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We proceed to obtain an exact analytical solution of the Brans–Dicke (BD) equations for the spatially flat (k = 0) Friedmann–Lamaître–Robertson–Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the "invariants of symmetry groups method" (ISG method). This method is based on the extended Prelle–Singer (PS) method and it employs the Lie point symmetries, λ -symmetries, and Darboux polynomials (DPs). Indeed, the ISG method tries to provide two independent first-order invariants associated to the one-parameter Lie groups of transformations keeping the ordinary differential equations (ODEs) invariant, as solutions. It should be noted for integrable ODEs that the ISG method guarantees the extraction of these two invariants. In this work, for the BD equations in FLRW cosmological model, we find the Lie point symmetries, λ -symmetries, and DPs, and obtain the basic quantities of the extended PS method (which are the null forms and the integrating factors). By making use of the extended PS method we find two independent first-order invariants in such a way that appropriate cosmological solutions from solving these invariants as a system of algebraic equations are simultaneously obtained. These solutions are wealthy in that they include many known special solutions, such as the O'Hanlon–Tupper vacuum solutions, Nariai's solutions, Brans–Dicke dust solutions, inflationary solutions, etc. [ABSTRACT FROM AUTHOR]

In this study, we investigate the deflection angle of a torus-like regular charged black hole in the limit approximation of a weak field to check the effects of non-magnetic plasma and non-plasma medium. Using spacetime optical geometry, we first compute the Gaussian optical curvature. We study the light deflection angle from a charged torus-like black hole using the Gibbons and Werner approach. By taking into account the well-known Keeton–Petters approach, we validate our results. Moreover, we examine the shadow of a charged torus-like black hole by using the ray-tracing algorithm under the influence of pressureless and non-magnetized plasma and study the graphical effects of cosmological constant and charge for both anti-de Sitter and de Sitter cases on the shadow of a black hole. [ABSTRACT FROM AUTHOR]

This study explores the cosmological constant problem and modified uncertainty principle within a unified framework inspired by a void-dominated scenario for cosmology. In a recent paper [E. Yusofi, M. Khanpour, B. Khanpour, M. A. Ramzanpour and M. Mohsenzadeh, Mon. Not. R. Astron. Soc. 511, L82 (2022)], voids were modeled as spherical bubbles of similar average sizes, and the surface energy on the voids’ borders was calculated across various scales in a heuristic manner. We show that these result in a significant discrepancy of approximately 풪(+122) between the cosmological constant values from the minimum to the maximum radii of bubbles. Furthermore, when considering the generalized form of the uncertainty principle with both minimum and maximum lengths, i.e. ΔXΔP≥ℏ211−βΔP211−αΔX2, a similar order of discrepancy is observed between αmax and αmin, indicating that α∝β−1∝Λ∝length−2(m−2). As a primary outcome of this finding, we offer a novel uncertainty principle that incorporates a nonzero cosmological constant. [ABSTRACT FROM AUTHOR]

A spherically symmetric black hole solution in the conformal Weyl gravity was found by Mannheim and Kazanas in 1988. While the quasinormal modes (QNMs) of these black holes have been considered in a few works, here we complement these studies by considering in detail the regime of vanishing cosmological constant and negative values of the Weyl parameter for which we find quasinormal frequencies for scalar, Dirac and electromagnetic perturbations with the time-domain integration and WKB methods. In particular, we derive the compact and remarkably accurate analytic formula for the frequencies in the form of expansion in terms of the inverse multipole number. Comparison with the time-domain integration shows that the 6th order WKB method with the Padé approximants is quite accurate, unless the black hole is in the near extreme state. [ABSTRACT FROM AUTHOR]

In this paper, we explore some cosmological solutions of the Friedmann–Lemaître–Robertson–Walker (FLRW) closed universe with nonlocal de Sitter gravity d S and nonlocal scalar field which has its origin in p -adic string theory. In this case, we have that both geometrical and matter sectors of equations of motion (EoM) are nonlocal. The cosmological constant Λ plays a role of dark energy (DE) and is related to the mass of scalar field as m = ℏ c Λ 6 = 1. 5 × 1 0 − 6 9 kg. We found that the cosmological constant Λ depends on prime number p as a discrete parameter and we conjectured that Λ is not constant during the universe evolution. [ABSTRACT FROM AUTHOR]

In this paper, we review the main features of modified theories of gravity containing higher-order curvature invariants in the action. After summarizing the main features of these theories, we consider their applications to cosmology, pointing out the differences with respect to general relativity that can eventually solve issues exhibited by the latter at low and high energy scales. Specifically, we explore a gravitational action that incorporates both the Ricci scalar R and the topological Gauss–Bonnet term, denoted as . Our investigation revolves around the cosmological properties of a specific category of modified gravity theories, chosen upon symmetry considerations. Within the framework of a spatially flat, homogeneous and isotropic cosmic background, we demonstrate that it is possible to account for the presently observed acceleration of the Universe by means of the extra geometric terms carried by the selected f (R ,) model. This approach offers a way to address the issues associated with the cosmological constant. To achieve this, we first examine the energy conditions and find that, under certain choices for the values of the cosmographic parameters, these conditions are all violated. In the second part of the work, to assess the feasibility of the selected f (R ,) model, we place observational constraints on its free parameters through a Bayesian Monte Carlo technique applied to late-time cosmic data. Our findings reveal that the f (R ,) model can effectively reproduce observations at low redshifts, providing an alternative to the standard Λ CDM scenario. [ABSTRACT FROM AUTHOR]

We explore a cosmological model inspired by the modified Kaniadakis entropy and disclose the influences of the modified Friedmann equations on the evolution of the Universe. We find that in modified Kaniadakis cosmology with only pressure-less matter, one can reproduce the accelerated Universe without invoking any kind of dark energy. We delve into the evolution of the Universe during the radiation-dominated era as well. We also investigate the behavior of the scale factor and the deceleration parameter for a multiple-component Universe consisting of pressure-less matter and a cosmological constant/dark energy. Interestingly enough, the predicted age of the Universe in the modified Kaniadakis cosmology becomes larger compared to the standard cosmology which may alleviate the age problem. Furthermore, the findings reveal that in the modified Kaniadakis cosmology, the transition from a decelerated phase to an accelerated Universe occurs at higher redshifts compared to the standard cosmology. These results shed light on the potential implications of incorporating Kaniadakis entropy into cosmological models and provide valuable insights into the behavior of the Universe in different cosmological scenarios. Moreover, they emphasize the crucial role of modifications to the geometry component and the significance of such modifications in understanding the dynamics of the Universe. [ABSTRACT FROM AUTHOR]

This work presents an anisotropic cylindrical source's gravitational expansion and collapse with the cosmological constant. For this purpose, we use the cylindrical symmetric metric and energy–momentum tensor to achieve Einstein's field equation component. The mass function is also used to assess the state of the trapped surface. The parametric form of the auxiliary solution is discovered. These presumptions enable us to examine the parameter range at the positive and negative expansion scalar transitions. The generated solution produces expanding and collapsing solutions correspondingly for positive and negative parameter values. A dimensionless measure of anisotropy, pressures and energy density are utilized as physical quantities. The included parameters are shown graphically. The cosmological constant has impacted both the expansion and collapse solutions to phenomena. [ABSTRACT FROM AUTHOR]

In this work, the considered model is contained in higher dimensional compactified space in the form of M4 × M6, where M6 is compact inner space. Since, for a higher dimensional cosmological model, Tachyon matter is an automatic and fantastic choice, we have supposed that the scalar field is driven by Tachyon together with the higher dimensional cosmological constant Λ ¯ . Our observation is that the theory provides a good solution for the cosmological scale factor of the present universe. Here, it is important that the forms of the tachyonic field ϕ and potential V are simple trigonometric hyperbolic functions. We study the cosmographical parameters like equation of state parameter, statefinder parameters, jerk, snap, and lerk parameters. The graphical representations of cosmological parameters show the overall evolution of the universe under a tachyonic field in a higher dimensional model. The classical stability of the model due to small perturbations both for dark energy and metric are examined by the study of the square speed of sound and by the linear perturbation method. We also analyzed the model in ω−ω′ and r−s cosmological plane. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study geometrical aspects of an almost Ricci soliton on (wRs)4 perfect fluid spacetime obeying Einstein’s field equation. Among others, we first find the soliton constant and cosmological constant in terms of scalar curvature and potential vector field in (wRs)4 perfect fluid spacetime. Next, we discuss some physical phenomena related to dust fluid, dark fluid, and radiation era in (wRs)4 perfect fluid spacetime admitting an almost Ricci soliton with potential vector field as solenoidal vector field and basic vector field ρ under matter collineation condition. Further, we find an inequality for soliton constant when (wRs)4 perfect fluid spacetime obeys the timelike convergence condition. Finally, we obtain some results in a (wRs)4 perfect fluid spacetime whose metric represents an almost Ricci soliton when basic vector field and potential vector field both are torseforming vector field ρ. Also, for such spacetime we find the soliton constant in terms of cosmological constant, gravitational constant, energy density, and isotropic pressure. We also provide an example of (wRs)4 spacetime whose metric represents an almost Ricci soliton. [ABSTRACT FROM AUTHOR]

The cosmological constant is normally introduced as an additional term entering the Einstein–Hilbert (EH) action. In this letter, we demonstrate that, instead, it appears naturally from the standard EH action as an invariant term emerging from spacetime symmetries. We then demonstrate that the same constraint emerging from this invariant suppresses the short wavelength modes and it favors the long wavelength ones. In this way, inside the proposed formulation, the observed value for the vacuum energy density is obtained naturally from the zero-point quantum fluctuations. [ABSTRACT FROM AUTHOR]

In this paper, we involve the galactic halo observational data to test the weak field General Relativity involving the cosmological constant. By using the data for 15 hydrogen (Hi) VLA super spirals and the Tully–Fisher relation, we obtain constraints for each galaxy. The results are consistent with previous results for spiral galaxies, as well as with the scaling relations for the halos, thus confirming the efficiency of the use of dark halo data and Tully–Fisher relation, including the baryonic Tully–Fisher index (BTFR), for testing modified gravity models. [ABSTRACT FROM AUTHOR]

We study a model of the neutron star in κ -deformed space-time in the presence of the cosmological constant (Λ ). The Einstein tensor and the energy-momentum tensor are generalized to κ -deformed space-time and we construct the field equations with the cosmological constant. Considering the interior of the star to be a perfect fluid as in the commutative case, we find the Tolman–Oppenheimer–Volkoff equations with the inclusion of the cosmological constant in κ -deformed space-time. The behavior of the maximum allowed mass of the star and its radius are studied with the variation in the cosmological constant as well as the deformation parameter. We see that the non-commutativity enhances the mass of the star and its maximum mass increases with a decrease in the cosmological constant. The maximum mass varies from 3.44 to 3.68 M ⊙ as Λ varies from 10 - 10 to 10 - 15 m - 2 . We also obtain the compactness factor and surface redshift of the star. We observe that the compactness of the star increases as the cosmological constant decreases, whereas the surface redshift of the star decreases with a decrease in the cosmological constant. The compactness factor and surface redshift corresponding to the maximum mass of the neutron star remains almost constant as Λ decreases. [ABSTRACT FROM AUTHOR]

The acceleration observed in cosmological expansion is often attributed to negative pressure, potentially arising from quintessence. We explore the relationship between the photon orbit radius and the phase transition of spherical AdS black holes in f(R, T) gravity influenced by quintessence dark energy, specifically Kiselev-AdS black holes in f(R, T) gravity. We are treating the negative cosmological constant Λ as the system's pressure to examine the impact of the state parameter ω and the f(R, T) gravity parameter γ . Interestingly, Kiselev-AdS black holes within the f(R, T) gravity framework exhibit a van der Waals-like phase transition. In contrast, these black holes display a Hawking–Page-like phase transition in general relativity. We demonstrate that below the critical point, the black hole undergoes a first-order vdW-like phase transition, with r ps and u ps serving as order parameters exhibiting a critical exponent of 1/2, similar to ordinary thermal systems. It suggests that r ps and u ps can serve as order parameters in characterizing black hole phase transitions, hinting at a potentially universal gravitational relationship near critical points within black hole thermodynamic systems. Investigating the correlation between photon sphere radius and thermodynamic phase transitions provides a valuable means of distinguishing between different gravity theory models, ultimately shedding light on the nature of dark energy. Finally, as γ tends towards zero, our results precisely align with those of Kiselev-AdS black holes. [ABSTRACT FROM AUTHOR]

A new form of the mathematical expression for the co-moving volume element of a flat universe with cosmological constant, cold matter, and stiff matter is presented. It is used to determine the constraints from the Planck measurements of the Hubble parameter on the amount of stiff matter in the universe. These constraints are used to investigate whether the presence of stiff matter can solve the Hubble tension. It is found that the Planck measurements lead to an upper bound on the present value of the density parameter of stiff matter Ω S 0 < 5 ⋅ 10 − 23 , and that this is too small to solve the Hubble tension. Report. The main objective of this article is to introduce a novel mathematical expression for the co-moving volume element in a flat universe that includes a cosmological constant, cold matter, and stiff matter. This expression is utilized to derive constraints on the amount of stiff matter in the universe based on the Planck measurements of the Hubble parameter. These constraints are then examined to assess whether stiff matter could potentially resolve the Hubble tension. The findings indicate that the Planck measurements impose an upper limit on the current value of the density parameter of stiff matter, Ω S 0 < 5 ⋅ 10 − 23 , which is insufficient to resolve the Hubble tension. [ABSTRACT FROM AUTHOR]

The superradiant growth of massive vector fields in rotating black hole spacetimes has garnered significant attention in recent literature. However, the majority of these studies overlook the influence of a cosmological constant, which likely constitutes the primary energy content of our universe. In this paper, we extend recent research by incorporating a cosmological constant into the Einstein+Proca system and numerically evolving the resulting equations of motion. Utilizing the newly released GRBoondi numerical relativity code, designed specifically for the numerical evolution of (generalized) Proca fields, we discover that parameters causing a growing instability in the Λ=0$\Lambda =0$ scenario transition to a decaying state when Λ>0$\Lambda >0$. This results in a more intriguing phenomenology. These simulations pave the way for future full Einstein+Proca simulations to explore the secular decay of the resultant cloud from gravitational emission. [ABSTRACT FROM AUTHOR]

In the recently suggested modified non-metricity gravity theory with boundary term in a flat FLRW spacetime universe, dark energy scenarios of cosmological models are examined in this study. An arbitrary function, f (Q , C) = Q + α C 2 , has been taken into consideration, where Q is the non-metricity scalar, C is the boundary term denoted by C = R ̈ − Q , and α is the model parameter, for the action that is quadratic in C. The Hubble function H (z) = H 0 [ c 1 (1 + z) n + c 2 ] 1 2 , where H 0 is the current value of the Hubble constant and n , c 1 and c 2 are arbitrary parameters with c 1 + c 2 = 1 , has been used to examine the dark energy characteristics of the model. We discovered a transit phase expanding universe model that is both decelerated in the past and accelerated in the present, and we discovered that the dark energy equation of state (EoS) ω (d e) behaves as (− 1 ≤ ω (d e) < 2). The Om diagnostic analysis reveals the quintessence behavior in the present and the cosmological constant scenario in the late-time universe. Finally, we calculated the universe's current age, which was found to be quite similar to recent data. [ABSTRACT FROM AUTHOR]

The spin-torsion theory is a gauge theory approach to gravity that expands upon Einstein's general relativity (GR) by incorporating the spin of microparticles. In this study, we further develop the spin-torsion theory to examine spherically symmetric and static gravitational systems that involve free-falling macroscopic particles. We posit that the quantum spin of macroscopic matter becomes noteworthy at cosmic scales. We further assume that the Dirac spinor and Dirac equation adequately capture all essential physical characteristics of the particles and their associated processes. A crucial aspect of our approach involves substituting the constant mass in the Dirac equation with a scale function, allowing us to establish a connection between quantum effects and the scale of gravitational systems. This mechanism ensures that the quantum effect of macroscopic matter is scale-dependent and diminishes locally, a phenomenon not observed in microparticles. For any given matter density distribution, our theory predicts an additional quantum term, the quantum potential energy (QPE), within the mass expression. The QPE induces time dilation and distance contraction, and thus mimics a gravitational well. When applied to cosmology, our theory yields a static cosmological model. The QPE serves as a counterpart to the cosmological constant introduced by Einstein to balance gravity in his static cosmological model. The QPE also offers a plausible explanation for the origin of Hubble redshift (traditionally attributed to the universe's expansion). The predicted luminosity distance–redshift relation aligns remarkably well with SNe Ia data from the cosmological sample of SNe Ia. In the context of galaxies, the QPE functions as the equivalent of dark matter. The predicted circular velocities align well with rotation curve data from the SPARC (Spitzer Photometry and Accurate Rotation Curves database) sample. Importantly, our conclusions in this paper are reached through a conventional approach, with the sole assumption of the quantum effects of macroscopic matter at large scales, without the need for additional modifications or assumptions. [ABSTRACT FROM AUTHOR]

Multiply lensed images of a same source experience a relative time delay in the arrival of photons due to the path length difference and the different gravitational potentials the photons travel through. This effect can be used to measure absolute distances and the Hubble constant ( H 0 ) and is known as time-delay cosmography. The method is independent of the local distance ladder and early-universe physics and provides a precise and competitive measurement of H 0 . With upcoming observatories, time-delay cosmography can provide a 1% precision measurement of H 0 and can decisively shed light on the current reported 'Hubble tension'. This manuscript details the general methodology developed over the past decades in time-delay cosmography, discusses recent advances and results, and, foremost, provides a foundation and outlook for the next decade in providing accurate and ever more precise measurements with increased sample size and improved observational techniques. [ABSTRACT FROM AUTHOR]

We investigate vacuum expectation value of the energy-momentum tensor for a massive Dirac field in flat spacetime with a toroidal subspace of a general dimension. Quasiperiodicity conditions with arbitrary phases are imposed on the field operator along compact dimensions. These phases are interpreted in terms of magnetic fluxes enclosed by compact dimensions. The equation of state in the uncompact subspace is of the cosmological constant type. It is shown that, in addition to the diagonal components, the vacuum energy-momentum tensor has nonzero off-diagonal components. In special cases of twisted (antiperiodic) and untwisted (periodic) fields the off diagonal components vanish. For untwisted fields the vacuum energy density is positive and the energy-momentum tensor obeys the strong energy condition. For general values of the phases in the periodicity conditions the energy density and stresses can be either positive or negative. The numerical results are given for a Kaluza-Klein type model with two extra dimensions. [ABSTRACT FROM AUTHOR]

We perform new measurements of the expansion rate and the sound horizon at the end of the baryon decoupling, and derive constraints on cosmic key parameters in the framework of the Λ CDM model, wCDM model, non-flat Λ CDM model and the phenomenological emergent dark energy (PEDE) model. We keep r d and H 0 completely free, and use the recent Dark Energy Spectroscopic Instrument (DESI) Year 1 and Dark Energy Survey (DES) Year 6 BAO measurements in the effective redshift range 0.3 < z < 2.33 , combined with the compressed form of the Pantheon sample of Type Ia supernovae, the latest 34 observational H (z) measurements based on the differential age method, and the recent H 0 measurement from SH0ES 2022 as an additional Gaussian prior. Combining BAO data with the observational H (z) measurements, and the Pantheon SNe Ia data, we obtain H 0 = 69.70 ± 1.11 km s − 1 Mpc − 1 , r d = 147.14 ± 2.56 Mpc in flat Λ CDM model, H 0 = 70.01 ± 1.14 km s − 1 Mpc − 1 , r d = 146.97 ± 2.45 Mpc in PEDE model. The spatial curvature is Ω k = 0.023 ± 0.025 , and the dark energy equation of state is w = − 1.029 ± 0.051 , consistent with a cosmological constant. We apply the Akaike information and the Bayesian information criterion test to compare the four models, and see that the PEDE model performs better. [ABSTRACT FROM AUTHOR]

In this paper, we explore the thermodynamic and phase transition properties of asymptotically AdS black holes within Einstein–Gauss–Bonnet gravity, focusing on Joule–Thomson expansion. Thermodynamics is studied in the extended phase space, where the cosmological constant serves as thermodynamic pressure. We observe that the black hole undergoes a phase transition similar to that of a van der Waals system. We analyze charged and neutral cases separately to distinguish the effect of charge and Gauss–Bonnet parameter on critical behavior and examine the phase structure. We find that the Gauss–Bonnet coupling parameter behaves similarly to black hole charge or spin, guiding the phase structure. To understand the underlying phase structure determined by the Gauss–Bonnet coefficient α , we introduce a new order parameter. We discover that the change in the conjugate variable to the Gauss–Bonnet parameter acts as an order parameter, demonstrating a critical exponent of 1 ∕ 2 in the vicinity of the critical point. Since the phase structure is analogous to that of a van der Waals fluid, we investigate the Joule–Thomson expansion of the black hole. We analytically study the Joule–Thomson expansion, focusing on three key characteristics: the Joule–Thomson coefficient, inversion curves and isenthalpic curves. We obtain isenthalpic curves in the T–P plane and illustrate the cooling–heating regions. [ABSTRACT FROM AUTHOR]

In this paper, we study the modifications induced on scalar field inflation produced by considering a general modification of the Heisenberg algebra. We proceed by modifying the Poisson brackets on the classical theory whenever the corresponding quantum commutator is modified. We do not restrict ourselves to a specific form for such modification, instead we constrain the functions involved by the cosmological behavior of interest. We present whenever possible the way in which inflation can be realized approximately via three slow roll Hubble parameters that depend on the standard slow roll parameters in a very different form than in the usual case and that can be less restrictive. Furthermore, we find a general analytical solution describing an expanding universe with constant Hubble parameter that generalizes the standard cosmological constant case by restricting the form of the modification of the Heisenberg algebra. It is found that even if such modification can be neglected in some limit and the cosmological constant is set to zero in that limit, the exponential expansion is present when the modification is important. Thus, an appropriate modification of the Heisenberg algebra is sufficient to produce an exponentially expanding universe without the need of any other source. [ABSTRACT FROM AUTHOR]

We show the need of the emergence of an invariant minimum speed in the space–time. So, we propose a deformed special relativity with two limits of speed so-called Symmetrical Special Relativity (SSR). It presents a universal minimum speed V that plays the role of a preferred reference frame S V associated with vacuum. This new paradigm of space–time allows us to understand the origin of the cosmological constant Λ 0 starting from first principles given by a new kinematic invariance at low energies, which leads us to build a space–time metric with the presence of a minimum speed, so that such metric is equivalent to a de Sitter metric. In order to do that, we use a model of spherical universe with Hubble radius R H filled by a low vacuum energy density ϵ that governs the accelerated expansion of the universe with negative pressure shown by the equation of state (EOS) of vacuum given by SSR-theory (p = − ϵ). Thus, we realize that such spherical universe made up of dark energy works like a black body with adiabatic expansion thermalized with a kind of dark gas that plays the role of the dark energy. From this model of virtual particles of dark gas that fills the sphere with dark energy, we are able to derive the law of universal gravitation, allowing us to understand the cosmological anti-gravity according to the EOS of vacuum in the space–time with a minimum speed. So, we estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this model, as the dark universe can be thought of as a black body with Hubble radius, we obtain its power and frequency of emission of radiation for a low temperature. We conclude that such radiation is a gravitational wave with an extremely low frequency and power due to the slight stretching of the fabric of space–time, since Λ 0 is very small. [ABSTRACT FROM AUTHOR]

We obtain a class of solutions that correspond to a generalization of the Bardeen black hole solution by solving the Einstein equations coupled to a particular nonlinear electromagnetic field. The generalization is realized by considering, additionally, the presence of the cosmological constant and a source corresponding to an anisotropic fluid, namely, a fluid of strings, which surrounds the black hole. We show that the obtained class of solutions preserve or not the regularity of the original Bardeen black hole solution, depending on the values of the parameter β which labels the different solutions. We discuss the characteristics of the solutions, from the point of view of the singularities of the spacetime, by examining the behavior of the Kretschmann scalar as well as of the geodesics with respect to their completeness. We analyze some aspects of the thermodynamics, particularizing to one of the solutions obtained, namely, for β = -1/2, in which case the regularity of Bardeen black hole is preserved. We also show that there is an incompatibility between the temperature arising from the first law of the black hole thermodynamics and the one using the surface gravity. Some thermodynamic quantities are obtained and analyzed, as for example, pressure, heat capacity, and the critical points, and we show how these quantities change for different values of the parameter q associated with the original Bardeen solution, as well as with the parameter b associated with the presence of the fluid of strings. The phase transitions are also analyzed by using the equation of state and the Helmholtz free energy. [ABSTRACT FROM AUTHOR]

Since the development of Brans–Dicke gravity, it has become well-known that a conformal transformation of the metric can reformulate this theory, transferring the coupling of the scalar field from the Ricci scalar to the matter sector. Specifically, in this new frame, known as the Einstein frame, Brans–Dicke gravity is reformulated as General Relativity supplemented by an additional scalar field. In 1959, Hans Adolf Buchdahl utilized an elegant technique to derive a set of solutions for the vacuum field equations within this gravitational framework. In this paper, we extend Buchdahl's method to incorporate the cosmological constant and to the scalar-tensor cases beyond the Brans–Dicke archetypal theory, thereby, with a conformal transformation of the metric, obtaining solutions for a version of Brans–Dicke theory that includes a quadratic potential. More specifically, we obtain synchronous solutions in the following contexts: in scalar-tensor gravity with massless scalar fields, Brans–Dicke theory with a quadratic potential, where we obtain specific synchronous metrics to the Schwarzschild–de Sitter metric, the Nariai solution, and a hyperbolically foliated solution. [ABSTRACT FROM AUTHOR]

The present paper dealt with the study of solitons of Lorentzian Kähler space-time manifolds. In this paper, we have discussed different conditions for solitons to be steady, expanding, or shrinking in terms of isotropic pressure, the cosmological constant, energy density, nonlinear equations, and gravitational constant in pseudo-quasi-conformally flat and pseudo-W8 flat Lorentzian Kahler space-time manifolds. [ABSTRACT FROM AUTHOR]

The present work deals with the study of a locally rotationally symmetric (LRS) Bianchi type-I cosmological model in the framework of a scalar-tensor theory of gravity formulated by Saez and Ballester with time varying cosmological constant. To obtain the explicit solutions of the Saez-Ballester field equations we assume the average scale factor to obey a power law expansion and the cosmological constant to be proportional to the energy density of the cosmic fluid. The dynamical behaviour of relevant cosmological parameters including the Hubble parameter, the deceleration parameter, the energy density, the pressure, the equation of state parameter, the cosmological constant, the shear scalar, the expansion scalar etc. are investigated graphically by examining their evolution versus the redshift parameter. The validation of the four energy conditions are also checked. We find the outcomes of the constructed model to be in good agreement with the recent observational data.

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature T in thermal equilibrium with a black-body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy. So, each dark particle occupies a very small area of space so-called Planck area L p 2 , which represents the minimum area of the whole space-time given by the spherical surface with area 4 π R H 2 , where R H is the Hubble radius. We realize that such spherical surface is the surface of the black-body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of 1 0 − 1 7 Hz due to the slight stretching of the fabric of space-time. [ABSTRACT FROM AUTHOR]

We use the spherical collapse model to demonstrate that the observable average density of virialized clusters depends on the properties of dark energy along with the properties of gravity on cluster scales and can therefore be used as a probe of these properties. As an application of this approach, we derive the predicted virialized densities and radii of cluster mass structures for a wide range of values of the cosmological constant (including negative values) as a function of the turnaround redshift. For the value of ΩΛ,0 = −0.7 (with Ω m ,0 = 0.3), we find an amplification of the density of virialized clusters which can be as large as 80 per cent compared to Planck18/lambda Cold Dark Matter (ΛCDM) for a turnaround redshift z max ≳ 2. Such an amplification may lead to more efficient early galaxy formation in this class of models, in accordance with the recent findings of JWST , which may be partially pertinent to the Λ sign switching models (ΛsCDM), which have been suggested as potential solutions to the observed Hubble and S 8 discrepancies. [ABSTRACT FROM AUTHOR]

Machine learning (ML) algorithms are becoming popular in cosmology for extracting valuable information from cosmological data. In this paper, we evaluate the performance of a convolutional neural network (CNN) trained on matter density snapshots to distinguish clustering dark energy (DE) from the cosmological constant scenario and to detect the speed of sound (c s) associated with clustering DE. We compare the CNN results with those from a Random Forest (RF) algorithm trained on power spectra. Varying the DE equation of state parameter w DE within the range of −0.7 to −0.99 while keeping |$c_s^2 = 1$|⁠ , we find that the CNN approach results in a significant improvement in accuracy over the RF algorithm. The improvement in classification accuracy can be as high as 40 per cent depending on the physical scales involved. We also investigate the ML algorithms' ability to detect the impact of the speed of sound by choosing |$c_s^2$| from the set {1, 10−2, 10−4, 10−7} while maintaining a constant w DE for three different cases: w DE ∈ {−0.7, −0.8, −0.9}. Our results suggest that distinguishing between various values of |$c_s^2$| and the case where |$c_s^2=1$| is challenging, particularly at small scales and when w DE ≈ −1. However, as we consider larger scales, the accuracy of |$c_s^2$| detection improves. Notably, the CNN algorithm consistently outperforms the RF algorithm, leading to an approximate 20 per cent enhancement in |$c_s^2$| detection accuracy in some cases. [ABSTRACT FROM AUTHOR]

In this work, a two-fluid interacting model in a flat FLRW universe has been studied considering particle creation mechanism with a particular form of particle creation rate |$\Gamma =\Gamma _0 H+\frac{\Gamma _1}{H}$| from different aspects. Statistical analysis with a combined data set of SNe Ia (Supernovae Type Ia) and Hubble data is performed to achieve the best-fitting values of the model parameters, and the model is compatible with current observational data. We also perform a dynamical analysis of this model to get an overall qualitative description of the cosmological evolution by converting the governing equations into a system of ordinary differential equations considering a proper transformation of variables. We find some non-isolated sets of critical points, among which some usually are normally hyperbolic sets of points that describe the present acceleration of the universe dominated by dark energy mimicking cosmological constant or phantom fluid. Scaling solutions are also obtained from this analysis, and they can alleviate the coincidence problem successfully. Statefinder diagnosis is also carried out for this model to compare it with the ΛCDM, and any other dark energy models byfinding various statefinder parameters. Finally, the thermodynamic analysis shows that the generalized second law of thermodynamics is valid in an irreversible thermodynamic context. [ABSTRACT FROM AUTHOR]

This paper deals with the study of quasi-spherical gravitational collapse in the framework of f (R , T) theory. We will divide geometry of the star into two distinct portions i.e. interior portion and exterior portion. In the interior portion, we consider quasi-spherical Szekeres line element and in the exterior portion we take Vaidya line element. The interior and exterior portions will be glued by using Israel's junction conditions [W. Israel, Il Nuovo Cimento B (1965–1970) 44, 1 (1966); W. Israel, Phys. Lett. A 24, 184 (1967)]. The field equations will be derived in the context of f (R , T) theory for a particular model. Apparent horizons and their time configuration for various desirable cases will also be discussed. [ABSTRACT FROM AUTHOR]

We prove nonlinear Lyapunov stability of a family of "(n + 1)"-dimensional cosmological models of general relativity locally isometric to the Friedman–Lemaître–Robertson–Walker (FLRW) spacetimes including a positive cosmological constant. In particular, we show that the perturbed solutions to the Einstein–Euler field equations around a class of spatially compact FLRW metrics (for which the spatial slices are compact negative Einstein spaces in general and hyperbolic for the physically relevant n = 3 case) arising from regular Cauchy data remain uniformly bounded and decay to a family of metrics with constant negative spatial scalar curvature. To accomplish this result, we employ an energy method for the coupled Einstein–Euler field equations in constant mean extrinsic curvature spatial harmonic (CMCSH) gauge. In order to handle Euler's equations, we construct energy from a current that is similar to the one derived by Christodoulou [The Formation of Shocks in 3-dimensional Fluids, EMS Monographs in Mathematics, Vol. 2 (European Mathematical Society, 2007)] (and which coincides with Christodoulou's current on the Minkowski space) and show that this energy controls the desired norm of the fluid degrees of freedom. The use of a fluid energy current together with the CMCSH gauge condition casts the Einstein–Euler field equations into a coupled elliptic–hyperbolic system. Utilizing the estimates derived from the elliptic equations, we first show that the gravity-fluid energy functional remains uniformly bounded in the expanding direction. Using this uniform boundedness property, we later obtain sharp decay estimates if a positive cosmological constant Λ is included, which confirms that the accelerated expansion of the physical universe that is induced by the positive cosmological constant is sufficient to control the nonlinearities in the case of small data. A few physical consequences of this stability result are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we examine stacky structures in certain Einstein gravity theories. In brief, using the classical formulation of (vacuum) gravity, with vanishing cosmological constant, we first construct the stack of solutions to Einstein field equations on any given fixed manifold. Using a similar approach and setup, we also study Einstein’s gravity on families of manifolds and define another stack encoding this situation. Later on, we focus on the gauge theoretical interpretation of 3D gravity and provide a natural stack associated with that interpretation. Finally, in a particular setup, we give a natural morphism between the two stacks arising from different descriptions of 3D gravity. [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]

A brief introduction of the Extended Relativity Theory in Clifford Spaces (C -space) paves the way to the explicit construction of the generalized relativistic transformations of the Clifford multivector-valued coordinates in C -spaces. The most general transformations furnish a full mixing of the grades of the multivector-valued coordinates. The transformations of the multivector-valued momenta follow leading to an invariant generalized mass ℳ in C -spaces which differs from m. No longer the proper mass appearing in the relativistic dispersion relation E 2 − p ⋅ p = m 2 remains invariant under the generalized relativistic transformations. It is argued how this finding might shed some light into the cosmological constant problem, dark energy, and dark matter. We finalize with some concluding remarks about extending these transformations to phase spaces and about Born reciprocal relativity. An appendix is included with the most general (anti) commutators of the Clifford algebra multivector generators. [ABSTRACT FROM AUTHOR]

In this paper, we use quasars calibrated from type Ia supernova (SN Ia) to constrain cosmological models. We consider three different X-ray luminosity (L X)–ultraviolet luminosity (L UV) relations of quasars, i.e. the standard L X– L UV relation and two redshift–evolutionary relations (Type I and Type II), respectively, constructed from copula and considering a redshift correction to the luminosity of quasars. Only in the case of the Type I relation, quasars can always provide effective constraints on the ΛCDM (cosmological constant Λ plus cold dark matter) model. Furthermore, we show that, when the observational Hubble data (OHD) are added, the constraints on the absolute magnitude M of SN Ia and the Hubble constant H 0 can be obtained. In the ΛCDM model, the OHD measurements plus quasars with the Type I relation yields M  =  |$-19.321^{+0.085}_{-0.076}$|⁠ , which is in good agreement with the measurement from SH0ES (M  = −19.253 ± 0.027), and H 0 =  |$70.80\pm 3.6~\mathrm{km~s^{-1}\, Mpc^{-1}}$|⁠ , falling between the measurements from SH0ES and the Planck cosmic microwave background radiation data. [ABSTRACT FROM AUTHOR]

We consider the (1 + 3) -dimensional Einstein equations with negative cosmological constant coupled to a spherically symmetric, massless scalar field and study perturbations around the anti-de Sitter spacetime. We derive the resonant systems, pick out vanishing secular terms and discuss issues related to small divisors. Most importantly, we rigorously establish (sharp, in most of the cases) asymptotic behaviour for all the interaction coefficients. The latter is based on uniform estimates for the eigenfunctions associated to the linearized operator as well as on some oscillatory integrals. [ABSTRACT FROM AUTHOR]

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, r → r − e H t a , where H is the Hubble parameter. For H → 0 , this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations r → r − a . Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature T = H / π , which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature T = H / π determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, S hor = 4 π K A , where K = 1 / (16 π G) . This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the f (R) gravity. In this thermodynamics, the Ricci scalar curvature R and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling K = d f / d R . Such a connection takes place only in the 3 + 1 spacetime, where there is a special symmetry due to which the variables K and R have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes. [ABSTRACT FROM AUTHOR]

We investigate a spherically symmetric exact solution of Einstein's gravity with cosmological constant in (2 + 1) dimensions, non-minimally coupled to a scalar field. The solution describes the gravitational field of a black hole, which is free of curvature singularities in the entire spacetime. We use the formalism of geometrothermodynamics to investigate the geometric properties of the corresponding space of equilibrium states and find their interpretation from the point of view of thermodynamics. It turns out that, as a result of the presence of thermodynamic interaction, the space of equilibrium states is curved with two possible configurations, which depend on the value of a coupling constant. In the first case, the equilibrium space is completely regular, corresponding to a stable thermodynamic system. The second case is characterized by the presence of two curvature singularities, which are shown to correspond to locations where the system undergoes two different phase transitions, one due to the breakdown of the thermodynamic stability condition and the second one due to the presence of a divergence at the level of the response functions. [ABSTRACT FROM AUTHOR]

I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de Sitter cosmological constant and horizon. This yields qualitative connections between microscopic ranges acquired by W ± or Z 0 gauge Bosons and the cosmological scale and minimal mass acquired by g-photons. I apply this procedure to an established Stueckelberg–Higgs mechanism, while I consider a similar procedure for a pair of Higgs fields that may spontaneously break all U(1) × SU(2) gauge invariances. My estimates of photon masses and their additional parity-breaking interactions with leptons and neutrinos may be detectable in suitable accelerator experiments. Their effects may also be observable astronomically through massive g-photon condensates that may contribute to dark matter and dark energy. [ABSTRACT FROM AUTHOR]

The radial acceleration relation (RAR) connects the total gravitational acceleration of a galaxy at a given radius, a tot(r), with that accounted for by baryons at the same radius, a bar(r). The shape and tightness of the RAR for rotationally-supported galaxies have characteristics in line with MOdified Newtonian Dynamics (MOND) and can also arise within the cosmological constant + cold dark matter (ΛCDM) paradigm. We use zoom simulations of 20 galaxies with stellar masses of M ⋆ ≃ 107–11 M⊙ to study the RAR in the FIRE-2 simulations. We highlight the existence of simulated galaxies with non-monotonic RAR tracks that 'hook' down from the average relation. These hooks are challenging to explain in Modified Inertia theories of MOND, but naturally arise in all of our ΛCDM-simulated galaxies that are dark-matter dominated at small radii and have feedback-induced cores in their dark matter haloes. We show, analytically and numerically, that downward hooks are expected in such cored haloes because they have non-monotonic acceleration profiles. We also extend the relation to accelerations below those traced by disc galaxy rotation curves. In this regime, our simulations exhibit 'bends' off of the MOND-inspired extrapolation of the RAR, which, at large radii, approach a tot ≈ a bar/ f b, where f b is the cosmic baryon fraction. Future efforts to search for these hooks and bends in real galaxies will provide interesting tests for MOND and ΛCDM. [ABSTRACT FROM AUTHOR]

We prove a strong localized gluing result for the general relativistic constraint equations (with or without cosmological constant) in n ≥ 3 spatial dimensions. We glue an ϵ -rescaling of an asymptotically flat data set (γ ^ , k ^) into the neighborhood of a point p ∈ X inside of another initial data set (X , γ , k) , under a local genericity condition (non-existence of KIDs) near p . As the scaling parameter ϵ tends to 0, the rescalings x ϵ of normal coordinates x on X around p become asymptotically flat coordinates on the asymptotically flat data set; outside of any neighborhood of p on the other hand, the glued initial data converge back to (γ , k) . The initial data we construct enjoy polyhomogeneous regularity jointly in ϵ and the (rescaled) spatial coordinates. Applying our construction to unit mass black hole data sets (X , γ , k) and appropriate boosted Kerr initial data sets (γ ^ , k ^) produces initial data which conjecturally evolve into the extreme mass ratio inspiral of a unit mass and a mass ϵ black hole. The proof combines a variant of the gluing method introduced by Corvino and Schoen with geometric singular analysis techniques originating in Melrose's work. On a technical level, we present a fully geometric microlocal treatment of the solvability theory for the linearized constraints map. [ABSTRACT FROM AUTHOR]

We describe a general constitutive framework for a teleparallel extension of the general theory of relativity. This approach goes beyond the teleparallel equivalent of general relativity (TEGR) by broadening the analogy with the electrodynamics of media. In particular, the main purpose of this paper is to investigate in detail a local constitutive extension of TEGR that is the local limit of non-local gravity. Within this framework, we study the modified Friedmann–Lemaître–Robertson–Walker cosmological models. Of these, the most cogent turns out to be the modified Cartesian flat model which is shown to be inconsistent with the existence of a positive cosmological constant. Moreover, dynamic dark energy and other components of the modified Cartesian flat model evolve differently with the expansion of the universe as compared to the standard flat cosmological model. The observational consequences of the modified Cartesian flat model are briefly explored and it is shown that the model is capable of resolving the H 0 tension. [ABSTRACT FROM AUTHOR]

The existence of 'peculiar' velocities due to the formation of cosmic structure marks a point of discord between the real universe and the usually assumed Friedmann–Lemaítre–Robertson–Walker metric, which accommodates only the smooth Hubble expansion on large scales. In the standard Λ CDM model framework, Type Ia supernovae data are routinely "corrected" for the peculiar velocities of both the observer and the supernova host galaxies relative to the cosmic rest frame, in order to infer evidence for acceleration of the expansion rate from their Hubble diagram. However, observations indicate a strong, coherent local bulk flow that continues outward without decaying out to a redshift z ≳ 0.1 , contrary to the Λ CDM expectation. By querying the halo catalogue of the Dark Sky Hubble-volume N-body simulation, we find that an observer placed in an unusual environment like our local universe should see correlations between supernovae in the JLA catalogue that are 2–8 times stronger than seen by a typical or Copernican observer. This accounts for our finding that peculiar velocity corrections have a large impact on the value of the cosmological constant inferred from supernova data. We also demonstrate that local universe-like observers will infer a downward biased value of the clustering parameter S 8 from comparing the density and velocity fields. More realistic modelling of the peculiar local universe is thus essential for correctly interpreting cosmological data. [ABSTRACT FROM AUTHOR]