticommutativity of the (anti-)BRST charges.

In this paper, we construct the diquark–diquark–diquark-type vector six-quark currents to investigate the vector and scalar hexaquark states in the framework of the QCD sum rules in a consistent way, and make predictions for the hexaquark masses. We can search for the fully heavy hexaquark states in the di-${\mathrm{\Omega }}_{ccc}$ and di-${\mathrm{\Omega }}_{bbb}$ invariant mass spectra in the future. Combined with our previous works on the fully heavy tetraquark states and pentaquark states, the present predictions can shed light on the nature of the fully heavy multiquark states.

In this paper, we consider Kasner space-time describing anisotropic three-dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative solution of relativistic Boltzmann equation with relaxation time approximation. We show that our results for second- and third-order evolution equations reduce to those of one-dimensional expansion case under suitable conditions for the anisotropic parameters in Kasner space-time.