This study performs a comparative cosmological analysis of Brans–Dicke theory (BDT) and [Formula: see text] gravity in the anisotropic Bianchi type-I spacetime. By using a hyperbolic sine form of the scale factor, we constrain the free parameters [Formula: see text] and [Formula: see text] against 77 [Formula: see text] data points via [Formula: see text] minimization, obtaining [Formula: see text] and [Formula: see text], with a reduced chi-square [Formula: see text]. The model predicts the present Hubble and deceleration parameters as [Formula: see text] and [Formula: see text], respectively. We derive and examine the dynamical evolution of energy density, pressure, and the equation of state (EoS) parameter. A key outcome is the marked difference in late-time behavior: the [Formula: see text] model exhibits stronger acceleration with an EoS parameter trending toward phantom regimes, whereas the BDT model shows a distinctive late-time re-acceleration phase driven by the scalar field dynamics. These results highlight how geometric and scalar-field modifications of gravity lead to observationally distinguishable cosmic evolution.

A comment on gravitational radiation in generalized Brans–Dicke theory: compact binary systems

We add a new scalar field in the no-scale Brans-Dicke gravity and require it to have a global O(2) symmetry with the original scalar field in the Brans-Dicke gravity. This gives us a new massless scalar field in the Einstein frame due to the SO(2) symmetry. We then explicitly break the O(2) symmetry to a $D_4$ symmetry, and this scalar field gains a periodic potential. This scalar field can serve as the quintessence field to explain dark energy. If we further add the $R^2$ term and the non-minimal coupling to the Higgs field, we can realize inflation and reheating, and this leads to a super-Planckian decay constant of the quintessence potential. The super-Planckian decay constant is consistent with the newly released observational data according to a recent analysis.

Abstract We consider the inhomogeneous Morris–Thorne wormhole metric with matter tensors characterised by a novel linear equation of state in f(R) gravity. Using the Einstein’s field equations in metric f(R) gravity we model solutions for both wormhole as well as f(R) gravity. We obtain four different wormhole models, two wormholes are characterised by solid angle deficit, three are not asymptotically extendible, while one is asymptotically flat with zero tidal force. These are supported by four different power law f(R) models. The parameter space of the models can support both null energy conditions (NEC) satisfying as well as violating wormhole. In case of NEC satisfying matter, the associated f(R) is ghost. The f(R) models obtained have been independently substantiated for cosmological feasibility and valid parameter space was obtained corresponding to cosmologically viable f(R). Suitable scalar-tensor representation of the corresponding f(R) models have been presented using the correspondence of f(R) gravity with Brans–Dicke (BD) theory of gravity. The robustness of the wormhole solutions were further analysed with the BD scalar fields in the hybrid metric-Palatini gravity, which showed excellent results. Lastly as an independent astrophysical probe for the wormhole we have obtained the location of their photon spheres and have connected them with the Herrera Complexity factor in f(R). Our results show that the relation between the complexity factor and existence of photon spheres remains fundamentally unaltered in f(R) as compared to Einstein’s gravity.

This study examines a holographic dark energy (HDE) model within the Brans–Dicke (BD) cosmology framework, integrating the holographic principle and employing Barrow entropy as an alternative to the conventional Bekenstein–Hawking entropy. Unlike standard HDE models, interacting and non-interacting cases are analyzed, incorporating sign-changeable and linear interactions to evaluate their role in explaining the universe’s accelerated expansion. Key cosmological parameters, including the deceleration parameter (DP) [Formula: see text], skewness parameter [Formula: see text], squared speed of sound [Formula: see text] and equation of state [Formula: see text], are investigated. Additionally, the evolution of the [Formula: see text] plane is studied. Graphical representations compare parameter behavior across different scenarios. The DP [Formula: see text] determines expansion rates, while the equation of state parameter [Formula: see text] distinguishes cosmic phases, such as quintessence and vacuum states. Stability is evaluated through squared sound speed analysis, and energy conditions offer insights into the universe’s ongoing rapid expansion. Comparative analysis with observational data indicates that the barrow holographic dark energy (BHDE) BD model effectively grows cosmic acceleration, maintains a modern EoS, [Formula: see text], aligns with [Formula: see text]CDM density ratios, and could decrease the [Formula: see text] tension, so establishing its validity as a dark energy model within scalar–tensor cosmology.

Cosmological insights of BHDE in anisotropic universe under Brans–Dicke theory

It is very much intriguing if the Planck scale M Pl is not a fundamental parameter. The Brans-Dicke gravity is nothing but the theory where the Planck scale M Pl is indeed an illusional parameter. The theory predicts a massless scalar boson whose exchanges between matters induce unwanted long range forces. We solve this problem imposing there is no dimensionful parameter in the theory, even at the quantum level.We further extend the theory by including a R 2 term and a non-minimal coupling of the Standard Model Higgs to gravity, as their coefficients are dimensionless. This extension provides a heavy inflaton field that is consistent with all cosmological observations, with a potential very similar to that of the Starobinsky model. The inflaton necessarily decays into the massless scalar bosons, resulting in a non-negligible amount of dark radiation in the present universe. We demonstrate that the inflation model yields a sufficiently high reheating temperature for successful leptogenesis, and we also discuss a possible candidate for dark matter.

The Advanced LIGO and Virgo collaborations recently detected a gravitational wave event, GW230529_181500, during the fourth observing run, which is most plausibly attributed to the merger of a neutron star and a black hole. This observation provides an opportunity to test a class of gravitational theories that deviate from general relativity. In such theories, additional terms contribute to the gravitational wave signal only in cases of asymmetric binaries. This study focuses on two scalar-tensor models within this class of theories: the Screened Modified Gravity and Brans-Dicke theory. These models have potential applications in areas such as dark matter, dark energy, cosmic inflation, and primordial nucleosynthesis. With the GW230529_181500 and Bayesian Markov-chain Monte Carlo analyses, we derive a 90% credible lower bound as and by using dominant mode correction. Asymmetric binary systems usually have a significant mass ratio, in such cases, higher harmonic modes cannot be neglected. Our work considers higher harmonic corrections from scalar-tensor theories and provides a tighter constraint of and , with a 13.3% and 30.1% improvement respectively. Combining GW230529_181500, GW200115 and GW190814 and including higher modes, the constraint is improved to and . This is currently the strongest constraint from GWs, contingent upon GW190814 being an NSBH event.

Abstract In our previous papers we have analyzed the stability of vacuum and electrovacuum static, spherically symmetric space-times in the framework of the Bergmann–Wagoner–Nordtvedt class of scalar-tensor theories (STT) of gravity. In the present paper, we continue this study by examining the stability of exceptional solutions of the Brans–Dicke theory with the coupling constant $$\omega =0$$ ω = 0 that were not covered in the previous studies. Such solutions describe neutral or charged wormholes and involve a conformal continuation: the standard conformal transformation maps the whole Einstein-frame manifold $${\mathbb {M}}_\textrm{E}$$ M E to only a part of the Jordan-frame manifold $${\mathbb {M}}_\textrm{J}$$ M J , which has to be continued beyond the emerging regular boundary S, and the new region maps to another manifold $${\mathbb {M}}_\textrm{E}$$ M E $${}_{-}$$ - . The metric in $${\mathbb {M}}_\textrm{J}$$ M J is symmetric with respect to S only if the charge q is zero. Our stability study concerns radial (monopole) perturbations, and it is shown that the wormhole is stable if $$q \ne 0$$ q ≠ 0 and unstable only in the symmetric case $$q=0$$ q = 0 .

Abstract We investigate exact vacuum solutions in Brans–Dicke (BD) gravity, focusing on their implications for black hole shadow imaging. Motivated by the Event Horizon Telescope (EHT) observations, we revisit a class of BD solutions that exhibit a naked singularity. These solutions, despite lacking a conventional event horizon, exhibit photon spheres and produce shadow-like features. We analyze null geodesics and perform ray-tracing simulations under an optically thin accretion disk model to generate synthetic images. Our results show that BD naked singularities can cast shadows smaller than those of Schwarzschild black holes of equivalent mass. This requires, however, negative values for the BD parameter $$\omega $$ ω (in the range $$-3/2< \omega < 0$$ - 3 / 2 < ω < 0 ). The lower bound on $$\omega $$ ω is compatible with the absence of ghosts. Although such $$\omega $$ ω range is outside the Solar System bounds, our results are relevant for a larger class of modified gravity models whose local behaviour can be approximated by Brans–Dicke gravity. These findings suggest that BD naked singularities are possible candidates for compact astrophysical objects.

Abstract We explore a model of interacting Early Dark Energy (EDE) in which a minimally coupled scalar field, representing the EDE, interacts with the radiation sector through an exponential coupling function in the radiation-dominated era. This framework can be inspired by modified theories of gravity, including f(R) gravity, the Einstein frame representation of Brans-Dicke theory, and chameleon gravity. We find that the traditional law of radiation conservation is modified, with ρ γ ∝ a −4+ϵ , where the parameter ϵ measures the rate of energy transfer between radiation and EDE. Assuming constant energy transfer, we demonstrate that the scalar field evolves as ϕ ∝ ln a , diverging as a approaches zero. Additionally, we demonstrate that the interacting scalar-photon system behaves similarly to an effective cosmological constant in the early stages of evolution of the Universe. Moreover, by solving the conservation equation associated with the scalar field, we derive an analytical expression for the ratio r = ρ ϕ /ρ γ . Our results indicate that r diminishes as the Universe expands, which is essential for a successful EDE model. Our parameter space analysis confirms that the predicted behavior of r during recombination is consistent with current cosmological observations. These insights underscore crucial aspects necessary for any feasible EDE model and present exciting possibilities for resolving the Hubble tension.

Generalized Brans-Dicke theory from Verlinde's entropic gravity

In this paper, we present a comprehensive analysis of the holographic dark energy model with Granda–Oliveros cutoff in Brans–Dicke theory. We assume that the scalar field has a logarithmic form [Formula: see text], where a is the scale factor, [Formula: see text] and [Formula: see text] are arbitrary constants. The evolution of the universe is discussed by calculating the equation of state parameter [Formula: see text] of holographic dark energy and deceleration parameter q. To discuss the cosmography of the model, we calculate the value of the Hubble parameter [Formula: see text] and constrain the model parameters using recent observational data sets. The best fit value of Hubble constant [Formula: see text] has been obtained which shows agreement with the recent observations. We plot graphs of [Formula: see text] and q using the best fit values of the parameters which depict their evolution against the redshift parameter z. The graphs show that the model explains the recent phase transition of the universe. We observe an interesting result which shows a decelerating universe in the far future. It is observed that [Formula: see text] does not cross the phantom divide line, i.e. the model is free from a big-rip singularity. The statefinder analysis shows, however, the model trajectory lies in the quintessence region for quite a long period, but the overall evolution is different from known dark energy models. We apply a thermodynamic analysis and find that the generalized second law of thermodynamics holds in the model for the best fit values of the parameters. We verify the stability of the model using the squared sound speed method and find that the model is stable. Moreover, we study the energy conditions for the present model. We observe that the strong energy condition is violated during the present epoch and in the future. However, we observe that it is again satisfied in the vicinity of the point [Formula: see text]. The null energy condition remains satisfied throughout which shows consistency with the behavior observed in the [Formula: see text]-CDM model.

Abstract In this paper, we investigate the coupling of a tachyonic field with a global monopole in the framework of the Brans-Dicke modified gravity theory. Global monopoles, formed during the early universe’s phase transitions due to spontaneous symmetry breaking, provide a unique insight into the Universe’s nascent stages. Motivated by earlier works on monopoles and tachyonic fields, we aim to analyse how Brans-Dicke gravity influences global monopoles and their associated tachyonic fields. We derive and solve the field equations under a weak field approximation, considering the effects of the Brans-Dicke parameter ω and the monopole’s scalar field on the resulting spacetime. Additionally, we study the geodesics and bending of light in this modified spacetime both for massless and massive particles. The findings reveal distinct gravitational effects caused by the tachyonic field and global monopole under Brans-Dicke gravity, potentially offering new perspectives on early universe physics and topological defects.

In this study, we search for a new class of wormhole solutions in the framework of Brans–Dicke (BD) theory in the presence of anisotropic matter distribution. Considering a linear equation of state (EoS) between radial pressure and energy density profile we find exact static spherically symmetric solutions to the BD field equations which represent wormhole configurations. The solutions we obtain include both cases with zero and nonzero redshift functions, for which, the conditions on wormhole geometry together with the weak (WEC) and null (NEC) energy conditions put constraints on model parameters such as, the BD coupling and EoS parameters. These constraints also depend on other model parameters such as, the value of BD scalar field and energy density at the wormhole throat. The regularity of the obtained solutions is verified by calculating the Kretschmann scalar in order to ensure that curvature singularities are absent in the wormhole spacetime. We then find that BD wormholes in the presence of anisotropic matter can exist without violating NEC and WEC, either at the throat or across the entire spacetime.

Cosmic and thermodynamic analysis of Barrow holographic dark energy model in logarithmic Brans-Dicke gravity

In this paper, we investigate the thermodynamics of charged Brans–Dicke (BD) black holes (BHs) in the presence of Euler-Heisenberg (EH) electrodynamics. We write the action and discuss that the equations of electromagnetic, scalar, and gravitational fields are strongly coupled, which make them difficult to be solved directly. To remove this problem, we use the conformal transformations (CTs) to transfer Jordan frame (JF) action to that of Einstein frame (EF). We solve the equations and introduce two new classes of BHs in the Einstein-dilaton theory. By detailed calculations, we show that if the EH nonlinearity parameter is treated as a conformal-invariant quantity, the first law of thermodynamics (FLT) is violated. To solve this problem, we allow the nonlinear parameter to change under CTs. Then, by using this proposal, we obtain the corrected solutions by exactly solving the field equations. Our solutions are asymptotically unusual and capable of exhibiting extreme and multi-horizon dilaton BHs. Then, we calculate the thermodynamic quantities and show that the FLT holds for the new EH BHs. The thermal stability or phase transition of the BHs is analyzed by using the canonical ensemble method. Finally, we introduce new EH-BD BHs solutions, from their EF counterparts, by reversing the transformations. We explore thermodynamic quantities, FLT and thermal stability of the BD BHs by utilizing the appropriate methods.

In this work, we investigate the cosmic analysis in detail by assuming squared speed of sound parameterizations in the framework of Brans-Dicke theory. For this purpose, we extract various cosmological parameters such as Hubble, deceleration, equation of state, Om diagnostic and jerk. We also explore the viability of the universe through the ω−ω′ plane and the statefinder plane. We present the analytical and graphical solutions for all of the above-mentioned parameters. From the graphical analysis, it is noted that the deceleration parameter demonstrates the deceleration to acceleration expansions of the universe. In most cases, the Om diagnostic shows a quintessence-like era, the jerk parameter and statefinder parameter show the ΛCDM limit and the ω−ω′ plane indicates a freezing region of the universe. Our investigation reveals that the squared speed of sound demonstrates stable behavior across all considered parameterizations. To analyze the thermodynamic properties of the proposed models, we examine the validity of the generalized second law of thermodynamics with generalized six parameters entropy as horizon entropy. We found the validity of this law for all squared speed of sound parameterizations.

Abstract We will summarize recent results on the Hamiltonian equivalence between the Jordan and Einstein frames based on the analysis of Brans-Dicke theory for both cases ω ≠ − 3 2 and ω = − 3 2 We will introduce and perform ADM analysis for spherically symmetric solutions of gravity. We will discuss with particular care the problem of the boundary terms to be introduced in the general case of spherical symmetry. These two frames are connected through a Hamiltonian canonical transformation on the reduced phase space obtained by gauge fixing the lapse and the radial shift functions. We introduce and discuss two static solutions (Fisher, Janis, Newman and Winicour solution in the Einstein frame and Bocharova-Bronnikov-Melnikov-Bekenstein black hole solution in the Jordan frame)

In this paper, we investigate dark energy scenarios in the Brans–Dicke theory of gravity in the Lyra manifold. We find an analytic solution of the field equations for a flat, homogeneous, and isotropic universe in the form of a hyperbolic solution. We made observational constraints on the model solutions using cosmic chronometer (CC) and Pantheon datasets in MCMC analysis. Using these constrained solutions, we investigate the evolution of universe history by investigating the decelerating parameter [Formula: see text], effective equation of state (EoS) [Formula: see text], dark energy EoS [Formula: see text], scalar field [Formula: see text], etc. We also analyze the Om diagnostic and age of the universe. We have measured the current value of the dark energy EoS parameter [Formula: see text] with the deceleration parameter [Formula: see text]. We have found the present age of the universe [Formula: see text] Gyrs with transition redshift [Formula: see text], which is consistent with recent observations. We have obtained a phantom dark energy transit phase-accelerating cosmological model.