Universe, Volume 8, Issue 11 (November 2022) – 60 articles

A study of the top-quark interactions via flavour-changing neutral current (FCNC) processes provides an intriguing connection between the heaviest elementary particle of the standard model (SM) of particle physics and the new scalar bosons that are predicted in several notable SM extensions. The production cross sections of the processes with top-scalar FCNC interactions can be significantly enhanced to the observable level at the CERN Large Hadron Collider. The present review summarises the latest experimental results on the study of the top-quark interactions with the Higgs boson via an FCNC and describes several promising directions to look for new scalar particles. Full article

Many exoplanets have been detected by the radial velocity method, according to which the motion of a binary system around its center of mass can produce a periodical variation of the Doppler effect of the light emitted by the host star. These variations are influenced by both Newtonian and non-Newtonian perturbations to the dominant inverse-square acceleration; accordingly, exoplanetary systems lend themselves to testing theories of gravity alternative to general relativity. In this paper, we consider the impact of the Standard Model Extension (a model that can be used to test all possible Lorentz violations) on the perturbation of radial velocity and suggest that suitable exoplanets’ configurations and improvements in detection techniques may contribute to obtaining new constraints on the model parameters. Full article

Active Galactic Nuclei (AGNs) and their relativistic jets belong to the most promising class of ultra-high-energy cosmic ray (UHECR) accelerators. This compact review summarises basic experimental findings by recent instruments, and discusses possible interpretations and astrophysical constraints on source energetics. Particular attention is given to potential sites and mechanisms of UHECR acceleration in AGNs, including gap-type particle acceleration close to the black hole, as well as first-order Fermi acceleration at trans-relativistic shocks and stochastic shear particle acceleration in large-scale jets. It is argued that the last two represent the most promising mechanisms given our current understanding, and that nearby FR I type radio galaxies provide a suitable environment for UHECR acceleration. Full article

There were 51 superactive regions (SARs) during solar cycles (SCs) 21–24. We divided the SARs into SARs₁, which produced extreme space weather events including ≥X5.0 flares, ground level events (GLEs), and super geomagnetic storms (SGSs, Dst < −250 nT), and SARs₂, which did not produce extreme space weather events. The total number of SARs₁ and SARs₂ are 31 and 20, respectively. The statistical results showed that 35.5%, 64.5%, and 77.4% of the SARs₁ appeared in the ascending phase, descending phase, and in the period from two years before to the three years after the solar maximum, respectively, whereas 50%, 50%, and 100% of the SARs₂ appeared in the ascending phase, descending phase, and in the period from two years before to the three years after the solar maximum, respectively. The total number of SARs during an SC has a good association with the SC amplitude, implying that an SC with a higher amplitude will have more SARs than that with a lower amplitude. However, the largest flare index of a SAR within an SC has a poor association with the SC amplitude, suggesting that a weak cycle may have a SAR that may produce a series of very strong solar flares. The analysis of the north–south asymmetry of the SARs showed that SARs₁ dominated in the southern hemisphere of the sun during SCs 21–24. The SAR₂ dominated in the different hemispheres by turns for different SCs. The solar flare activities caused by the SARs with source locations in the southern hemisphere of the sun were much stronger than those caused by the SARs with source locations in the northern hemisphere of the sun during SCs 21–24. Full article

The correspondence between the shadow radius and the real part of the quasinormal modes (QNMs) of a Kerr–Sen black hole is studied. By using the equation of the shadow radius of Kerr–Sen black hole and the angular separation constant of the QNMs, the expression of QNMs related to shadow radius is established in the eikonal limit. We found that, our formula can reduce to the previous result of Kerr black hole when Kerr-Sen parameter b sets to zero. Full article

Black hole horizons interact with external fields when matter or energy falls through them. Such non-stationary black hole horizons can be described using viscous fluid equations. This work attempts to describe this process using effective field theory methods. Such a description can provide important insights beyond classical black hole physics. In this work, we construct a low-energy effective field theory description for the horizon-fluid of a 4-dimensional, asymptotically flat, Einstein black hole. The effective field theory of the dynamical horizon has two ingredients: degrees of freedom involved in the interaction with external fields and symmetry. The dual requirements of incorporating near-horizon symmetries ($\mathcal{S}1$ diffeomorphism) and possessing length scales due to external perturbations are naturally satisfied if the theory on the non-stationary black hole horizon is a deformed Conformal Field Theory (CFT). For the homogeneous external perturbations, at the lowest order, this leads to a $(2+1)$-dimensional massive scalar field where the mass is related to the extent of the deformation of the CFT. We determine the mass by obtaining the correlation function corresponding to the effective field and relating it to the bulk viscosity of the horizon-fluid. Additionally, we show that the coefficient of bulk viscosity of the horizon-fluid determines the time required for black holes to scramble. Furthermore, we argue that matter-field modes with energy less than $m_{\mathrm{eff}}$ falling into the horizon thermalize more slowly. Finally, we construct a microscopic toy model for the horizon-fluid that reduces to the effective field theory with a single scalar degree of freedom. We then discuss the usefulness of the effective field model in understanding how information escapes from a black hole at late times. Full article

We examined Hubble Space Telescope images of Saturn’s northern UV aurora in 2013–2017, identified 29 short-lived flashes, and examined simultaneous magnetometer data collected by the Cassini orbiter. When observation cadence permitted, a flash lifetime of 4–17 min (subject to exposure time-related uncertainties), and a 40–70 min recurrence period were found. An occurrence map shows a strong preference in both local time (14–19 LT) and latitude (75–85${}^{°}$). These transient flashes are identified in both the presence and absence of Saturn’s main auroral oval, indicating the lack of dependence on the main emission power. The concurrent magnetic field pulsations generally form a sawtooth shape, and the local field strength experiences a change of 0.2 to 2.0 nT (depending on the distance of Cassini). The quasiperiodic pulsation events were all detected when the spacecraft was in the southern hemisphere with conjugate flashes in northern aurora, suggesting these events occur on closed field lines, and typically showing a sudden transition to a less lagging, more southward magnetic field configuration. We also found the ionospheric footprint of the spacecraft must be close to the region of flashes for magnetic field pulsations to be detected, implying a localised rather than global driving process. Full article

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar–scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo-field dynamics and the Schwinger–Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at finite times and other non-equilibrium processes, including those found in the theory of open quantum systems. Full article

The holographic space-time (HST) model of inflation has a potential explanation for dark matter as tiny primordial black holes. Motivated by a recent paper of Barrau, we propose a version of this model where some of the inflationary black holes (IBHs), whose decay gives rise to the Hot Big Bang, carry the smallest value of a discrete symmetry charge. The fraction f of IBHs carrying this charge is difficult to estimate from first principles, but we determine it by requiring that the crossover between radiation and matter domination occurs at the correct temperature $T_{eq}\sim 1\mathrm{eV}={10}^{-28}{M}_P$. The fraction is small, $f\sim 2\times {10}^{-9}$, so we believe this gives an extremely plausible model of dark matter. Full article

This paper is devoted to computing the weak deflection angle for the Kalb–Ramond traversable wormhole solution in plasma and dark matter mediums by using the method of Gibbons and Werner. To acquire our results, we evaluate Gaussian optical curvature by utilizing the Gauss–Bonnet theorem in the weak field limits. We also investigate the graphical influence of the deflection angle $\tilde{\alpha }$ with respect to the impact parameter $\sigma$ and the minimal radius $r_0$ in the plasma medium. Moreover, we derive the deflection angle by using a different method known as the Keeton and Petters method. We also examine that if we remove the effects of plasma and dark matter, the results become identical to that of the non-plasma case. Full article

We give a general overview of various flavours of the equivalence principle in classical and quantum physics, with special emphasis on the so-called weak equivalence principle, and contrast its validity in mechanics versus field theory. We also discuss its generalisation to a theory of quantum gravity. Our analysis suggests that only the strong equivalence principle can be considered fundamental enough to be generalised to a quantum gravity context since all other flavours of equivalence principle hold only approximately already at the classical level. Full article

In the present paper, we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field, whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in the literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantities, namely, internal energy and entropy. For each one of them, we also investigate the limits of high and low temperatures. At high temperatures, we found that the renormalized Casimir free energy presents classical contributions, along with a logarithmic term. Also in this limit, the internal energy presents a classical contribution and the entropy a logarithmic term, in addition to a classical contribution as well. Conversely, at low temperatures, it is demonstrated that both the renormalized Casimir free energy and internal energy are dominated by the vacuum energy at zero temperature. It is also demonstrated that the entropy obeys the third law of thermodynamics. Full article

Based on the spectra with high resolution and a high signal-to-noise ratio, we investigate the enrichment history of the s-process element in seven barium (Ba) stars by measuring their Ba odd isotope fraction. It is found that the relative contributions of the s-process to their Ba abundance are $91.4\pm 25.7\%$, $91.4\pm 34.3\%$, $82.9\pm 28.5\%$, $77.1\pm 31.4\%$, and $71.4\pm 37.1\%$ for REJ 0702+129, HD 13611, BD+${80}^{°}670$, HR 5692, and HD 202109, respectively. Our results suggest that these five Ba stars have a prominent s-process signature, which indicates that their heavy elements mainly come from their former AGB companions (now WDs) by mass transfer, while the r-process contribution can naturally be explained by the evolution of the Milky Way. The s-process contribution of BD+${80}^{°}670$ is $51.4\pm 31.4\%$, which is the lowest among our seven sample stars. Considering its lower values of both [Ba/Nd] and [Ba/Eu], we suspect that BD+${68}^{°}1027$ is likely to be a r-rich Ba star and has similar origins to the CEMP-r/s stars. HD 218356 has an unreasonable s-process contribution over $100\%$. Combining its stellar atmospheric parameters and the evolutionary stage, we speculate that HD 218356 is a more evolved extrinsic Ba star, and its massive companion should have the largest s-process efficiency in our samples. Full article

In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type $(\alpha ,\beta )$ admits a Ricci soliton where the covariant derivative of potential vector field V in the direction of unit vector field $\xi$ is orthogonal to $\xi$. It is also demonstrated that if the structure functions meet ${\alpha }^2={\beta }^2$, then the covariant derivative of V in the direction of $\xi$ is a constant multiple of $\xi$. Furthermore, the nature of scalar curvature is evolved when the manifold of type $(\alpha ,\beta )$ satisfies *-conformal Ricci soliton, provided $\alpha \ne 0$. Finally, an example is presented to verify the findings. Full article

In a previous paper we have shown that superluminal particles are allowed by the general relativistic theory of gravity provided that the metric is locally Euclidean. Here we calculate the probability density function of a canonical ensemble of superluminal particles as function of temperature. This is done for both space-times invariant under the Lorentz symmetry group, and for space times invariant under an Euclidean symmetry group. Although only the Lorentzian metric is stable for normal matter density, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time consisting of the very early universe, which is characterized by extremely high densities and temperatures. Superluminal particles also allow attaining thermodynamic equilibrium at a shorter duration and suggest a rapid expansion of the matter density. Full article

The sampling effect of the imaging acquisition device is an integration of the input signal within the pixel, resulting in an additional error in the pixel value. Additionally, a sampler with asymmetric intra-pixel quantum efficiency leads to position errors in high-precision astrometry. This paper proposes a model for the integral sampling process. An algorithm that solves the sampling effect, as well as the position error with high accuracy, is also provided. This algorithm provides an accuracy increase of ${10}^6$ for Gaussian images with a uniform integral sampler. The accuracy limit of the Gaussian image comes from the truncation error. Also, this algorithm provides about 4 times accuracy improvement by eliminating the systematic error caused by the integral sampler with asymmetric intra-pixel quantum efficiency. Full article

In this paper, the extended simple equation method (ESEM) and the generalized Riccati equation mapping (GREM) method are applied to the nonlinear third-order Gilson–Pickering (GP) model to obtain a variety of new exact wave solutions. With the suitable selection of parameters involved in the model, some familiar physical governing models such as the Camassa–Holm (CH) equation, the Fornberg–Whitham (FW) equation, and the Rosenau–Hyman (RH) equation are obtained. The graphical representation of solutions under different constraints shows the dark, bright, combined dark–bright, periodic, singular, and kink soliton. For the graphical representation, 3D plots, contour plots, and 2D plots of some acquired solutions are illustrated. The obtained wave solutions motivate researchers to enhance their theories to the best of their capacities and to utilize the outcomes in other nonlinear cases. The executed methods are shown to be practical and straightforward for approaching the considered equation and may be utilized to study abundant types of NLEEs arising in physics, engineering, and applied sciences. Full article

Computer modeling of the outflow from Be stars is performed. In our approach, processes of turbulence excitation and turbulent viscosity are added to the conventional model of the radiation driven winds. The objective of our study is to reproduce from the first principles the main features of the outflow from Be stars: a fast polar wind and a slow viscous Keplerian disk at the equator. At sub-critical velocity of rotation up to 0.999 of the critical velocity, our model reproduces the formation of the fast polar wind together with a slow highly turbulent outflow at the equatorial region. This outflow, however, does not reassemble a Keplerian disk. We link this to the absence of the angular moment transfer from the star to the disk. This process provides an increase of the angular momentum of the disk matter with radius. We consider a star with super critical rotation as the simplest way to supply the angular momentum to the disk. In this case, the star surface has a higher azimuthal speed than the matter at the inner edge of the disk. The angular momentum transfer becomes unavoidable. Already at rotation velocity 0.5% above the critical one, a quasi Keplerian disk at the equator is formed with size ∼10 stellar radius. At rotation 1% higher than the critical speed, the disk reaches ∼15 stellar radius. The main conclusion following from our work is that the conventional model of the radiation driven winds is able to reproduce the main features of the outflow from Be stars provided that the process of turbulence excitation and a process of angular momentum supply of the disk from the central source are added in to this model. Full article

Nuclear matter, at sufficiently energy density and high temperature, undergoes a transition to a state of strongly interacting QCD matter in which quarks and gluons are not confined known as the Quark–Gluon Plasma (QGP). QGP is usually produced in high-energy collisions of heavy nuclei in the laboratory, where an enhancement of strange hadrons’ production is observed. Many of the effects which are typical of heavy ion phenomenology have been observed in high-multiplicity proton–proton (pp) collisions. The enhancement of strange particles’ production in pp collisions was reported at $\sqrt{s}=7$ TeV and $\sqrt{s}=13$ TeV in 2017 and 2020, respectively, and it was found that the integrated yields of strange particles, relative to pions, increase notably with the charged-particle multiplicity of events. Here, we report the multiplicity dependence of strange particles at $\left|y\right|<0.5$ in pp collisions at $\sqrt{s}$ = 7 TeV, 13 TeV, 20 TeV, and 27 TeV from a Monte Carlo simulation using PYTHIA8, EPOS-LHC, and Herwig7. Full article

We exploit the recent determination of the cosmic star formation rate (SFR) density at high redshifts $z\gtrsim 4$ to derive astroparticle constraints on three common dark matter (DM) scenarios alternative to standard cold dark matter (CDM): warm dark matter (WDM), fuzzy dark matter ($\psi$DM) and self-interacting dark matter (SIDM). Our analysis relies on the ultraviolet (UV) luminosity functions measured from blank field surveys by the Hubble Space Telescope out to $z\lesssim 10$ and down to UV magnitudes $M_{\mathrm{UV}}\lesssim -17$. We extrapolate these to fainter yet unexplored magnitude ranges and perform abundance matching with the halo mass functions in a given DM scenario, thus, obtaining a redshift-dependent relationship between the UV magnitude and the halo mass. We then computed the cosmic SFR density by integrating the extrapolated UV luminosity functions down to a faint magnitude limit $M_{\mathrm{UV}}^{\lim }$, which is determined via the above abundance matching relationship by two free parameters: the minimum threshold halo mass $M_{\mathrm{H}}^{\mathrm{GF}}$ for galaxy formation, and the astroparticle quantity X characterizing each DM scenario (namely, particle mass for WDM and $\psi$DM, and kinetic temperature at decoupling $T_X$ for SIDM). We perform Bayesian inference on such parameters using a Monte Carlo Markov Chain (MCMC) technique by comparing the cosmic SFR density from our approach to the current observational estimates at $z\gtrsim 4$, constraining the WDM particle mass to $m_X\approx 1.2_{-0.4(-0.5)}^{+0.3\left(11.3\right)}$ keV, the $\psi$DM particle mass to $m_X\approx 3.7_{-0.4(-0.5)}^{+1.8(+12.9.3)}\times {10}^{-22}$ eV, and the SIDM temperature to $T_X\approx 0.{21}_{-0.06(-0.07)}^{+0.04(+1.8)}$ keV at $68\%$ ($95\%$) confidence level. Finally, we forecast how such constraints will be strengthened by upcoming refined estimates of the cosmic SFR density if the early data on the UV luminosity function at $z\gtrsim 10$ from the James Webb Space Telescope (JWST) will be confirmed down to ultra-faint magnitudes. Full article

We study the gamma-ray burst (GRB) afterglow light curves produced by an off-axis jet in a stratified circumburst medium and summarize the temporal indices of the coasting phase, the deceleration phase, the Newtonian phase, and the deep Newtonian phase for various viewing angles and power-law indices of medium density. Generally, the afterglow light curves of off-axis GRBs in the homogeneous interstellar medium have a steep rise arising due to jet deceleration. In the stratified medium, the flux rises is more shallow but peaks earlier for the same viewing angle due to faster deceleration of the jet running into the denser stratified medium, compared with the case of the interstellar medium (ISM). Observations of off-axis bursts will possibly increase over the coming years due to the arrival of the multi-messenger era and the forthcoming surveys in multiple bands. The temporal indices of off-axis afterglows derived in the paper will provide a reference for comparison with the observations and can diagnose the circumburst environment. The numerical code calculating the afterglow light curve also can be used to fit the multi-wavelength light curves. Full article

We considered the fourth catalog of gamma-ray point sources produced by the Fermi Large Area Telescope (LAT) and selected only jetted active galactic nuclei (AGN) or sources with no specific classification, but with a low-frequency counterpart. Our final list is composed of 2980 gamma-ray point sources. We then searched for optical spectra in all the available literature and publicly available databases, to measure redshifts and to confirm or change the original LAT classification. Our final list of gamma-ray emitting jetted AGN is composed of BL Lac Objects (40%), flat-spectrum radio quasars (23%), misaligned AGN (2.8%), narrow-line Seyfert 1, Seyfert, and low-ionization nuclear emission-line region galaxies (1.9%). We also found a significant number of objects changing from one type to another, and vice versa (changing-look AGN, 1.1%). About 30% of gamma-ray sources still have an ambiguous classification or lack one altogether. Full article

We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal transformations for a Dirac fermion in curved spacetime are considered and we obtain the expression for the energy-momentum tensor on the cosmological background. Full article

The origin of gamma-ray flares of blazars is still an open issue in jet physics. In this work, we reproduce the multiwavelength spectral energy distribution (SED) of flat-spectrum radio quasars 3C 454.3 under a one-zone leptonic scenario, investigate the variation of the physical parameters in different activity states, and analyze the possible origin of its $\gamma$-ray outburst. Based on the analysis of multiwavelength quasi-simultaneous observations of 3C 454.3 during MJD 55,400–56,000, we consider that the radiation includes synchrotron (Syn), synchrotron self-Compton (SSC), and external Compton (EC) radiations by the simulation, and the seed photons of the external Compton component mainly comes from the broad-line region and dusty molecular torus. The model results show that: (1) We can well reproduce the multiwavelength quasi-simultaneity SED of 3C 454.3 in various activity states by using a one-zone Syn+SSC+EC model. (2) By comparing the physical model parameters of the bright and the quiescent states, we suggest that this $\gamma$-ray flaring activity is more likely to be caused by the increase in the doppler factor. Full article

In this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the $(2+1)$-dimensional Hirota–Maccari system. The $(2+1)$-dimensional Hirota–Maccari system is a special kind of nonlinear Schrödinger equation (NLSEs) that models the motion of isolated waves localized in a small part of space, and is used in such various fields as fiber optics telecommunication systems, nonlinear optics, plasma physics, and hydrodynamics. In addition, the Hirota–Maccari system defines the dynamical characters of femtosecond soliton pulse propagation in single-mode fibers. Analytical solutions of the model are successfully acquired with the assistance of symbolic computation utilizing these methods. Finally, 3D, 2D, and contour graphs of solutions are depicted at specific values of parameters. It is shown that the new Kudryashov method and the tanh-coth method are uncomplicated, very effective, easily applicable, reliable, and indeed vital mathematical tools in solving nonlinear models. Full article

The Newtonian Lagrangian perturbation theory is a widely used framework to study structure formation in cosmology in the nonlinear regime. We review a general-relativistic formulation of such a perturbation approach, emphasizing results on an already developed extensive formalism including among other aspects: the non-perturbative modeling of Ricci and Weyl curvatures, gravitational waves, and pressure-supported fluids. We discuss subcases of exact solutions related to Szekeres Class II and, as an exact average model, Ricci-flat LTB models. The latter forms the basis of a generalization that we then propose in terms of a scheme that goes beyond the relativistic Lagrangian perturbation theory on a global homogeneous-isotropic background cosmology. This new approximation does not involve a homogeneous reference background and it contains Szekeres class I (and thus general LTB models) as exact subcases. Most importantly, this new approximation allows for the interaction of structure with an evolving “background cosmology”, conceived as a spatial average model, and thus includes cosmological backreaction. Full article

Nuclear pasta phases in the neutron stars mantle can affect the mechanical and transport properties of superdense matter, thus playing an important role in the dynamics and evolution of neutron stars. In this paper, we compare results obtained by the Extended Thomas–Fermi (ETF) method with the compressible liquid drop model (CLDM), based on the thermodynamically consistent description of the surface properties calculated for the two-phase plane interface and the same energy-density functional (for numerical illustration, we applied the Skyrme-type functional SLy4). Our ETF calculations found that pasta phases in cylindrical form cover a significant crustal region (both normal and inverse phases, aka spaghetti and bucatini are presented). Meanwhile, within the applied CLDM framework, which includes the thermodynamically required effect of neutron adsorption on the cluster’s surface but neglects curvature corrections, only the spaghetti phase was found to be energetically favorable in the small density range prior to crust–core transition. On the other hand, the recent CLDM of Dinh Thi et al., 2021, which, on the contrary, accounts for curvature term but neglects neutron adsorption, predicts pasta phase onset in better agreement with the ETF. This fact highlights the importance of the curvature effects and allows counting on the potential validity of the CLDMs as a convenient, transparent and accurate tool for investigation of the pasta-phase properties. Full article

We explore wormhole geometry in spiral galaxies under the third order Lovelock gravity. Using the cubic spline interpolation technique, we find the rotational velocity of test particles in the halo region of our spiral galaxy from observed values of radial distances and rotational velocities. Taking this value of the rotational velocity, we are able to show that it is possible to present a mathematical model regarding viable existence of wormholes in the galactic halo region of the Milky Way under the Lovelock gravity. A very important result that we obtain from the present investigation is that galactic wormhole in the halo region can exist with normal matter as well as exotic matter. Full article

The equation for canonical gravity produced by Wheeler and DeWitt in the late 1960s still presents difficulties both in terms of its mathematical solution and its physical interpretation. One of these issues is, notoriously, the absence of an explicit time. In this short note, we suggest one simple and straightforward way to avoid this occurrence. We go back to the classical equation that inspired Wheeler and DeWitt (namely, the Hamilton–Jacobi–Einstein equation) and make explicit, before quantization, the presence of a known, classically meaningful notion of time. We do this by allowing Hamilton’s principal function to be explicitly dependent on this time locally. This choice results in a Wheeler–DeWitt equation with time. A working solution for the de Sitter minisuperspace is shown. Full article