The tensor-vector-scalar theory and its cosmology

Numerical N -body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore important to understand which degrees of freedom and which features are lost when the relativistic universe is approximated, or rather replaced, by a Newtonian one. This is the main purpose of our investigation. We first define Newtonian cosmology and we give an overview on general relativity, both in its standard and covariant formulations. We show how the two theories deal with inhomogeneous cosmological models and we explain the role that inhomogeneities play in the dynamics of the universe on large scales. We define averaging in cosmology and we introduce the backreaction conjecture. Then we review on how Newtonian gravity and general relativity relate to each other in the fully non-linear regime. For this purpose we discuss frame theory, whose aim is to reconcile Newton's and Einstein's theories under the same formal structure. We carry out the same investigation also in the weak-field, small-velocity limit of general relativity, and we derive the Newtonian limit resorting to the framework of post-Newtonian cosmology. Finally we remark that there are solutions of Newtonian gravity which do not have any relativistic counterpart. This suggests that there are cases in cosmology in which the two theories are irreconcilable and that the reliability of the Newtonian approximation requires further theoretical investigation.

Journal of Modern Physics

Modified Newtonian Dynamics (MoND) is an empirically motivated modification of Newtonian gravity at largest scales, to explain rotation curves of galaxies, as an alternative to nonbaryonic dark matter. But MoND theories can hardly connect to the formalism of relativistic cosmology type Friedmann-Robertson-Walker. Presently work intends the existence of one scalar potential, with non gravitational origin, that would solve these problems. This potential Yukawa type inverse is build starting from a specular reflection of the potential of Yukawa: null in very near solar system, slightly attractiveness in ranges of interstellar distances, very attractiveness in distance ranges comparable to galaxies cluster and repulsive to cosmic scales. The consequences of this potential are discussed, through Cosmological Model Tipe Friedmann-Roberston-Walker with cosmological term in function of the distance (lambda like function of r). In the cosmological model so raised the critical density of matt...

Astronomy and Astrophysics, 2008

Aims. We study cosmological models in scalar tensor theories of gravity with power-law potentials as models of an accelerating universe. Methods. We consider cosmological models in scalar tensor theories of gravity that describe an accelerating universe and study a family of inverse power-law potentials, for which exact solutions of the Einstein equations are known. We also compare theoretical predictions of our models with observations. For this we use the following data: the publicly available catalogs of type Ia supernovae and high redshift gamma ray bursts, the parameters of large-scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS), and measurements of cosmological distances based on the Sunyaev-Zel'dovich effect, among others. Results. We present a class of cosmological models that describe the evolution of a homogeneous and isotropic universe filled with dust-like matter and a scalar field that is non minimally-coupled to gravity. We show that this class of models depends on three parameters: V 0 -the amplitude of the scalar field potential, H 0 -the present value of the Hubble constant, and a real parameter s that determines the overall evolution of the universe. It turns out that these models have a very interesting feature naturally producing an epoch of accelerated expansion. We fix the values of these parameters by comparing predictions of our model with observational data. It turns out that our model is compatible with the presently available observational data.

Phys Rev D, 2008

I consider an extented version of Bekenstein's Tensor-Vector-Scalar theory where the action of the vector field is of a general Einstein-Ether form. This work presents the cosmological equations of this theory, both at the background and perturbed level, for scalar, vector and tensor perturbation modes. By solving the background equations in the radiation era analytically, to an excellent approximation, I construct the primordial adiabatic perturbation for a general family of scalar field kinetic functions.

Classical and Quantum Gravity, 2013

In this paper we lay down the foundations for a purely Newtonian theory of cosmology, valid at scales small compared with the Hubble radius, using only Newtonian point particles acted on by gravity and a possible cosmological term. We describe the cosmological background which is given by an exact solution of the equations of motion in which the particles expand homothetically with their comoving positions constituting a central configuration. We point out, using previous work, that an important class of central configurations are homogeneous and isotropic, thus justifying the usual assumptions of elementary treatments. The scale factor is shown to satisfy the standard Raychaudhuri and Friedmann equations without making any fluid dynamic or continuum approximations. Since we make no commitment as to the identity of the point particles, our results are valid for cold dark matter, galaxies, or clusters of galaxies. In future publications we plan to discuss perturbations of our cosmological background from the point particle viewpoint laid down in this paper and show consistency with much standard theory usually obtained by more complicated and conceptually less clear continuum methods. Apart from its potential use in large scale structure studies, we believe that our approach has great pedagogic advantages over existing elementary treatments of the expanding universe, since it requires no use of general relativity or continuum mechanics but concentrates on the basic physics: Newton's laws for gravitationally interacting particles.

Classical and Quantum Gravity

This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current observational astronomy. Our approach is formulated as a classical Einstein-vector-scalar-Maxwell-fluid field theory on a spacetime with three-sphere spatial sections. Analytic cosmological solutions are found using local charts familiar from standard LFRW cosmological models. These solutions can be used to describe different types of evolution for the metric scale factor, the Hubble, jerk and de-acceleration functions, the scalar spacetime curvature and the Kretschmann invariant constructed from the Riemann-Christoffel spacetime curvature tensor. The cosmological sector of the theory accommodates a particular single big-bang scenario followed by an eternal exponential acceleration of the scale factor. Such a solution does not require an externally prescribed fluid equation of state and leads to a number of new predictions including a current value of the "jerk" parameter, "Hopfian-like" source-free Maxwell field configurations with magnetic helicity and distributional "bi-polar" solutions exhibiting a new charge conjugation symmetry. An approximate scheme for field perturbations about this particular cosmology is explored and its consequences for a thermalisation process and a thermal history are derived, leading to a prediction of the time interval between the big-bang and the decoupling era. Finally it is shown that field couplings exist where both vector and scalar localised linearised perturbations exhibit dispersive wave-packet behaviours. The scalar perturbation may also give rise to Yukawa solutions associated with a massive Klein-Gordon particle. It is argued that the vector and scalar fields may offer candidates for "dark-energy" and "dark-matter" respectively.

Astronomy and Astrophysics, 2006

Aims. To study the possibility of appearance of accelerated universe in scalar tensor cosmological models Methods. We consider scalar tensor theories of gravity assuming that the scalar field is non minimally coupled with gravity. We use this theory to study evolution of a flat homogeneous and isotropic universe.

Physical Review Letters, 2000

The present acceleration of the Universe strongly indicated by recent observational data can be modeled in the scope of a scalar-tensor theory of gravity. We show that it is possible to determine the structure of this theory (the scalar field potential and the functional form of the scalar-gravity coupling) along with the present density of dustlike matter from the following two observable cosmological functions: the luminosity distance and the linear density perturbation in the dustlike matter component as functions of redshift. Explicit results are presented in the first order in the small inverse Brans-Dicke parameter ω −1 .

2007

The non{linear dynamics of self{gravitating collisionless matter with vanishing vorticity is studied in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. Writing the equations in terms of the metric tensor of the spatial sections orthogonal to the uid ow allows an unambiguous expansion in inverse powers of the speed of light. The Newtonian and post{Newtonian approximations are derived in Lagrangian form. A general formula for the gravitational waves generated by the non{linear evolution of cosmological perturbations is given. It is argued that a stochastic gravitational{wave background is produced by non{linear cosmic structures, with present{day closure density gw 10 ?5 { 10 ?6 on the scale of 1 { 10 Mpc. 0

2011

In this paper, I draw the list of weaknesses of the mainstream gravity and cosmology theories. First, the special and general relativity theory are discussed, where the emphasis is on the physical meaning of length contraction, the time expansion and the time delay. Then, the hypothesis of dark matter inside disk galaxies is treated. Since my paper of 2004 [10], this hypothesis has fainted, and I explain the reasons of it. The hypotheses of dark energy, the expanding and the accelerating universe are historically edified upon the big bang hypothesis and I criticize it by using physical objections which lead to obvious alternatives. Also the weakness of the planetary system’s creation theory is physically analyzed. Finally, I explain the evolution process of the modern gravity and cosmology theories and the possible reasons and causes for the increasing alienation from rational thinking.

2015

In this paper, I draw the list of weaknesses of the mainstream gravity and cosmology theories. First, the special and general relativity theory are discussed, where the emphasis is on the physical meaning of length contraction, the time expansion and the time delay. Then, the hypothesis of dark matter inside disk galaxies is treated. Since my paper of 2004 [10], this hypothesis has fainted, and I explain the reasons of it. The hypotheses of dark energy, the expanding and the accelerating universe are historically edified upon the big bang hypothe-sis and I criticize it by using physical objections which lead to obvious alternatives. Also the weakness of the planetary system’s creation theory is physically analyzed. Finally, I explain the evolution process of the modern gravity and cosmology theories and the possible reasons and causes for the increasing alienation from rational thinking. WEAKNESSES IN THE THEORIES

Modern Physics Letters A, 2020

A correspondence between the Equivalence principle and the homogeneity of the universe is discussed. In Newtonian gravity, translation of co-moving coordinates in a uniformly expanding universe defines an accelerated frame. A consistency condition for the invariance of this transformation which requires a well defined transformation for the Newtonian potential, yields the Friedmann equations. All these symmetries are lost when we modify NSL (Newton's Second Law) or the Poisson equation. For example by replacing NSL with non-linear function of the acceleration the concept of relative acceleration is lost and the homogeneity of the universe breaks.

Gravitation and Cosmology

We study the cosmological implications of scalar-tensor theories compatible with solar-system experiments, binary pulsar dynamics, etc. In particular, homogeneous and isotropic cosmological models and the primordial light element production have are computed. We succeed for the first time in constructing a class of scalar-tensor models which predict correct primordial light element abundances allowing for the Universe closure by only baryons. The reason why such predictions have been possible is that the speed-up factor (the ratio between the present-theory Hubble parameter and that obtained in General Relativity) in this class of theories has a non-monotonic time evolution during the primordial nucleosynthesis. These theories have also important consequences on inflation and on the large-scale structure formation.

Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory (Cosmic Defect theory). We show that the latter ¯fits reasonably well the cosmic observed data with only one, or at most two, adjustable parameters, whilst other vector theories use much more. The Newtonian limits are also compared. Finally we show that the CD theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.