Narrow Results

In this paper, we implement the Einsenhart–Duval lift in scalar–tensor gravity as a means to construct integrable cosmological models and analytic cosmological solutions. Specifically, we employ a geometric criterion to constrain the free functions of the scalar–tensor theory such that the field equations can be written in the equivalent form of linear equations. This geometric linearization is achieved by the introduction of an extended minisuperspace description. The results are applied to construct analytic solutions in modified theories of gravity such as the $f(R)$-theory and the hybrid metric-Palatini $f({ℛ})$-gravity.

We discuss the gravitomagnetic time delay and the Lense–Thirring effect in the context of Brans–Dicke theory of gravity. We compare the theoretical results obtained with those predicted by general relativity. We show that within the accuracy of experiments designed to measure these effects both theories predict essentially the same results.

In order to investigate more features of the Brans–Dicke cosmology in the five-dimensional spacetime, we explore the solutions of its dynamical systems. A behavior of the universe in its early and late time by means of the scale factor is considered. As a result, we show that it is possible to avoid the big rip singularity and to cross the phantom divide line. Furthermore, we review the dark energy component of the universe and its agreement with the observation data for this 3-brane Brans–Dicke cosmology by means of the cosmological parameters.

We consider the effect of matter in the anisotropic universe of the scalar–tensor theory. We study Brans–Dicke model as a scalar–tensor theory. The matter is treated as perfect fluid type one. Just as the spacetime is anisotropic, the matter is also considered to be anisotropic. In order to give the present universe which is isotropic, the spacetime should be filled with the particular type of matter.

We discuss the gravitomagnetism in the context of Brans-Dicke theory of gravity. We obtain the equation of motion of a particle in terms of gravitoelectric and gravitomagnetic fields. Comparing the result obtained with that predicted by general relativity we show that the difference between the two theories lies in the gravitomagnetic force.

We derive a new analytic solution of (n + 1)-dimensional (n ≥ 4) Brans–Dicke–Maxwell theory in the presence of a potential for the scalar field, by applying a conformal transformation to the dilaton gravity theory. Such solutions describe topological charged black holes with unusual asymptotics. We obtain the conserved and thermodynamic quantities through the use of the Euclidean action method. We also study the thermodynamics of the solutions and verify that the conserved and thermodynamic quantities of the solutions satisfy the first law of black hole thermodynamics.

Deci-Hertz Interferometer Gravitational Wave Observatory (DECIGO) Pathfinder (DPF) has an ability to detect gravitational waves (GWs) from galactic intermediate mass black hole binaries. If the signal is detected, it would be possible to determine parameters of the binary components. Furthermore, by using future space-borne GW interferometers, it would be possible to test alternative theories of gravity in the strong field regime. In this review paper, we first explain how the detectors like DPF and DECIGO/BBO work and discuss the expected event rates. Then, we review how the observed gravitational waveforms from precessing compact binaries with slightly eccentric orbits can be calculated both in general relativity and in alternative theories of gravity. For the latter, we focus on Brans–Dicke (BD) and massive gravity (MG) theories. After reviewing these theories, we show the results of the parameter estimation with DPF using the Fisher analysis. We also discuss a possible joint search of DPF and ground-based interferometers. Then, we show the results of testing alternative theories of gravity using future space-borne interferometers. DECIGO/BBO would be able to place 4–5 orders of magnitude stronger constraint on BD theory than the solar system experiment. This is still 1–2 orders of magnitude stronger than the future solar system mission such as ASTROD I. On the other hand, LISA should be able to put four orders of magnitude more stringent constraint on the mass of the graviton than the current solar system bound. DPF may be able to place comparable constraint on the MG theories as the solar system bound. We also discuss the prospects of using eLISA and ASTROD-GW in testing alternative theories of gravity. The bounds using eLISA are similar to the LISA ones, but ASTROD-GW performs the best in constraining MG theories among all the GW detectors considered in this paper.

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

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 $\omega$ (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 $\mathrm{\Lambda }$ cold dark matter (CDM) limit in the far future. Then we study the $w_D-w_D^{\prime }$ 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.

We develop the covariant formalism of the cosmological perturbation theory for the Brans-Dicke gravity, and use it to calculate the cosmic microwave background (CMB) anisotropy and large scale structure (LSS) power spectrum. We introduce a new parameter ζ which is related to the Brans-Dicke parameter ζ = ln(1/ω + 1), and use the Markov-Chain Monte Carlo (MCMC) method to explore the parameter space. Using the latest CMB data published by WMAP, ACBAR, CBI, Boomerang teams, and the LSS data from the SDSS survey DR4, we find that the the 2σ (95.5%) bound on ζ is about |ζ| > 10^-2, or |ω| > 10², the precise limit depends somewhat on the prior used.

We consider a five dimensional DGP-brane scenario endowed with a non-minimally coupled scalar field within the context of Brans-Dicke theory. We consider the effective four dimensional field equations on a 3+1 dimensional brane where the fifth dimension is assumed to have an orbifold symmetry. Finally, we discuss the cosmological implications of this setup, predicting an accelerated expanding universe with a value of the Brans-Dicke parameter ω consistent with values resulting from the solar system observations.

The effect of a universal scalar/matter coupling are investigated in Scalar-Tensor theories where the scalar potential is null. It is shown that the metric can be put in its standard post-Newtonian form. However, considering an effective Lagrangian for the matter field, it is pointed out that 1 − γ could be either positive, null or negative for finite value of ω, depending on the coupling function; while Scalar-Tensor theories without coupling always predict γ < 1 for finite value of ω.