International Journal of Modern Physics D

In this paper, the criterion used to determine whether a density perturbation will collapse to form a primordial black hole (PBH) is re-examined in respect of its use to determine the abundance of PBHs. There is particular focus on which parameter to use, the time at which the abundance should be calculated, and the use of different smoothing functions. It is concluded that, with the tools currently available, the smoothed density contrast should be used rather than the peak value, and should be calculated from the time-independent component of the density contrast in the super-horizon limit (long before perturbations enter the horizon) rather than at horizon crossing. For the first time, the effect of the choice of smoothing function upon the formation criterion is calculated, and, for a given abundance of PBHs, it is found that the uncertainty in the amplitude of the power spectrum due to this is ${𝒪}(10\%)$, an order of magnitude smaller than that suggested by previous calculations. The relation between the formation criterion stated in terms of the density contrast and the curvature perturbation ${ℛ}$ is also discussed.

We investigate the observational constraints on inflationary parameters in the context of a holographic cosmology with an induced gravity correction. We consider two situations where a universe is first filled with a scalar field and second with a tachyon field. Both cases are investigated in a slow-roll regime. We adopt a quadratic potential and an exponential potential for the scalar and the tachyon inflation, respectively. In this regard, the standard background and perturbative parameters characterizing the inflationary era are modified by correction terms. We show a good agreement between theoretical model parameters and Planck2018 observational data for both scalar and tachyon fields.

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory (QFT). Experimental developments are finally discussed.

The early-time expansion of the spacetime, namely, inflation, is introduced to solve some cosmological problems. $F(R)$ gravity is a simple extension of the general relativity to induce the inflationary expansion. The precise observation of the Cosmic Microwave Background gives us the information to inspect the model of the inflation. $F(R)$ gravity can be transformed to the Einstein–Hilbert term with a scalar field that plays the role of the inflaton. The inflaton potential is described as an explicit function of the inflaton field with a noncanonical kinetic term. In this paper, we obtain general formulae to derive the inflationary parameters including the models with a noncanonical kinetic term. The inflationary parameters are described as functions of the inflaton potential and its derivatives. We evaluate a well-known model, $F(R)=R+\gamma R^n$, to confirm the validity of our formulae. Then, we apply the procedure to a model, $R{(1+\gamma R^n)}^{1/n}$, in which it is not possible to represent the potential as an explicit function of the inflaton field with a canonical kinetic term.

We study the force-free electrodynamics on rotating black holes in the Born–Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realize that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the nonlinear theory and the extraction rate gets the maximum in the Maxwell theory.

In this paper, we have worked on the concept of complexity factor for nonstatic spherically-symmetric self-gravitating source filled with anisotropic fluid distribution in $f(R,T)$ gravity theory. The definition of complexity for dynamical sources, proposed by Herrera, is examined in the framework of $f(R,T)$ gravity. We intended to analyze the behavior of complexity factor in modified theory. For this, we defined the scalar functions through orthogonal splitting of Reimann tensor in $f(R,T)$ gravity and worked out the structure scalars. We considered the structure scalar $Y_{TF}$ as a complexity factor to evaluate the complexity of the structure of dynamical system and also to analyze the complexity of the evolutionary patterns of the system under consideration. We took into account the homologous condition and homogeneous expansion condition in order to present the simplest mode of evolution, and found that homologous evolution is the simplest one. We considered both dissipative and nondissipative cases and found that shearing behavior of the fluid is not the same in both cases, however it remained geodesic in both cases. In the end, we established the results for the vanishing of the complexity factor. It has been found that zero complexity condition is satisfied if the energy density inhomogeneity and pressure anisotropy of the fluid configuration cancel each other.

In this work, we study and compare the features of gravitational entropy near the throat of transversable wormholes formed by exotic matter and wormholes in galactic halos. We have verified that gravitational entropy and entropy density of these wormholes in regions near their throats are indistinguishable for objects of same throat, despite the fact that they are described by different metrics and by distinct energy–momentum tensors. We have found that the gravitational entropy density diverges near the throat for both cases, probably due to a nontrivial topology at this point, however, allowing the interesting interpretation that a maximum flux of information can be carried through the throat of these wormholes. In addition, we have found that both are endowed with an entropic behaviour similar to Hawking–Bekenstein’s entropy of nonrotating and null charge black holes.

We study the stability properties of static, spherically symmetric configurations in $k$-essence theories with the Lagrangians of the form $F(X)$, $X\equiv {\varphi }_{,\alpha }{\varphi }^{,\alpha }$. The instability under spherically symmetric perturbations is proved for the two recently obtained exact solutions for $F(X)=F_0{X}^{1/3}$ and for $F(X)=F_0{X}^{1/2}-2\mathrm{\Lambda }$, where $F_0$ and $\mathrm{\Lambda }$ are constants. The first solution describes a black hole in an asymptotically singular spacetime, the second one contains two horizons of infinite area connected by a wormhole. It is argued that spherically symmetric $k$-essence configurations with $n<1/2$ are generically unstable because the perturbation equation is not of hyperbolic type.

We analyze a few illustrative examples of scenarios in which relativistic symmetries are deformed by Planck-scale effects in particle-type-dependent manner. The novel mathematical structures required by such scenarios are the mixing coproducts, which govern the (deformed) law of conservation of energy and momentum when particles with different relativistic properties interact. We also comment on the relevance of these findings for the recent proposals concerning the possibility that neutrinos might have relativistic properties which are different from those of photons and/or the possibility that composite particles might have relativistic properties which are different from those of fundamental ones.

Intending to describe the dark matter (DM) of dwarf galaxies, we concentrate on one model of the slowly rotating and gravitating Bose–Einstein condensate (BEC). For a deeper understanding of its properties, we calculate the partition function and compare the characteristics derived from it with the results based on the solution of Gross–Pitaevskii equation (GPE). In our approach, which uses Green’s functions of spatial evolution operators, we formulate in a unified way the boundary conditions, important for applying the Thomas–Fermi approximation. Taking this into account, we revise some of the results obtained earlier. We also derive the spatial particle distribution, similar to the model with rotation, by using the deformation of commutation relations for a macroscopic wave function and modifying the GPE. It is shown that such an approach leads to the entropy inhomogeneity and makes the distribution dependent on temperature.

A geometric torsion (GT) underlying a $2$-form in a $(4+1)$-dimensional $U(1)$ gauge theory is revisited with a renewed perspective for a nonperturbation (NP) gravity in $d=4$. In this context, we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a $(B_2\wedge F_2)$ coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is identified as a mass dipole and is shown to be sourced by a propagating GT. A detailed analysis is performed in a bulk GT to show a modification to the precession of perihelion in a boundary NP gravity. The perspective of an electromagnetic (EM) wave in the bulk is investigated to reveal a spin $2$ (mass-less) quantum sourced by an apparent 2-form. A Goldstone scalar is absorbed by the apparent 2-form to describe a massive $2$-form in the coulomb gauge. Alternately a Goldstone scalar together with a local degree of GT and 2-form is argued to govern a composite (mass-less) spin $2$ particle in Lorentz gauge. Both the scenarios, further ensure a graviton in a boundary NP gravity. A qualitative analysis reveals a (noninteracting) graviton underlying a plausible gravitational wave/particle duality in NP gravity.