Time Variation of Cosmic and Quantum Masses in Dirac’s Cosmology

It is shown that the expressions of five fundamental masses appearing in physics and cosmology can be written in terms of the constants of nature. We study the time variation of them in the context of a generalized Dirac’s cosmology based on the large number hypothesis (LNH). This generalization allows one to have the gravitational constant not depending upon time contrary to Dirac’s original theory. It also allows the rest mass of the particle to vary with cosmological time. Further, we show that there exist simple algebraic relations between them and that their ratios can be expressed as powers of the large dimensionless number 10⁴⁰.     

Cosmological models with generalised gravitational and cosmological constants

We consider cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einstein’s theory. A general method of solving the field equations is given. We study here the exact solutions for negative pressure models satisfying G=G ₀(R/R ₀) ⁿ .     

Quintessence cosmology with a traversable wormhole,massive decaying gravitons and with varying <Emphasis Type="Italic">G</Emphasis> and <Emphasis Type="Italic">Λ</Emphasis>

In this work, we explore many cosmological implications of a four-dimensional cosmology dominated by quintessence with a static traversable wormhole, spatio-temporal varying G and by taking into account a decaying cosmological constant and a decaying graviton mass by means of an additional bimetric tensor in Einstein’s field equations proposed by Visser in 1998.     

New agegraphic dark energy in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

In this paper, we study a cosmological application of the new agegraphic dark energy density in the f(R) gravity framework. We employ the new agegraphic model of dark energy to obtain the equation of state for the new agegraphic energy density in a spatially flat universe. Our calculations show, taking n<0, that it is possible to have w _Λ crossing −1. This implies that one can generate a phantom-like equation of state from a new agegraphic dark energy model in a flat universe in the modified gravity cosmology framework. Also, we develop a reconstruction scheme for the modified gravity with f(R) action.     

Physical constants and evolution of the Universe

A cosmological model is discussed which is based on interpretation of the red shift by decrease of the light speed with time everywhere in the Universe beginning with a certain moment of time in the past. The model is described by a metric in which the light speed depends on time and the radius of the curvature of three-dimensional space remains constant (c-metric). It is shown that this metric leads to the same observed facts and formulas of different characteristics that the metric of standard cosmology does but with essentially different physical interpretation. Such a property is the consequence of conformity of spaces being defined by both metrics. The agreement with the fundamental physics laws is achieved by introducing the evolution of a number of other fundamental constants synchronously with the variation of the light speed. The model considered connected the evolution of the Universe with evolution of physical constants and permits explaining some unclear cosmological phenomena — for example, a high isotropy of the relict background and superluminal speed in quasars.     

The number of information bits related to the minimum quantum and gravitational masses in a vacuum dominated universe

Wesson obtained a limit on quantum and gravitational mass in the universe by combining the cosmological constant Λ, Planck’s constant ?, the speed of light c, and also the gravitational constant G. The corresponding masses are 2.0×10^?62 kg and 2.3×10⁵⁴ kg respectively, and in general can be obtained with the help of a generic dimensional analysis, or from an analysis where the cosmological constant appears in a four dimensional space-time and as a result of a higher dimensional reduction. In this paper our goal is to establish a relation for both quantum and gravitational mass as function of the information number bit N. For this reason, we first derive an expression for the cosmological constant as a function of information bit, since both masses depend on it, and then various resulting relations are explored, in relation to information number of bits N. Fractional information bits imply no information extraction is possible. We see, that the order of magnitude of the various parameters as well as their ratios involve the large number 10¹²², that is produced naturally from the fundamental parameters of modern cosmology. Finally, we propose that in a complete quantum gravity theory the idea of information the might have to be included, with the quantum bits of information (q-bits) as one of its fundamental parameters, resulting thus to a more complete understanding of the universe, its laws, and its evolution.     

From Big to Little Rip in modified F(R,G) gravity

We discuss the cosmological reconstruction in modified Gauss-Bonnet (GB) gravity. It is demonstrated that the modified GB gravity may describe the most interesting features of late-time cosmology. We derive explicit form of effective phantom cosmological models ending by the finite-time future singularity (Big Rip) and without singularities in the future (Little Rip).     

Testing Bekenstein's relativistic Modified Newtonian Dynamics with lensing data

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specifically tensor–vector–scalar (TeVeS) theory, a theory which is consistent with fundamental relativistic principles and the phenomenology of Modified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we analytically derive the deflection angle for the point lens and the Hernquist galaxy profile, and study their patterns in convergence, shear and amplification. Applying our analytical lensing models, we fit galaxy-quasar lenses in the CfA-Arizona Space Telescope Lens Survey (CASTLES) sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all the cases, we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy μ function provides more efficient lensing than the standard MOND μ function. But for a handful of lenses, a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function μ and modification scale a ₀ for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND μ function. We also show that the simplest TeVeS 'minimal-matter' cosmology, a baryonic universe with a cosmological constant, can fit the distance–redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity.     

Why Newtonian gravity is reliable in large-scale cosmological simulations

Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.     

Revisiting the coincidence problem in f(R) gravitation

The energy densities of dark matter (DM) and dark energy (DE) are of the same order at the present epoch despite the fact that both these quantities have contrasting characteristics and are presumed to have evolved distinctively with cosmic evolution. This is a major issue in standard ΛCDM cosmology and is termed “The Coincidence Problem” which hitherto cannot be explained by any fundamental theory. In this spirit, Bisabr (2010) reported a cosmological scenario in f(R) gravity where DM and DE interact and exchange energy with each other and therefore evolve dependently. We investigate the efficiency and model independancy of the technique reported in Bisabr (2010) in addressing the Coincidence problem with the help of two f(R) gravity models with model parameters constrained from various observations. Our result confirm the idea that not all scalar-tensor gravity theories and models can circumvent the Coincidence Problem and any cosmological scenario with interacting fluids is highly model dependent and hence alternate model independent theories and ideas should be nominated to solve this mystery.     

Cosmology of f(T) gravity in a holographic dark energy and nonisotropic background

It is shown that the acceleration of the universe can be understood by considering a f(T) gravity models. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. For these f(T) gravity models, a variant of the accelerating cosmology reconstruction program is developed. We consider spatially homogenous and anisotropic Bianchi type I universe in the context of f(T) gravity. The de Sitter, power-law and general exponential solutions are assumed for the scale factor in each spatial direction and the corresponding cosmological models are reconstructed. We reconstruct f(T) theories from two different holographic dark energy models in different time durations. For the holographic dark energy model, the dark energy dominated era with new setting up is chosen for reconstruction, and the Ricci dark energy model, radiation, matter and dark energy dominated time durations are all investigated. Finally we have obtained a modified gravity action consistent with the holographic dark energy scenario.     

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical G and Λ. We take a non-scale invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of G and Λ. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach’s cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach’s cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as ρ∼a ⁻⁴. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.     

Modified equations in the theory of induced gravity. Solution to the cosmological constant problem

This research is an extension of the author’s works, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein’s theory of gravity and string theory. This work is devoted to the formation of self-consistent equations of the theory of induced gravity in the presence of matter in the form of a perfect fluid that interacts with scalar fields. The study is done to solve these equations for the case of the cosmological model. In this model time-evolving gravitational and cosmological “constants” take place which are determined by the square of scalar fields. The values of which can be matched with the observational data. The equations that describe the theory have solutions that can both match with the solutions of the standard theory of gravity as well as it can differ from it. This is due to the fact that the fundamental “constants” of the theory, such as gravitational and cosmological, can evolve over time and also depend of the coordinates. Thus, in a rather general case the theory describes the two systems (stages): Einstein and “evolving”. This process is similar to the phenomenon of phase transition, where the different phases (Einstein gravity system, but with different constants) transit into each other.     

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (“quintessence”) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi V, VII₀ and IX, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive at the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.     

Universality of the self gravitational potential energy of any fundamental particle

Using the relation proposed by Weinberg in 1972, combining quantum and cosmological parameters, we prove that the self gravitational potential energy of any fundamental particle is a quantum, with physical properties independent of the mass of the particle. It is a universal quantum of gravitational energy, and its physical properties depend only on the cosmological scale factor R and the physical constants ℏ and c. We propose a modification of the Weinberg’s relation, keeping the same numerical value, but substituting the cosmological parameter H/c by 1/R.     

Exact self-similar Bianchi II solutions for some scalar-tensor theories

We study how may behave the gravitational and the cosmological “constants”, (G and Λ) in several scalar-tensor theories with Bianchi II symmetries. By working under the hypothesis of self-similarity we find exact solutions for three different theoretical models, which are: the Jordan-Brans-Dicke (JBD) with Λ(?), the usual JBD model with potential U(?) (that mimics the behavior of Λ(?)) and the induced gravity (IG) model proposed by Sakharov and Zee. After a careful study of the obtained solutions we may conclude that the solutions are quite similar although the IG model shows some peculiarities.     

Magnetic Bianchi type II string cosmological model in loop quantum cosmology

The loop quantum cosmology of the Bianchi type II string cosmological model in the presence of a homogeneous magnetic field is studied. We present the effective equations which provide modifications to the classical equations of motion due to quantum effects. The numerical simulations confirm that the big bang singularity is resolved by quantum gravity effects.     

Varying Fundamental Constants from a String-inspired Brane World Model

We report results on the construction of cosmological braneworld models in the context of the Einstein-Gauss-Bonnet gravity, which include the leading correction to the Einstein-Hilbert action suggested by superstring theory. We obtain and study the equations governing the dynamics of the standard cosmological models. We find that they can be written in the same form as in the case of the Randall-Sundrum model but with time-varying four-dimensional gravitational and cosmological constants. Finally, we discuss the cosmological evolution predicted by these models and their compatibility with observational data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cosmic microwave background anisotropy: deviations from Gaussianity caused by non-linear gravity

Non-linear evolution of cosmological energy density fluctuations triggers deviations from Gaussianity in the temperature distribution of the cosmic microwave background. A method to estimate these deviations is proposed. N -body simulations – in a Λ cold dark matter cosmology – are used to simulate the strongly non-linear evolution of cosmological structures. It is proved that these simulations can be combined with the potential approximation to calculate the statistical moments of the cosmic microwave background anisotropies produced by non-linear gravity. Some of these moments are computed and the resulting values are different from those corresponding to Gaussianity.     

Full Causal Bulk Viscous LRS Bianchi I With Time Varying Constants

In this paper we study the evolution of a LRS Bianchi I Universe, filled with a bulk viscous cosmological fluid in the presence of time varying constants “but” taking into account the effects of a c-variable into the curvature tensor. We find that the only physical models are those which “constants” G and c are growing functions on time t, while the cosmological constant Λ is a negative decreasing function. In such solutions the energy density obeys the ultrastiff matter equation of state i.e. ω = 1.