Brans–Dicke Theory and Primordial Black Holes in Early Matter-Dominated Era

We show that primordial black holes can be formed in the matter-dominated era with gravity described by the Brans–Dicke theory. Considering an early matter-dominated era between inflation and reheating, we found that the primordial black holes formed during that era evaporate at a quicker rate than those of early radiation-dominated era. Thus, in comparison with latter case, less number of primordial black holes could exist today. Again the constraints on primordial black hole formation tend towards the larger value than their radiation-dominated era counterparts indicating a significant enhancement in the formation of primordial black holes during the matter-dominaed era.     

On Dynamics of Brans–Dicke Theory of Gravitation

We study longstanding problem of cosmological clock in the context of Brans–Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogeneous cosmological models. Then, we show that formulation of the Brans–Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann–Robertson–Walker cosmological models.     

Isotropization of Bianchi Models and a New FRW Solution in Brans–Dicke Theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans–Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curved (k 0) Friedmann–Robertson–Walker (FRW) cosmologies in Brans–Dicke theory is analyzed.     

Modified Holographic Ricci Dark Energy in Chameleon Brans–Dicke Cosmology and Its Thermodynamic Consequence

The objective of this paper is to discuss the Chameleon Brans–Dicke gravity with non-minimally matter coupling of scalar field. We take modified Holographic Ricci dark energy model in this gravity with its energy density in interaction with energy density of cold dark matter. We assume power-law ansatz for scale factor and scalar field to discuss potential as well as coupling functions in the evolving universe. These reconstructed functions are plotted versus scalar field and time for different values of power component of scale factor n. We observe that potential and coupling functions represent increasing behavior, in particular, consistent results for a specific value of n. Finally, we have examined validity of the generalized second law of thermodynamics and we have observed its validity for all values of n.     

Equations of state in the Brans–Dicke cosmology

We investigate the Brans–Dicke (BD) theory with the potential as cosmological model to explain the present accelerating universe. In this work, we consider the BD field as a perfect fluid with the energy density and pressure in the Jordan frame. Introducing the power-law potential and the interaction with the cold dark matter, we obtain the phantom divide which is confirmed by the native and effective equation of state. Also we can describe the metric f(R) gravity with an appropriate potential, which shows a future crossing of the phantom divide in viable f(R) gravity models when employing the native and effective equations of state.     

Einstein and Brans–Dicke Frames in Multidimensional Cosmology

Inhomogeneous multidimensional cosmological models with a higher-dimensional space-time manifold _{0 i=1} ⁿ M_i (n 1) are in stigated under dimensional reduction to a D ₀-dimensional effective non-minimally coupled -model which generalizes the familiar Brans–Dicke model. The general form of the Einstein frame representation of multidimensional solutions known in the Brans–Dicke frame is given with respect to cosmic synchronous time. As an example, the transformation is demonstrated explicitly for the generalized Kasner solutions where it is shown that solutions in the Einstein frame show no inflation of the external space although they can undergo deflation after the cosmic synchronous time inversion.     

LETTER: A Remark on Brans–Dicke Cosmological Dust Solutions with Negative ω

Analysing the Brans–Dicke solutions for the dust phase, we show that, for negative values of , they contain scenarios that display an initial subluminal expansion followed by an inflationary phase. This is due to a repulsive cosmic effect. We discuss these solutions with respect to the results of the observation of high redshift supernova as well as the age problem and structure formation. We establish possible connections of these solutions with those emerging from string effective models.     

Stationarity and large ω Brans–Dicke solutions versus general relativity

It is often claimed that the asymptotic behaviour of the Brans–Dicke solutions versus general relativity, when , is related to the trace of the stress tensor. Considering the standard Euclidean cosmological model, we argue that this claim is not correct. On the other hand, we argue that this behaviour depends on the property of the considered solutions versus stationarity and asymptotical flatness.     

Brans—Dicke理论中的非Accetta真空虫洞解

给出与Ａｃｃｅｔｔａ等人所得到的完全不同的Ｂｒａｕｓ－Ｄｉｃｋｅ（B－Ｄ）理论真空虫洞解，且表明这类虫洞与所得到的其他虫洞不同，其喉的尺度是随着Ｅｕｃｌｉｄｅａｎ宇宙时间的增大而线性增大。     

Stability analysis and observational measurement in 5-D Brans–Dicke cosmology

This Letter is a study of the effects of higher dimensional gravity and Brans–Dicke (BD) scalar field on cosmic acceleration in 5-D BD cosmological model. We assume a flat cosmological model in which the matter content of the universe is either cold dark matter or radiation. In a framework to study attractor solutions in the phase space we simultaneously constrain the model parameters with the observational data for distance modulus. The phase space analysis illustrates that the universe begins from an unstable state in the past and eventually reaches an asymptotically stable state (attractor). We examine the model by performing Hubble parameter test in addition to statefinder diagnosis. We also reconstruct the equation of state parameter, the scale factor in 3-D space and along extra dimension. The results show that due to the presence of extra dimension and Brans–Dicke scalar field in the model, the universe undergoes a period of acceleration.     

Conformally flat Stäckel spaces in the Brans–Dicke theory

A problem of classification of the conformally flat St?ckel spaces admitting complete separation of variables in the Hamilton–Jacobi equation is studied within the framework of the Brans–Dicke scalar-tensor gravitational theory. Solutions to the field equations of the theory are found for the conformally flat St?ckel spaces of type (1.1), and explicit forms of the metric and scalar field are presented. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 54–58, February, 2009.     

Regular Charged Solutions in Mφller＇s Tetrad Theory of Gravitation

We find the most general tetrads which give a regular charged spacetime in tetrad theory of gravitation. The metric is a static one and it includes the Schwarzschild and Fteissner Nordstrom black holes. The energy content contained in a sphere of radius R is calculated using the superpotential given by Mφller in the context of Weitzenbock spacetime.     

Phantom energy accretion and primordial black holes evolution in Brans–Dicke theory

In this work, we study the evolution of primordial black holes within the context of Brans–Dicke theory by considering the presence of a dark energy component with a super-negative equation of state, called phantom energy, as a background. Besides Hawking evaporation, here we consider two types of accretion—radiation accretion and phantom energy accretion. We found that radiation accretion increases the lifetime of primordial black holes whereas phantom accretion decreases the lifespan of primordial black holes. Investigating the competition between the radiation accretion and phantom accretion, we found that there is an instant during the matter-dominated era beyond which phantom accretion dominates radiation accretion. So the primordial black holes which are formed in the later part of radiation-dominated era and in matter-dominated era are evaporated at a quicker rate than by Hawking evaporation. But for presently evaporating primordial black holes, radiation accretion and Hawking evaporation terms are dominant over the phantom accretion term and hence presently evaporating primordial black holes are not much affected by phantom accretion.     

Static Axially Symmetric Models and Structure Scalars in Self-Interacting Brans–Dicke Gravity

This paper investigates static axially symmetric models in self-interacting Brans–Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi identities and construct structure scalars. Using these scalars and evolution equations, the inhomogeneity factors of the system are evaluated. It is found that structure scalars related to double dual of Riemann tensor control the density inhomogeneity.Finally, we obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models. It turns out that homogenous solutions reduce to Schwarzschild type interior solutions for a spherical case. We conclude that homogenous models involve homogenous distribution of scalar field whereas inhomogeneous correspond to inhomogeneous scalar field.     

Axially Symmetric Space-Time with Strange Quark Matter Attached to String Cloud in Brans–Dicke Theory of Gravitation

The axially symmetric space times with strange quark matter attached to string cloud in Brans–Dicke theory of gravitation and general relativity have been studied. The field equations of the two theories have been solved by using the anisotropy feature of the universe in the axially symmetric space time. Some important features of the models, thus obtained, have been discussed. We noticed that the presence of scalar field doesn’t affect the geometry of the space-time but changes the matter distribution.     

Bianchi Type-II, VIII & IX Cosmological Models with Strange Quark Matter Attached to String Cloud in Brans–Dicke and General Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi type-II, VIII & IX cosmological models with strange quark matter attached to string cloud in Brans and Dicke (Phys. Rev. C 71:054905, 1961) scalar tensor theory and general theory of gravitation. Some important features of the models, thus obtained, have been discussed. We noticed that these universes always expand isotropically and the presence of scalar field doesn’t affect the geometry of the space-time but changes the matter distribution.     

Energy–Momentum Tensor in the Relativistic Theory of Gravity

It has been shown that the following modification of the symmetric (Gilbert) total energy–momentum tensor (EMT) density \({t^{\mu v}} \to {t^{\mu v}} - \frac{{{m^2}}}{{16\pi G}}{\tilde \varphi ^{\mu v}}\) leads to incorrect results in basic energetic calculations. It is pointed out that some attempts to prove the positive definiteness of the gravitational radiation flux in the RTG are based on the nonconservative energy–momentum tensor.     

Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's

We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.     

On Dark Energy,Weyl’s Geometry,Different Derivations of the Vacuum Energy Density and the Pioneer Anomaly

Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the (Anti) de Sitter solutions in terms of a family of radial functions R(r) that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared (UV/IR) entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of is derived in agreement with the experimental observations. A correct lower estimate of the mass of the observable universe related to the Dirac–Eddington–Weyl’s large number N = 10⁸⁰ is also obtained. The presence of the radial function R(r) is instrumental to understand why the cosmological constant is not zero and why it is so tiny. Finally, we rigorously prove why the proper use of Weyl’s Geometry within the context of Friedman–Lemaitre–Robertson–Walker cosmological models can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan–Brans–Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. The full theory involving the dynamics of Weyl’s gauge field A_μ is very rich and may explain also the anomalous Pioneer acceleration and the temporal variations (over cosmological scales) of the fundamental constants resulting from the expansion of the Universe. This is consistent with Dirac’s old idea of the plausible variation of the physical constants but with the advantage that it is not necessary to invoke extra dimensions. Dedicated to the loving memory of Rachael Bowers.