Constraining extended theories of gravity using Solar System tests

Solar System tests give nowadays constraints on the estimated value of the cosmological constant, which can be accurately derived from different experiments regarding gravitational redshift, light deflection, gravitational time-delay and geodesic precession. Assuming that each reasonable theory of gravitation should satisfy Solar System tests, we use these limits on the estimated value of the cosmological constant to constrain extended theories of Gravity, which are nowadays studied as possible theories for cosmological models and provide viable solutions to the cosmological constant problem and the explanation of the present acceleration of the Universe. We obtain that the estimated values, from Solar System tests, for the parameters appearing in the extended theories of Gravity are orders of magnitude bigger than the values obtained in the framework of cosmologically relevant theories.     

The cosmological term,compensation and singularities

The necessity for the cosmological term in the Einstein and other theories of gravitation is emphasized; in these theories a “compensation” interpretation of the gravitational field as a calibration field is of fundamental importance and it leads, in particular, to torsion and nonlinearities for spinor and other fields. In conjunction with these ideas, the importance of allowing for exposed singularities is pointed out and their analogy with the latest elementary particle models is stressed.     

Effect of the Earth's gravitational field on the detection of gravitational waves

We consider the laboratory detection of high-frequency gravitational waves in theories of gravitation based on a pseudo-Euclidean space-time. We analyze the effects due to the Earth's gravitational field on the propagation velocities of gravitational and electromagnetic waves in these theories. Experiments to test the predictions of this class of theories are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, 93–98, November, 1987.Finally, the authors thank A. A. Logunov for interest in the work.     

Conformal cosmological model and SNe Ia data

Now there is a huge scientific activity in astrophysical studies and cosmological ones in particular. Cosmology transforms from a pure theoretical branch of science into an observational one. All the cosmological models have to pass observational tests. The supernovae type Ia (SNe Ia) test is among the most important ones. If one applies the test to determine parameters of the standard Friedmann-Robertson-Walker cosmological model one can conclude that observations lead to the discovery of the dominance of the ?? term and as a result to an acceleration of the Universe. However, there are big mysteries connected with an origin and an essence of dark matter (DM) and the ?? term or dark energy (DE). Alternative theories of gravitation are treated as a possible solution of DM and DE puzzles. The conformal cosmological approach is one of possible alternatives to the standard ??CDM model. As it was noted several years ago, in the framework of the conformal cosmological approach an introduction of a rigid matter can explain observational data without ?? term (or dark energy). We confirm the claim with much larger set of observational data.     

Exploring the expansion history of the universe

Exploring the recent expansion history of the universe promises insights into the cosmological model, the nature of dark energy, and potentially clues to high energy physics theories and gravitation. We examine the extent to which precision distance-redshift observations can map out the history, including the acceleration-deceleration transition, and the components and equations of state of the energy density. We consider the ability to distinguish between various dynamical scalar field models for the dark energy, as well as higher dimension and alternate gravity theories. Finally, we present a new, advantageous parametrization for the study of dark energy.     

New cosmological models in the framework of a gauge theory of gravity

The paper is devoted to the presentation of the new cosmological solutions obtained by the author within the framework of a gauge theory of gravitation. The models are a combination of evolving models and steady-state models.     

The cosmological principle and a generalization of Newton's theory of gravitation

Using the notion of Galilei manifolds a geometric formulation of the cosmological principle for the prerelativistic theory of gravitation is presented. This is applied to a generalization of the Newton-Cartan theory which admits solutions with a curved Galilei structure. Furthermore, the limit relation between this theory and some relativistic theories is discussed.     

On the uniqueness of the Newtonian theory as a geometric theory of gravitation

A study is made of geometric theories of gravitation that are consistent with the local validity of Newtonian dynamics. This involves an analysis of the representations of the Galilean group provided by the curvature tensor of a Newtonian spacetime, and by the contravariant mass-momentum tensor. Subject to certain assumptions that are made also in the foundations of general relativity, it is shown that there exists essentially only one such theory that does not place unacceptable restrictions on the mass density of the source. This is the Newtonian theory, generalized by a cosmological term. Any other theory is weaker and is given by a subset of the geometrical equations of the Newtonian theory.     

Nonstationary Cosmological Models with Rotation

Two nonstationary cosmological models with rotation are constructed for the Bianchi II metric within the Einstein gravitation theory. The first model is filled with a co-moving perfect liquid and radiation field and is characterized by nonzero expansion, rotation, and acceleration. A perfect liquid which is not co-moving with a reference system is a source of gravitation for the second model. The second model corresponds to nonzero rotations and accelerations.     

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.     

A bimetric machian approach to gravitation

We propose a bimetric machian approach to gravitation with a mathematical structure much simpler than the one of Rosen's bimetric theories. We obtain two cosmological models based on the simplest assumption that the Universe be filled of pure dust matter. One of the two cosmological models is compatible with the currently observed value of the density of dust matter, and provides an age of the Universe which is of the order of the inverse of the present Hubble parameter. One also obtains the Schwarzschild-like solution and its Newtonian limit together with the modified three Kepler laws which allow us to find that presently 0.5×10^?10 (yr)^?1 δ(A/A)δ 0.625×10^?10 (yr)^?1, a denoting the semimajor axis of the orbit of the test particle. Lastly we obtain the Newtonian limit of the theory.     

Bianchi Types II, VIII and IX String Cosmological Models with Bulk Viscosity in Brans-Dicke Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi types II, VIII and IX string cosmological models with bulk viscosity in a scalar tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). It is observed that in case of Bianchi type-IX universe, only bulk viscous cosmological model exists. Some physical and geometrical properties of the models are also discussed.     

Is a cosmological substratum compatible with relativity?

A cosmological substratum for energy propagation is defined in terms of a hypothesis by McCrea. It has been shown that the assumption of such a substratum for a uniformly expanding universe provides a cosmological interpretation of Special Relativity, and leads further to a theory of gravitation in terms of a universal acceleration field. Following a critical discussion of the bases of General Relativity, it is suggested that the proposed substratum model and its consequences are also compatible with the General Relativistic approach, providing that this is applied in a manner which recognises the centrally directed character of gravitational fields, and hence employs harmonic coordinates as proposed by Fock. It is shown that Fock's procedure leads to results which are consistent with the assumption of a uniformly expanding cosmological substratum. Finally, it is suggested that the cosmological substratum concept is also implied by the formulation of the Robertson-Walker metric.     

Induction of strong gravitation and the heirarchical structure of the universe

A nontraditional approach to strong gravitation is proposed from the position of induced gravitation. Induction of strong gravitation constants and a strong gravitation “cosmological term” due to quantum effects in curved space is considered. The relationship between induced gravitation and the concept of a heirarchical structure of the universe is studied.     

Some cosmological models in the bimetric theory of gravitation

It is shown that the field equations of the bimetric theory of gravitation have solutions corresponding to a class of homogeneous isotropic cosmological models with negative spatial curvature (k=–1). Some examples are given.     

Some Anisotropic Homogeneous Cosmological Models in Self-creation Cosmology

The paper presents an exact solution of cylindrically symmetric cosmological models which are of Petrov type-I or Petov type-D in Barber’s second self-creation theory of gravitation. Some physical and geometrical properties of these models are also discussed.     

On Treder-Type Tetrad Theories of Gravitation I. Equivalence Principle and Invariance Properties

The Principle of relativity and the equivalence principle are the most important foundation of any theory of gravitation. We can formulate these principles by the help of the LORENTZ and the EINSTEIN groups. If we start with an action functional, the demand of invariance of this action with respect to these groups makes possible to get detailed conclusions about the general structure of theories of gravitation. EINSTEIN'S idea, to interpret gravitation as deformation of the local inertial systems of the special theory of relativity, leads to bi-tetrad theories, which we call TREDER-type tetrad theories. In this theories a sufficient number of gauge parameters is introduced in order to ensure the invariance of the action functional without limitations for the field variables.     

Equations of motion in Rosen's bimetric theory of gravitation

The paper contains an investigation of Rosen's bimetric theory of gravitation in the case of slow velocities and weak fields. Newtonian and post-Newtonian approximations are obtained. The post-Newtonian equation of motion is integrated for an insular system of spherical bodies that move translationally at large mutual distances. It appears that the post-Newtonian law of motion obtained in this way contains terms that depend on the self-energy of the test body (a self-influence phenomenon). It is proved that also in the Einsteinian gravitation this influence is present, but it can be canceled out from the post-Newtonian law of motion if one takes into account the de Donder conditions. The self-influence discovered here seems to be a general gravitation phenomenon, which usually appears in theories of gravitation in the post-Newtonian approximation.     

Are f(R) dark energy models cosmologically viable?

All f(R) modified gravity theories are conformally identical to models of quintessence in which matter is coupled to dark energy with a strong coupling. This coupling induces a cosmological evolution radically different from standard cosmology. We find that, in all f(R) theories where a power of R is dominant at large or small R (which include most of those proposed so far in the literature), the scale factor during the matter phase grows as t(1/2) instead of the standard law t(2/3). This behavior is grossly inconsistent with cosmological observations (e.g., Wilkinson Microwave Anisotropy Probe), thereby ruling out these models even if they pass the supernovae test and can escape the local gravity constraints.