International Journal of Modern Physics A

We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, 2050104 (2020)]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum formula but for different energy polynomials and bases are found. In this work, we obtain a class of potential functions associated with the Wilson polynomial and “Jacobi basis.”

In the same way as the energy density associated with the tensor modes of the geometry modifies the evolution of the curvature perturbations, the scalar modes may also indirectly affect the cosmic backgrounds of relic gravitons by inducing higher-order corrections that are only superficially gauge-invariant. This spurious gauge-invariance gets manifest when the effective anisotropic stresses, computed in different coordinate systems, are preliminarily expressed in a form that only depends on the curvature inhomogeneities defined on comoving orthogonal hypersurfaces and on their corresponding time derivatives. Using this observation we demonstrate in general terms that the higher-order contributions derived in diverse coordinate systems coincide when the wavelengths are smaller than the sound horizon defining the evolution of the curvature inhomogeneities but they lead to sharply different results in the opposite limit. A similar drawback arises when the energy density of the relic gravitons is derived from competing energy–momentum pseudotensors and should be consistently taken into account in the related phenomenological discussions.

The experimental transverse momentum spectra of the charged pions and kaons, protons and antiprotons, produced at midrapidity in inelastic $p+p$ collisions at ${(s)}^{1/2}=2.76$, 5.02, and 7 TeV, measured by ALICE collaboration, are analyzed systematically using the thermodynamically consistent Tsallis distribution function as well as Hagedorn function with the embedded transverse flow. To compare directly the results obtained from combined (simultaneous) fits with the above theoretical model functions of midrapidity spectra of the charged pions and kaons, protons and antiprotons in $p+p$ collisions at ${(s)}^{1/2}=2.76$, 5.02, and 7 TeV, we use the optimal identical fitting $p_t$ ranges $(p_t\ge 0.5\mathrm{\text{GeV}}/c)$ in $p+p$ collisions at ${(s)}^{1/2}=2.76$, 5.02, and 7 TeV. The parameter $q$ increases consistently for all the particle species with increasing ${(s)}^{1/2}$ of $p+p$ collisions from 2.76 to 5.02 TeV, remaining practically constant within fit errors in the collision energy range ${(s)}^{1/2}=5\text{–7}$ TeV, suggesting probably a saturation and limiting behavior of the $q$ value in $p+p$ collisions at ${(s)}^{1/2}>5$ TeV. Approximate equality of the extracted nonextensivity parameter $q$ for the pions and kaons ($q\mathrm{\text{(pions)}}\approx q\mathrm{\text{(kaons)}}$) and relation $q\mathrm{\text{(mesons)}}>q\mathrm{\text{(baryons)}}$ are obtained in $p+p$ collisions at ${(s)}^{1/2}=2.76$, 5.02, and 7 TeV. Very negligible transverse (radial) flow velocity (consistent with zero value within the fit errors) is obtained in $p+p$ collisions at ${(s)}^{1/2}=2.76$, 5.02, and 7 TeV from fitting the $p_t$ distributions of the charged pions and kaons, protons and antiprotons with the Hagedorn formula with the embedded transverse flow in the selected optimal identical $p_t$ ranges as well as in the full measured $p_t$ ranges.

The root of most of the technicolor (TC) problems lies in the way the ordinary fermions acquire their masses, where an ordinary fermion $(f)$ couples to a technifermion $(F)$ mediated by an extended technicolor (ETC) boson leading to fermion masses that vary with the ETC mass scale $(M_E)$ as $1/M_E^2$. Recently, we discussed a new approach consisting of models where TC and QCD are coupled through a larger theory, in this case the solutions of these equations are modified compared to those of the isolated equations, and TC and QCD self-energies are of the irregular form, which allows us to build models where ETC boson masses can be pushed to very high energies. In this work we extend these results for 331-TC models, in particular considering a coupled system of Schwinger–Dyson equations, we show that all technifermions of the model exhibit the same asymptotic behavior for TC self-energies. As an application we discuss how the mass splitting of the order $O$(100) GeV could be generated between the second and third generation of fermions.

We investigate the relations between the black hole shadow and charged AdS black hole critical behavior in the extended phase space. Using the thermo-shadow formalism built in Ref. 1, we reveal that the shadow radius can be considered as an efficient tool to study thermodynamical black hole systems. Based on such arguments, we build a thermal profile by varying the RN–AdS black hole temperature on the shadow silhouette. Among others, the Van der Waals-like phase transition takes place. This could open a new window on the thermal picture of black holes and the corresponding thermodynamics from the observational point of view.

We suggest definition of effective interaction intensity for soft hadron collisions and discuss its energy dependence in the preasymptotic region. Practical importance of this quantity consists in separation of rising interaction radius from effective interaction intensity increase both contributing to the total cross-section growth. It would be helpful for understanding the origin of this growth at the accelerator energies. The essential feature is that the effective interaction intensity is an experimentally measurable quantity.

In this work, a new class of black hole solutions in dilaton gravity has been obtained where the dilaton field is coupled with nonlinear Maxwell invariant as a source. The background space–time in this works is considered as the $d$-dimensional toroidal metric. In the presence of the dilaton field (for some unique values of $N$), the electric field increases as we got farther away from the origin. In the absence of the dilaton field $(N=1)$, the electric field always decreases as one goes farther away from the origin. In the thermodynamical analysis, we obtain the Smarr formula for our solution. We find that the presence of the dilaton field makes the solutions to be locally stable near the origin. Also, this field vanishes the global stability near the origin compared to the no dilaton field case $(N=1)$. We can say that the dilaton field has a crucial impact on the thermodynamical stability and it is a key factor in stability analysis. We study the quasinormal modes (QNMs) of black hole solutions in dilaton gravity. For this purpose, we use the WKB approximation method upto first order corrections. We have shown the perturbations decay in corresponding diagrams when the dilaton parameter $N$ and coupling constant $\lambda$ change. Motivated by the thermodynamical analogy of black holes and Van der Waals liquid/gas systems, in this work, we investigate PV criticality of the obtained solution. We extend the phase space by considering the cosmological constant as thermodynamic pressure. We obtain the equation of state (EOS) and plot the relevant PV $(P-r_{+})$ diagrams. We also present a class of interior solutions corresponding to the exterior solution in dilaton gravity. The solution which is obtained for a linear equation of state is regular and well-behaved at the stellar interior.

In this work, we study bulk viscous Friedmann–Robertson–Walker cosmologies with hybrid expansion law. The bulk viscous theory of dissipative effects described by Eckart theory, truncated Israel–Stewart theory and full Israel–Stewart theory are implemented here. The hybrid expansion law model of scale factor is a general analytic type of evolution from which one can recover power-law and exponential expansion as a special cases. Hybrid expansion law model are applied to describe the present accelerating phase and early phases of evolution. We have determined the cosmological parameters such as Hubble parameter, deceleration parameter, jerk parameter, energy density, bulk viscous pressure and coefficient of bulk viscosity of the universe to construct physically acceptable cosmological model. We have considered both flat and closed space–time of Friedmann–Robertson–Walker cosmology to implement hybrid expansion law with dissipative effect. The variations of the coefficient of bulk viscosity with cosmic evolution are studied here in Eckart, truncated and full Israel–Stewart theory for flat and closed space–time to obtain physically acceptable hybrid expansion models driven by viscosity. We have also estimated observational constraints of the parameters of hybrid expansion law model by considering recent observational data set. We further reveal possible connections of our models with $H_0$ tension problem.

We study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebański, we apply a Dirac constraint analysis and derive an effective Hamiltonian. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing local minima in which the field strength acquires a nonzero vacuum expectation value, thereby breaking Lorentz invariance spontaneously. These possible vacua can be classified in four classes, depending on the way Lorentz symmetry is broken. We show that the small field fluctuations around these vacua involve modes for which the dynamics can develop degeneracies, resulting in shock-wave-like and/or superluminal motion. Finally, we study the physical applicability of these models, and show how the Lorentz breaking vacua might in principle be detected by coupling the model to a suitable external current, or to gravity.

String geometry theory is a candidate of the nonperturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how string backgrounds are described in string geometry theory. In this paper, we show that the string backgrounds are embedded in configurations of the fields of a string geometry model. Especially, we show that the configurations satisfy the equations of motion of the string geometry model if and only if the embedded string backgrounds satisfy their equations of motion. This means that classical dynamics of the string backgrounds are described as a part of classical dynamics in string geometry theory. Furthermore, we define an energy of the configurations in the string geometry model because they do not depend on the string geometry time. A string background can be determined by minimizing the energy.