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Abstract: This paper focuses on the implications of a commutative formulation that integrates branch‐cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Building on a mini‐superspace structure, we explore the impact of an inflaton‐type scalar field on the wave function of the Universe. Specifically analyzing the dynamical solutions of branch‐cut gravity within a mini‐superspace framework, we emphasize the scalar field's influence on the evolution of the evolution of the wave function of the Universe. Our research unveils a helix‐like function that characterizes a topologically foliated spacetime structure. The starting point is the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as . The corresponding wave equations are derived and are resolved. The commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. Additionally, we delve into a mini‐superspace of variables, incorporating scalar‐inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions for the wave equations without recurring to numerical approximations.

We continue studying the phenomenological model in which dark energy in the form of the cosmological constant is identified with the mean of the energy–momentum tensor of the causally disconnected region. We completely define the time-dependent model parameter and clarify its physical meaning. We find the scalar field potential corresponding to the proposed approach. We show that two stages of superfast expansion of the Universe existed. The the Universe heating stage occurred naturally due to the positive definiteness requirement for the energy and is reflected in the obtained scalar field potential. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the scalar field dark energy (DE) models within the context of F (T , T G) gravity. Scalar field models are known for their dynamic nature. Parameters in the dynamical equation of state are responsible for the acceleration of the cosmos in recent epochs. We determined that the power-law cosmology fits the OHD and Pantheon data nicely. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo (MCMC) method, we examine the three sets of the model parameters H 0 = 6 3. 2 6 − 0. 9 7 + 0. 7 7 q = − 0. 0 3 9 0. 0 0 2 9 + 0. 0 0 2 9 obtained by 57 points of the H (z) data, H 0 = 7 0. 9 3 − 0. 0 0 3 7 + 0. 0 0 2 4 q = − 0. 3 3 8 4 0. 0 0 2 6 + 0. 0 0 2 7 1048 points of the Pantheon data and H 0 = 7 0. 7 6 7 3 2 − 0. 0 0 0 8 8 + 0. 0 0 3 0 q = − 0. 6 4 7 8 0. 0 0 7 5 + 0. 0 0 9 3 by using joint data (H (z) + BAO + Pantheon), respectively. We solved the modified Einstein's field equations by taking the bulk-viscosity component ξ = ξ 0 ρ α . We also establish a correspondence between the F (T , T G) gravity model and scalar field DE models such as quintessence, k -essence, and DBI-essence. The nature of scalar fields and their corresponding potentials are being graphically analyzed. To check the validity of F (T , T G) gravity model, we also analyze the behavior of energy conditions. [ABSTRACT FROM AUTHOR]

This paper focuses on the examination of stable and unstable geometrical structures of thin-shell wormholes constructed from Henneaux–Martinez–Troncoso–Zanelli black holes through the Visser cut-and-paste approach. We use the Israel thin-shell formalism for evaluating the stress–energy tensor components of the matter distribution near the wormhole throat. Equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter, are used to conduct an extensive investigation into the stability of the thin-shell. The radial perturbation around the equilibrium throat radius is also considered to explore the stable configuration for specific values of physical parameters. Our results show that the stable zones of these thin-shell wormholes increase as the scalar field parameter ℰ approaches −1. This study gives light on the behavior and dynamics of these wormholes throw light on their potential stability and lead the way for additional theoretical physics research. [ABSTRACT FROM AUTHOR]

We consider dynamics of a scalar field in compactification scenario of Einstein-Gauss-Bonnet cosmology. It is shown that if the field is non-minimally coupled to curvature, its asymptotic value under certain conditions may be shifted from the minimum of its potential. This means that due to influence of extra dimensions a scalar field with λ ϕ 4 potential can stabilise away from ϕ = 0 stable point which means an effective symmetry breaking occurs in such a system. [ABSTRACT FROM AUTHOR]

The entire classical cosmological history between two extreme de Sitter vacuum solutions is discussed based on Einstein's equations and non-equilibrium thermodynamics. The initial non-singular de Sitter state is characterised by a very high energy scale, which is equal or smaller than the reduced Planck mass. It is structurally unstable, and all of the continuous created matter, energy, and entropy of the material component comes from the irreversible flow powered by the primeval vacuum energy density. The analytical expression describing the running vacuum is obtained from the thermal approach. It opens a new perspective to solve the old puzzles and current observational challenges plaguing the cosmic concordance model driven by a rigid vacuum. Such a scenario is also modelled through a non-canonical scalar field. It is demonstrated that the resulting scalar field model is shown to be a step-by-step a faithful analytical representation of the thermal running vacuum cosmology. [ABSTRACT FROM AUTHOR]

Abstract The motivation for constructing a thin-shell wormhole from a (2+1)-dimensional rotating black hole arises from the desire to study the effects of a nonminimally coupled scalar field in this particular spacetime. By investigating the behavior of such a field in the presence of rotation, we can gain insights into the interplay between gravity and scalar fields in lower-dimensional systems. Additionally, this construction allows us to explore potential connections between black hole physics and exotic phenomena like traversable wormholes. The radial perturbation around the equilibrium throat radius is considered to explore the stable configuration for specific values of physical parameters. Then, the equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter is used to conduct an extensive investigation into the stability of the counter-rotating thin-shell wormholes. Our results show that the presence of a scalar field enhances the stability of the counter-rotating thin-shell wormholes.

The present study examines the Kaniadakis holographic dark energy in the context of the Brans-Dicke scalar-tensor theory of gravity (Phys. Rev. 124: 925, 1961). This paper focuses on a background with an anisotropic Kantowski-Sachs space-time that is homogeneous in space. Under these circumstances, the Brans-Dicke scalar field denoted as ϕ is used as a function of the average scale factor a(t). Using a graphical model to analyze the model's physical behaviour is part of the inquiry into the Universe's accelerating expansion. We evaluate the cosmological parameters such as the scalar field, the equation of state parameter and the deceleration parameter. Furthermore, the models' stability is assessed through the application of the squared sound speed (ν2S). For our models, we derive the widely accepted cosmic planes such as ωkde-ω'kde and statefinder (r,s) planes. It is found that the scalar field is a decreasing function of cosmic time and hence the corresponding kinetic energy increases. The deceleration parameter exhibits accelerated expansion of the universe. It is mentioned here that the equation of state parameter lies in the phantom region and finally attains the ΛCDM model. Also, the ωkde-ω'kde plane provides freezing and thawing regions. In addition, the statefinder plane also corresponds to the ΛCDM model. Finally, it is remarked that all the above constraints of the cosmological parameters show consistency with Planck observational data.

With a Kiselev spacetime around Schwarzschild black holes that have undergone quantum correction, the goal of this work is to examine the geometric structure of a thin-shell. In order to do so, we take into consideration black hole solutions and match the inner Minkowski spacetime using a cut and paste method. Our findings indicate that the use of a phantom-like equation of state, such as quintessence, dark energy, and phantom energy, in the linearized radial perturbation technique shows stable thin-shell configurations that lie beyond the outer manifold’s predicted position of the event horizon. Moreover, we discover that the characteristics of the black hole solutions have a significant impact on the thin-shell stability. We examine the behavior of a thin-shell configuration with massless and massive scalar fields by using Klein–Gordon’s equation of motion. According to our findings, the thin-shell system dynamics are significantly influenced by the scalar field, resulting in interesting phenomena including expansion and collapse. These results provide fresh light on the behavior of black hole solutions by providing important insights into the interaction between quantum correction factors related to scalar fields and thin-shell dynamics. In particular, our research suggests that the quantum correction parameter decreases the stable configuration of a Schwarzschild black hole encircled by a quintessence field. [ABSTRACT FROM AUTHOR]

The motivation for constructing a thin-shell wormhole from a (2+1)-dimensional rotating black hole arises from the desire to study the effects of a nonminimally coupled scalar field in this particular spacetime. By investigating the behavior of such a field in the presence of rotation, we can gain insights into the interplay between gravity and scalar fields in lower-dimensional systems. Additionally, this construction allows us to explore potential connections between black hole physics and exotic phenomena like traversable wormholes. The radial perturbation around the equilibrium throat radius is considered to explore the stable configuration for specific values of physical parameters. Then, the equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter is used to conduct an extensive investigation into the stability of the counter-rotating thin-shell wormholes. Our results show that the presence of a scalar field enhances the stability of the counter-rotating thin-shell wormholes. [ABSTRACT FROM AUTHOR]

We explore the impact of the chameleon mechanism in scalar field Einstein-Gauss-Bonnet gravity on the dynamics of cosmological parameters. Conducting a thorough analysis of the phase space, we identify conditions under which the future attractor does not depict a singular universe. Our conclusion is that although Einstein-Gauss-Bonnet scalar field gravity offers an inflationary solution as a future attractor, it is unable to account for the late-time acceleration of the universe and it can not describe a universe similar to that provide by the -CDM model. On the other hand, when the matter source is described by a massless scalar field, then the de Sitter universe is a future attractor. However, the hyperbolic inflationary solution provided by the two scalar fields does not exist. [ABSTRACT FROM AUTHOR]

In this study, we explore the enigma of late-time cosmic acceleration in the framework of a general scalar field playing the role of dark energy. Our investigation yields an exact solution to Einstein's field equations, achieved through a parametrization of the deceleration parameter q (a) in quadratic form in the homogeneous and isotropic background geometry represented by Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. This parametrization unveils a seamless transition from a decelerated to an accelerated phase in the cosmic evolution. Furthermore, we leverage this parametrization to reconstruct cosmological parameters with respect to redshift z, elucidating their dependency on certain model parameters that govern the universe's evolutionary trajectory. The model parameters are subsequently constrained using diverse observational datasets. We provide a comprehensive analysis of the evolution of geometrical and physical parameters, complete with the numerically constrained values. To gain deeper insights into the nature of dark energy, we employ Statefinder diagnostics, conducting a thorough examination. Our findings shed light on the intricate interplay between cosmic acceleration, quintessential dark energy and the parametrization of deceleration parameter, offering valuable insights into the fundamental dynamics of the universe. [ABSTRACT FROM AUTHOR]

The current study is devoted to exploring the geometrical configuration of a thin‐shell in the background of symmetric teleparallel gravity. For this purpose, the well‐known cut‐and‐paste approach by matching the inner flat and outer newly calculated class of approximated black hole (BH) solutions in symmetric teleparallel gravity are considered, i.e., uncharged, charged, and anti‐de‐Sitter BHs. The dynamical analysis of thin‐shell configuration by adopting the massive and massless scalar field via Klein‐Gordon's equation of motion is discussed. The effective potential and proper time derivative of shell radius for both massive and massless scalar shells are used to discuss the collapse, expansion, and oscillatory behavior. The stable configuration of thin‐shell is observed through the linearized radial perturbation approach with a phantomlike equation of state, i.e., quintessence, dark energy, and phantom energy. It is noted that stable/unstable behavior of thin‐shell is found after the expected position of the event horizon of an exterior manifold. It is concluded that the stability of a thin‐shell is greater for f(Q)$f(\mathbb {Q})$ BH with cosmological constant as compared to the uncharged and charged f(Q)$f(\mathbb {Q})$ BHs. [ABSTRACT FROM AUTHOR]

Abstract: This article focuses on the implications of the recently developed commutative formulation based on branch‐cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Assuming a mini‐superspace of variables, we explore the impact of an inflaton‐type scalar field on the dynamical equations that describe the trajectories evolution of the scale factor of the Universe, characterized by the dimensionless helix‐like function . This scale factor characterizes a Riemannian foliated spacetime that topologically overcomes the big bang and big crunch singularities. Taking the Hořava–Lifshitz action as our starting point, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as , the commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. We investigate both chaotic and nonchaotic inflationary scenarios, demonstrating the sensitivity of the branch‐cut Universe's dynamics to initial conditions and parameterizations of primordial matter content. The results suggest a continuous connection of Riemann surfaces, overcoming primordial singularities and exhibiting diverse evolutionary behaviors, from big crunch to moderate acceleration.

In this paper, we consider the problem of elasticity and stability of the collision of two kinks with low speed v for the nonlinear wave equation known as the ϕ 6 model in dimension 1 + 1. We construct a sequence of approximate solutions ( ϕ k ( v , t , x ) ) k ∈ N ⩾ 2 for this model to understand the effects of the collision in the movement of each soliton during a large time interval. The construction uses a new asymptotic method which is not only restricted to the ϕ 6 model. [ABSTRACT FROM AUTHOR]

The f (R , T) theory of gravity investigated by Harko et al. [T. Harko, F. S. N. Lobo, S. Nojiri and S. D. Odintsov, Phys. Rev. D 84 (2011) 024020; T. Harko, Phys. Rev. D 90(4) (2014) 044067] serves as the inspiration for the homogeneous and isotropic cosmological model presented in generalized f (R , T ϕ) theories connected with a scalar field. Assuming that T ϕ is the trace of the energy-momentum tensor, f (R , T ϕ) gravity can be understood as f (R , T) gravity with a self-interacting scalar field ϕ. To address this, we provide a novel model-independent method for the parametrization of the Hubble parameter, and we apply it to the Friedmann equations in the FLRW Universe. The Markov Chain Monte Carlo (MCMC) approach is then used to estimate the best-fit values of the model parameters using a combination of the updated H (z) dataset, which comprises 57 points, and the Pantheon dataset, which contains 1048 points. The evolution of the deceleration parameter shows a transition from the universe's deceleration phase to its acceleration phase. We also investigate the behavior of the statefinder and the Om diagnostic parameter. Finally, a thorough discussion of the model's physical attributes has been carried out. [ABSTRACT FROM AUTHOR]

The triumph of general relativity under the banner "gravity is geometry" began with confirming the crucial effects within the Solar system and proceeded recently to the strong-field shadow effect for the compact object in the center of the Milky Way. Here, we examine some of those phenomena for the Einstein-scalar equations in the antiscalar regime to reveal the difference from vacuum both in weak and strong fields. As a result, we find that for week-field perihelion shift the difference between vacuum and antiscalar cases proves to be observationally imperceptible in practice, even for S-cluster stars with high eccentricities, except for the S62 star with measurable difference per century. In strong-field case, we reconsider the shadow effect (this time without involving complex-valued scalar field) as the most perspective from an observational viewpoint. Even though the resulting difference is quite appreciable (about 5%), no conclusion can be made until the mass of the central object is known with the accuracy an order of magnitude higher than the currently available. [ABSTRACT FROM AUTHOR]

The present study examines the Kaniadakis holographic dark energy in the context of the Brans-Dicke scalar-tensor theory of gravity (Phys. Rev. 124: 925, 1961). This paper focuses on a background with an anisotropic Kantowski-Sachs space-time that is homogeneous in space. Under these circumstances, the Brans-Dicke scalar field denoted as 𝜙 is used as a function of the average scale factor 𝑎(𝑡). Using a graphical model to analyze the model's physical behaviour is part of the inquiry into the Universe's accelerating expansion. We evaluate the cosmological parameters such as the scalar field, the equation of state parameter and the deceleration parameter. Furthermore, the models' stability is assessed through the application of the squared sound speed (𝑣􀯦 􀬶). For our models, we derive the widely accepted cosmic planes such as 𝜔􀯞􀯗􀯘 - 𝜔􀯞􀯗􀯘 􁇱 and statefinder (r,s) planes. It is found that the scalar field is a decreasing function of cosmic time and hence the corresponding kinetic energy increases. The deceleration parameter exhibits accelerated expansion of the Universe. It is mentioned here that the equation of state parameter lies in the phantom region and finally attains the ΛCDM model. Also, the 𝜔􀯞􀯗􀯘 - 𝜔􀯞􀯗􀯘 􁇱 plane provides freezing and thawing regions. In addition, the statefinder plane also corresponds to the ΛCDM model. Finally, it is remarked that all the above constraints of the cosmological parameters show consistency with Planck observational data. [ABSTRACT FROM AUTHOR]

The distribution of dark matter in four low surface brightness spiral galaxies is studied using two models within the scalar field theory of dark matter, an alternative to the cold dark matter paradigm. The first model is a Bose-Einstein condensate, in which bosons occupy the ground state at zero temperature. The second model includes finite temperature corrections to the scalar field potential, which allows the introduction of excited states. A nonlinear least squares approximation method is used to determine the free parameters of the models, including scale radius, characteristic (central) density and total mass, based on observational data of rotation curves. Quantitative analysis shows the importance of considering finite temperatures at the galactic level. In addition, the two models are compared with results from widely used and accepted phenomenological dark matter profiles such as the isothermal sphere, Navarro-Frank-White and Burkert profiles. The reliability of each model was assessed based on the Bayesian information criterion of completeness. Statistical analysis provides meaningful interpretation of the choice of a particular profile. Ultimately, this study contributes to a better understanding of the distribution of dark matter in low surface brightness spiral galaxies by shedding light on the performance of scalar field models compared to traditional phenomenological profiles. [ABSTRACT FROM AUTHOR]

A modified SU(2) Georgi-Glashow model is considered here, and it is shown that besides the well-known Julia-Zee dyon solution, the model can also have a modified dyon solution. The properties of the modified dyon solution are studied using analytical and numerical methods. A comparative analysis of the modified dyon and the Julia-Zee dyon shows that their properties are significantly different. In particular, except for the BPS case, the energy and electric charge of the modified dyons exceed considerably those of the Julia-Zee dyons. At the same time, the energy and electric charge of the modified dyon are bounded for all admissible parameter values, whereas those of the Julia-Zee dyon can be arbitrarily large in the BPS case.

The entire classical cosmological history between two extreme de Sitter vacuum solutions is discussed based on Einstein’s equations and non-equilibrium thermodynamics. The initial non-singular de Sitter state is characterised by a very high energy scale, which is equal or smaller than the reduced Planck mass. It is structurally unstable, and all of the continuous created matter, energy, and entropy of the material component comes from the irreversible flow powered by the primeval vacuum energy density. The analytical expression describing the running vacuum is obtained from the thermal approach. It opens a new perspective to solve the old puzzles and current observational challenges plaguing the cosmic concordance model driven by a rigid vacuum. Such a scenario is also modelled through a non-canonical scalar field. It is demonstrated that the resulting scalar field model is shown to be a step-by-step a faithful analytical representation of the thermal running vacuum cosmology.

The Scalar Field Dark Matter model has been known in various ways throughout its history; Fuzzy, BEC, Wave, Ultralight, Axion-like Dark Matter, etc. All of them consist in proposing that dark matter of the universe is a spinless field Φthat follows the Klein-Gordon (KG) equation of motion □Φ-dV/dΦ=0, for a given scalar field potential V. The difference between different models is sometimes the choice of the scalar field potential V. In the literature we find that people usually work in the non-relativistic, weak-field limit of the Klein- Gordon equation, where it transforms into the Schrödinger equation and the Einstein equations into the Poisson equation, reducing the KG-Einstein system, to the Schrödinger-Poisson system. In this paper, we review some of the most interesting achievements of this model from the historical point of view and its comparison with observations, showing that this model could be the last answer to the question about the nature of dark matter in the universe. [ABSTRACT FROM AUTHOR]

Experiments were performed in vacuum to examine a modified Kaluza–Klein theory. Originally proposed by Mbelek and Lachièze-Rey, the 5D Kaluza–Klein- ψ theory includes an external scalar field ψ to couple gravitational and electromagnetic fields and can be used to explain some misunderstood phenomena in physics. The theory predicts that a pendulum will experience detectable forces exceeding predictions from classical electromagnetism when interacting with a scalar field. In this experiment, a dielectric mirror is hung as a pendulum inside a vacuum chamber and its oscillations are examined with two laser interferometers. In proximity to the pendulum, different solenoids and toroids will induce magnetic fields that can also be shielded to a great extent using a Gauss chamber. The experiments were conducted in a vacuum chamber to allow the measurement of torsion angles as low as 0.1 arcsec above the noise, as well as 0.1 μ m translations of the pendulum. The phenomenon observed differs from what was observed by Mbelek at ambient pressure in both magnitude and behavior. Dummy test results hint at the presence of convection effects to explain the pendulum's rotation, which was eliminated under higher vacuum and by placing a wall between the solenoid and pendulum. In the presence of stronger magnetic fields, the pendulum's translation was observed to agree with effects predicted by a consideration of diamagnetic effects. [ABSTRACT FROM AUTHOR]

We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, with one that acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian for the theory. In previous papers, we studied the theory for large values of the radial coordinate, i.e., far away from any black hole or star that may be present. This makes the calculations considerably more tractable. We have shown that in the asymptotic region, the theory admits a large family of quantum vacua for quantum matter fields coupled to quantum gravity, as is expected from the well-known results of quantum field theory on classical curved space-time. Here, we study perturbative corrections involving terms that we neglected in our previous work. Using the time-dependent perturbation theory, we show that the states that represent different possible vacua are essentially stable. This ensures that one recovers from a totally quantized gravitational theory coupled to matter the standard behavior of a matter quantum field theory plus low probability transitions due to gravity between particles that differ at most by a small amount of energy. [ABSTRACT FROM AUTHOR]

This article focuses on a recently developed formulation based on the noncommutative branch‐cut cosmology, the Wheeler‐DeWitt (WdW) equation, the Hořava–Lifshitz quantum gravity, chaotic and the coupling of the corresponding Lagrangian approach with the inflaton scalar field. Assuming a mini‐superspace of variables obeying the noncommutative Poisson algebra, we examine the impact of the inflaton scalar field on the evolutionary dynamics of the branch‐cut Universe scale factor, characterized by the dimensionless helix‐like function ln−1[β(t)]$$ {\ln}^{-1}\left[\beta (t)\right] $$. This scale factor characterizes a Riemannian foliated spacetime that topologically overcomes the primordial singularities. We take the Hořava–Lifshitz action modeled by branch‐cut quantum gravity as our starting point, which depends on the scalar curvature of the branched Universe and its derivatives and which preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. We then investigate the sensitivity of the scale factor of the branch‐cut Universe's dynamics. [ABSTRACT FROM AUTHOR]

This article focuses on the implications of a noncommutative formulation of branch‐cut quantum gravity. Based on a mini‐superspace structure that obeys the noncommutative Poisson algebra, combined with the Wheeler–DeWitt equation and Hořava–Lifshitz quantum gravity, we explore the impact of a scalar field of the inflaton‐type in the evolution of the Universe's wave function. Taking as a starting point the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, the corresponding wave equations are derived and solved. The noncommutative quantum gravity approach adopted preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner Formalism. In this work we delve deeper into a mini‐superspace of noncommutative variables, incorporating scalar inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions to the wave equations without resorting to numerical approximations. The results indicate that the noncommutative algebraic space captures low and high spacetime scales, driving the exponential acceleration of the Universe. [ABSTRACT FROM AUTHOR]

This article focuses on the implications of the recently developed commutative formulation based on branch‐cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Assuming a mini‐superspace of variables, we explore the impact of an inflaton‐type scalar field ϕ(t)$$ \phi (t) $$ on the dynamical equations that describe the trajectories evolution of the scale factor of the Universe, characterized by the dimensionless helix‐like function ln−1[β(t)]$$ {\ln}^{-1}\left[\beta (t)\right] $$. This scale factor characterizes a Riemannian foliated spacetime that topologically overcomes the big bang and big crunch singularities. Taking the Hořava–Lifshitz action as our starting point, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as gi$$ {g}_i $$, the commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. We investigate both chaotic and nonchaotic inflationary scenarios, demonstrating the sensitivity of the branch‐cut Universe's dynamics to initial conditions and parameterizations of primordial matter content. The results suggest a continuous connection of Riemann surfaces, overcoming primordial singularities and exhibiting diverse evolutionary behaviors, from big crunch to moderate acceleration. [ABSTRACT FROM AUTHOR]

In this paper, we are fundamentally interested in minimally coupled scalar field as source of unimodular Friedmann–Robertson–Walker (FRW) spacetime. We obtain dynamical quantities related with scalar field in FRW cosmologies by using field equations of unimodular f(R, T) theory. Equation of motion for a test particle and kinematical quantities are also obtained. We achieve Newtonian limit of unimodular f(R, T) theory by using weak field approximation. Energy conditions are presented for scalar field in unimodular f(R, T) theory. Energy conditions are examined by using graphics for massive and massless scalar field. Obtained results are discussed by comparing with viable cosmological models and previous works. Validity of unimodular f(R, T) theory is concluded. [ABSTRACT FROM AUTHOR]

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ϕ n where ϕ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ϕ 2 potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of "apparent horizon thermodynamics", the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ϕ 2 potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene. [ABSTRACT FROM AUTHOR]

The prediction about the accelerating expansion of the universe introduced the concept of dark energy. Since then, a plethora of work has been done to explain the origin and nature of dark energy. This work deals with the possibility of obtaining cosmic acceleration of a new kind of dark energy, viz., Yang–Mills condensate dark energy in generalized Brans–Dicke theory with variable or constant ω (Brans–Dicke parameter) and vanishing and non-vanishing self-interacting potential. We assume the scale factor and scalar field in power law form. Then we investigate the above model to determine whether the universe is accelerating. We obtain a redshift-dependent equation of state parameter, which describes the phase transition of the universe. We notice that the equation of the state parameter meets the Λ cold dark matter (CDM) limit in the far future. Then we study the w D − w D ′ analysis to get the thawing or freezing region. We study the stability of the model by studying the square speed of sound. Last, the nature of the scalar field and the potential are analyzed for four cases. [ABSTRACT FROM AUTHOR]

The Scalar Field Dark Matter model has been known in various ways throughout its history; Fuzzy, BEC, Wave, Ultralight, Axion-like Dark Matter, etc. All of them consist in proposing that dark matter of the universe is a spinless field Φ that follows the Klein-Gordon (KG) equation of motion □Φ − dV/dΦ = 0, for a given scalar field potential V. The difference between different models is sometimes the choice of the scalar field potential V. In the literature we find that people usually work in the non-relativistic, weak-field limit of the Klein-Gordon equation, where it transforms into the Schrödinger equation and the Einstein equations into the Poisson equation, reducing the KG-Einstein system, to the Schrödinger-Poisson system. In this paper, we review some of the most interesting achievements of this model from the historical point of view and its comparison with observations, showing that this model could be the last answer to the question about the nature of dark matter in the universe.

We present a comparison between the bosonic Feynman propagator in an external magnetic field calculated by Ritus’ method with summation over Landau levels and its integral expression obtained via Schwinger’s proper time method. Also, we have investigated the behavior boson system in a thermal reservoir under an increase in the external magnetic field strength.

This study proposes a novel parametrization approach for the dimensionless Hubble parameter i.e. E2(z)=A(z)+β(1+γB(z)) in the context of scalar field dark energy models. The parametrization is characterized by two functions, A(z) and B(z), carefully chosen to capture the behavior of the Hubble parameter at different redshifts. We explore the evolution of cosmological parameters, including the deceleration parameter, density parameter, and equation of state parameter. Observational data from Cosmic Chronometers (CC), Baryonic Acoustic Oscillations (BAO), and the Pantheon＋ datasets are analyzed using MCMC methodology to determine model parameters. The results are compared with the standard ΛCDM model using the Planck observations. Our approach provides a model-independent exploration of dark energy, contributing to a comprehensive understanding of late-time cosmic acceleration.

We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner–Nordström-like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a NC scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed U (1) ⋆ gauge symmetry. We find the equation of motion and conclude that the same equation is obtained from the commutative theory in a modified geometrical background described by an effective metric. This correspondence we call "duality between formal and effective approach". We also show that a NC deformation via semi-Killing twist operator cannot be rewritten in terms of an effective metric. There is dual description for those particular deformations. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the fields described by Dirac wave equation written in Clifford algebra based on Macfalane quaternions. It is shown that the strengths of these fields are nonzero only in the area of sources and the interaction of such fields occurs by overlapping. We consider both the simple spherically symmetric models of sources, which demonstrate attractive and repulsive interaction, and more complicated core-shell systems, which provide the bound states formation. [ABSTRACT FROM AUTHOR]

This paper investigates the static spherically symmetric vacuum solutions of Brans–Dicke Theory of Gravity. In this paper, we systematically derive the static spherically symmetric solutions by starting with the general static spherically symmetric anzats, discovering the nonzero Christoffel symbols, nonzero Ricci tensor components and the Ricci Scalar. These results allow us to rewrite the four Brans–Dicke gravitational field equations explicitly in terms of the metric components, the scalar field and its scalar potential. This paper systematically explains and shows how to modify these linear second-order ordinary differential equations in order to be able to find the solution of the scalar field, the metric components and the scalar potential analytically. We successfully find the most general solution of the static spherically symmetric vacuum solutions of Brans–Dicke gravity and the well-known Schwarzschild solution is recovered as the simplest solution. [ABSTRACT FROM AUTHOR]

Recently, scalar field approaches have been widely considered in cosmological models due to their potential for useful investigation of the cosmological evolution of the Universe. The use of a scalar field as a matter source in a cosmological model within symmetric teleparallel gravity is as interesting as many other modified gravity models sourced by a scalar field. In this paper, we investigate the repercussions of power law and hybrid expansion laws in symmetric teleparallel gravity using an associated scalar field as a total matter source. We find that for both models, a normal scalar field is required to provide a viable description of the Universe’s evolution, as opposed to a phantom scalar field, from an ad-hoc introduction of these two expansion laws. To back up this method of implementing these two ad-hoc expansion laws we also examined the evolution of the Hubble parameter by solving the Raychaudhuri equation which yields power law solutions in early radiation and matter dominated epochs and de-Sitter like solution in late Universe. We analysed this evolution in relation to observed Hubble data and found that the dependence of the model parameters in reproducing various epochs of the Universe is non-minimal. Furthermore, to test the stability of our models, we looked into the evolution of the speed of sound squared, which indicates that our models are stable to density perturbations. Finally, we utilize the geometrical method of Om diagnostics to conclude that our model exhibits quintessence like behaviour. [ABSTRACT FROM AUTHOR]

In statistical theory, the Tsallis entropy is an extended form of the Boltzmann–Gibbs entropy. The dimensionless parameter δ is employed to state the quantitative difference from the standard scenario. The concepts of Tsallis entropy and the future event horizon are employed in formulating the present new Tsallis holographic dark energy (NTHDE) model. The model attempts to explain the properties of dark energy using the foundation of quantum gravity. The differential equation characterizing the evolution of the NTHDE density parameter is obtained. Expressions stating the dynamic behavior such as equation of state (EoS), deceleration and jerk parameters are obtained in terms of the NTHDE density parameter. For δ < 1 , the quintessence nature of scalar field could completely characterize the NTHDE. A reconstruction of the scalar field's dynamics and quintessence potential is attempted. We demonstrate that the diagnosis made by statefinder is adaptive enough to distinguish between quintessence and cosmological constant-based dark energy models. Additionally, observational data obtained from CC + SNIa + 5 8 0 union 2.1 sources are used to evaluate the model's effectiveness. [ABSTRACT FROM AUTHOR]

The extremum graph is a succinct representation of the Morse decomposition of a scalar field. It has increasingly become a useful data structure that supports topological feature‐directed visualization of 2D/3D scalar fields, and enables dimensionality reduction together with exploratory analysis of high‐dimensional scalar fields. Current methods that employ the extremum graph compute it either using a simple sequential algorithm for computing the Morse decomposition or by computing the more detailed Morse–Smale complex. Both approaches are typically limited to two and three‐dimensional scalar fields. We describe a GPU–CPU hybrid parallel algorithm for computing the extremum graph of scalar fields in all dimensions. The proposed shared memory algorithm utilizes both fine‐grained parallelism and task parallelism to achieve efficiency. An open source software library, tachyon, that implements the algorithm exhibits superior performance and good scaling behaviour. [ABSTRACT FROM AUTHOR]

A detailed analysis of the phase‐space for the field equations in scalar field cosmology with a chameleon cosmology in a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime is presented. For the matter source it is assumed that it is an ideal gas with a constant equation of state parameter, while for the scalar field potential and the coupling function of the chameleon mechanism it is considered that four different sets which provide four different models. The H‐normalization approach and the field equations with the help of dimensionless variables written is considered. The asymptotic solutions are determined from where the theory can describe the main eras of cosmological history and evolution that are found. Future attractors which describe acceleration exist; however, acceleration solutions related to the inflationary era is found in past, as also the radiation epoch and the matter dominated eras are provided by the dynamics. The Chameleon dark energy model can be used as a unified model for the elements which contribute to the dark sector of the universe that are concluded. [ABSTRACT FROM AUTHOR]

In this article, an anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I metric in the presence of cloud string fluid and zero mass scalar field in reference to f (R) gravity have been investigated. To obtain the deterministic solutions we assumed the weak field limit for a point-like source f (R) = R3/2 and the very well-known expansion-shear scalar proportionality relation. Furthermore, some physical and kinematical parameters have been calculated to study the astrophysical consequences of obtained model, which shows a good resemblance to the recent observational data. [ABSTRACT FROM AUTHOR]

Exact models of primordial gravitational waves in the Bianchi type-III universe were constructed on the basis of the quadratic theory of gravity with a scalar field and pure radiation in Shapovalov wave spacetimes of type II (subtype 2). Exact solutions of the field equations and scalar equation were obtained. The characteristics of pure radiation were determined. An explicit form of the scalar field functions included in the Lagrangian of the considered quadratic theory of gravity was found. The trajectories of the propagation of light rays in the considered gravitational wave models were obtained. [ABSTRACT FROM AUTHOR]

We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case. [ABSTRACT FROM AUTHOR]

The prime goal of this paper is to analyze the conditions for the stability of the isotropic pressure condition with hydrostatic equilibrium constraint under the influence of Chameleonic Brans–Dicke gravity. We have formulated various expressions through the field equations, Bianchi identities, mass function, etc., to govern the spherically symmetric dissipative configuration. We have also evaluated the evolution equations for the conformal scalar and pressure isotropy in the modified theory. These equations exhibit the anisotropy factor as an inherent property of unequal principal stresses. The findings inferred the existence of some physical variables resulting in an initially isotropic matter content to produce anisotropy in pressure. These dynamical factors comprise density inhomogeneity, dissipative flux, or shear flow. [ABSTRACT FROM AUTHOR]

Abstract The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called geons, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name boson stars. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single Killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.

In the present paper, we focused on exploring the possibility of providing a new class of exact solutions for viable anisotropic stellar systems by means of the massive Brans–Dicke (BD) theory of gravity. In this respect, we used the decoupling of gravitational sources by minimal geometric deformation (MGD) ( e − η = Ψ + β h ) for compact stellar objects in the realm of embedding class-one space-time to study anisotropic solutions for matter sources through the modified Einstein field equations. For this purpose, we used the ansatz for Ψ relating to the prominent, well-known and well-behaved Finch–Skea model via Karmarkar condition, and the determination scheme for deformation function h (r) was proposed via mimic requirement on radial pressure component: θ 1 1 (r) = p r (r) and matter density: θ 0 0 (r) = ρ (r) for the anisotropic sector. Moreover, we analyzed the main physical highlights of the anisotropic celestial object by executing several physical tests for the case θ 1 1 (r) = p r (r) . We have clearly shown how the parameters α , β and ω B D introduced by massive BD gravity via the MGD approach incorporating the anisotropic profile of the matter distribution have an immense effect on many physical parameters of compact bodies such as LMC X-4, LMC X-4, Her X-1, 4U 1820-30, 4U 1608-52, SAX J1808.4–658 and many others that can be fitted. [ABSTRACT FROM AUTHOR]

Using purely geometrical methods we present a mechanism to solve the scalar field equations of motion (non-minimally coupled with gravity) in a spherically symmetric background. We found that the full set of spacetimes, which are of Petrov type O (conformally flat) and admit a gradient conformal vector field, can be determined completely. It is shown that the full group of scalar field equations reduced to a single equation that depends only on the distance w = r 2 − t 2 leaving the metric function (equivalently the functional form of the scalar field or the potential) freely chosen. Depending on the structure of the metric or the potential V (as a function of φ) a solution can be found either analytically or via numerical integration. We provide physically sound examples and prove that (Anti)-de Sitter fits this scheme. We also reconstruct a recently found solution (Strumia and Tetradis 2022 J. High Energy Phys. JHEP09(2022)203) representing an expanding scalar bubble with metric that has a singularity and corresponds to what is termed as Anti-de Sitter crunch. [ABSTRACT FROM AUTHOR]