Modern Physics Letters A

Hatayama et al. described generalized Rogers–Ramanujan (GRR) expressions for the string functions of the singlet representation of twisted affine algebras. We give here such GRR expressions for some non-singlet string functions. In the case of the algebra $A_2^{(2)}$, this gives all the string functions. We verify these expressions using Freudenthal–Kac formula.

It is well known that classical Unimodular Gravity (UG) is equivalent to General Relativity, but the equivalence at the quantum level is not clear. Here we exhibit, in the UG framework, the Quantum Cosmology (QC) for a Friedmann–Lemaitre–Robertson–Walker (FLRW) universe, considering an inflationary scenario and also introducing a deformation on the commutation relations for the minisuperspace variables (NCC).

In this paper, we study various cosmological parameters and quantities in scalar–tensor gravity (STG) from inflation and swampland conjecture. Therefore, by selecting different models as power-law, exponential, and logarithmic in the framework of scalar–tensor theory, we obtain potential, tensor-to-scalar ratio, and the scalar spectral index. Next, we examine new constraints and compare the corresponding results with the latest observable data. Here, we take advantage of the obtained results and determine the compatibility or incompatibility of the corresponding model with the swampland conjectures.

This study examines a dark energy cosmological model in the classical domain, where a generic scalar field is considered a dark energy source. Einstein’s field equations are solved in a model independent way, i.e. using a scheme of cosmological parametrization. A simple parametrization of the density parameter as a function of the cosmic scale factor is considered and investigated extensively. The results obtained are noteworthy as it shows a smooth transition from a decelerating to an accelerating phase in the recent past. Certain external datasets are used here to limit the model parameters involved in the functional form of the considered parametrization of energy density of the scalar filed. The updated Hubble datasets containing 57 data points, 1048 points of recently compiled Pantheon datasets, and also the Baryon Acoustic Oscillation (BAO) datasets are used here to determine the best-fitting model parameter values. The expressions of several significant cosmological parameters are represented as a function of redshift “$z$” and illustrated visually for the best fit values of the model parameters to better comprehend cosmic evolution. The obtained model is also compared with the $\mathrm{\Lambda }$CDM model. Our model has a distinct behavior in future and shown a big crunch type collapse. The best fit values of the model parameters are also used to compute the current values of several physical and geometrical parameters, as well as phase transition redshift. To examine the nature of dark energy, certain cosmological tests and diagnostic analyses are done on the derived model.

In this paper, we study the effect of nonfactorizable background geometry on the thermodynamics of the clustering of galaxies. A canonical partition function is derived for the gravitating system of galaxies treated as point particles contained in cells of appropriate dimensions. Various thermodynamic equations of state, like Helmholtz free energy and entropy, among others, are also obtained. We also estimate the effect of the corrected Newton’s law on the distribution function of galaxies. Remarkably, the effect of the modified Newton’s law is seen only in the clustering parameter while the standard structure of the equations is preserved. A comparison of the modified clustering parameter $(b^{\ast })$ with that of the original clustering parameter is made to visualize the effect of the correction on the time scale of clustering. The possibility of system symmetry breaking is also analyzed by investigating the behavior of the specific heat with increasing system temperature.

The main objective of this paper is to examine the physical features and stability of anisotropic compact stellar objects in energy–momentum squared gravity. For this purpose, we apply Krori–Barua metric solutions and consider three different models of this modified theory to examine the physical characteristics of Her X-1, 4U 1538-52 and SAX J1808.4-3658 compact stars. We analyze the behavior of various physical quantities such as energy density, pressure components, energy conditions, equation of state parameter and anisotropic factor in the interior of these stars. We then use the estimated values of the sound speed and of the adiabatic index to explore the stability of these compact stars. It is found that all the required conditions are satisfied corresponding to all the selected models. We are therefore allowed to conclude that this modified theory provides viable and stable anisotropic compact stars.

Based on the Standard Model Extension, we study the influences of Lorentz symmetry breaking effects on the interaction of a neutral spin-zero Duffin–Kemmer–Petiau particle. This particle is non-minimal coupled to a Cornell-type potential, which represents a generalized relativistic quantum oscillator model. This system is considered in the background of the Lorentz symmetry breaking mechanics generated by an electric field and a fixed vector field, which in turn provides a type of magnetic dipole moment. The generalized Duffin–Kemmer–Petiau equation is constructed incorporating that non-minimal CPT-odd coupling. Exact analytical spectral properties are derived for two special configurations of the electric and fixed vector field, both exhibiting a cylindric symmetry.