Artificial contradiction between cosmology and particle physics: the Λ problem

It is shown that the usual choice of units obtained by taking G=c=ℏ=1, giving the Planck’s units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with ℏ. We note that the choice of ℏ=1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is ℏ≈1/10¹²², while the choice of ℏ=1 corresponds to the cosmological scale. This is due to the scale factor of 10⁶¹ that converts the Planck scale to the cosmological scale. By choosing the ratio G/c ³=constant=1, which includes the choice G=c=1, and the momentum conservation mc=constant, we preserve the derivation of the Einstein field equations from the action principle. Then the product Gm/c ²=r _g , the gravitational radius of m, is constant. For a quantum black hole we prove that ℏ≈r _g ²≈(mc)². We also prove that the product Λℏ is a general constant of order one, for any scale. The cosmological scale implies Λ≈ℏ≈1, while the Planck scale gives Λ≈1/ℏ≈10¹²². This explains the Λ problem. We get two scales: the cosmological quantum black hole (QBH), size ∼10²⁸ cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size ∼10⁻¹³ cm, as well as the Planck’ scale, size ∼10⁻³³ cm.      

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.     

Anisotropic cosmological model with variable G and Λ

Anisotropic Bianchi-III cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Without assuming any specific forms for Λ and the metric potentials, we have tried to extract the time variation of G and Λ from the anisotropic model. The extracted G and Λ are in conformity with the present day observations. Basing upon the observational limits, the behavior and range of the effective equation of state parameter are discussed.     

Five dimensional universe model with variable cosmological term Λ and a big bounce

We assume the four dimensional induced matter of the 5D Ricci flat bouncing cosmological solution contains a perfect fluid. The big bounce singularity of simple 5D cosmological model is studied with the cosmological term Λ=α ρ and Λ=β H ² where α and β are constants and ρ and H are respectively energy density and Hubble parameter. This big bounce singularity is found to be an event horizon at which the scale factor and mass density of the universe are finite, while the pressure is infinite.      

A new class of bulk viscous universe with time dependent deceleration parameter and Λ-term

A new class of exact solutions of Einstein’s field equations with a bulk viscous fluid for an LRS Bianchi type-Ia obtained by using a time dependent deceleration parameter and cosmological term Λ. The coefficient of bulk viscosity is assumed to be a power function of mass density (ξ=ξ ₀ ρ ⁿ ). We have obtained a general solution of the field equations from which six models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.      

Bulk viscous fluid hypersurface–homogeneous cosmological models with time varying G and Λ

Hypersurface–homogeneous cosmological models containing a bulk viscous fluid with time varying G and Λ have been presented. We have shown that the field equations are solvable for any arbitrary cosmic scale function. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of the energy density. Exact solutions of Einstein’s field equations are obtained which represent an expanding, shearing and accelerating/decelerating models of the universe. The physical and kinematical behaviours of the models are also discussed.     

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 solution of perfect fluid massive string cosmology in Bianchi type?III space-time with decaying vacuum energy density?Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.     

Early Cosmological Models with Bulk Viscosity in Brans-Dicke Theory

The effect of time dependent bulk viscosity on the evolution of Friedmann models with zero curvature in Brans-Dicke theory is studied. The solutions of the field equations with ‘gamma-law’ equation of state p = (γ-1) ρ, where γ varies continuously as the Universe expands, are obtained by using the power-law relation φ = bR ⁿ , which lead to models with constant deceleration parameter. We obtain solutions for the inflationary period and radiation dominated era of the universe. The physical properties of cosmological solutions are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bulk viscous LRS Bianchi-I Universe with variable G and decaying Λ

The present study deals with spatially homogeneous and totally anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with variable G and Λ in presence of imperfect fluid. To get the deterministic model of Universe, we assume that the expansion (θ) in the model is proportional to shear (σ). This condition leads to A=ℓB ⁿ , where A, B are metric potential. The cosmological constant Λ is found to be decreasing function of time and it approaches a small positive value at late time which is supported by recent Supernovae Ia (SN Ia) observations. Also it is evident that the distance modulus curve of derived model matches with observations perfectly.     

Large-scale periodicity in the distribution of QSO absorption-line systems

The spatial-temporal distribution of absorption-line systems (ALSs) observed in QSO spectra within the cosmological redshift interval z=0.0–4.3 is investigated on the base of our updated catalog of absorption systems. We consider so-called metallic systems including basically lines of heavy elements. The sample of the data displays regular variations (with amplitudes ∼15–20%) in the z-distribution of ALSs as well as in the η-distribution, where η is a dimensionless line-of-sight comoving distance, relatively to smoother dependences. The η-distribution reveals the periodicity with period Δη=0.036±0.002, which corresponds to a spatial characteristic scale (108±6)h ⁻¹ Mpc or (alternatively) a temporal interval (350±20)h ⁻¹ Myr for the ΛCDM cosmological model. We discuss the possibility of a spatial interpretation of the results, treating the pattern obtained as a trace of an order imprinted on the galaxy clustering in the early Universe.     

Conformal analogs of the Jordan-Brans-Dicke theory. I.

Recent cosmological observations of large-scale structures (red shift of type Ia supernovae) confirm that the universe is currently expanding at an accelerating rate and its dominant component is dark energy. This has stimulated the development of the theory of gravity and led to many alternative variants, including tensor-scalar ones. This paper deals with the role of conformal transformations in the Jordan-Brans-Dicke theory. Variants of intrinsic, conformally coupled, and Einstein representations are examined. In the Einstein representation an exact analytic solution for the standard cosmological model is obtained. It is expressed in terms of the relative energy contributions of ordinary matter Ω _m , the scalar field Ω _CK , and a term Ω_Λ related to the cosmological constant Λ . Information on the evolution of the universe for the case with a minimally coupled scalar field is given in the form of graphs.     

Oscillating Universe – An Alternative Approach in Cosmology

A new paradigm in cosmology is presented: A geometrical phase transition from the Minkowski space to an anti-deSitter space at its maximum of extension instead of a big bang with inflation. This scenario implies an open universe with a negative cosmological constant which replaces completely the cold dark matter in galaxy clusters. Baryonic matter and radiation are created from the gravitational field over a very long period of about 30 billion years. The contracting universe runs then after a further period of 13 billion years through a minimum with T _max ≃ 1.8 × 10¹² K and a particle density n _max ≃ 5 × 10³⁸ cm^-3 due to Hagedorn’s theory of a hadron gas. After the run through the minimum the universe expands like a big bang universe and reaches due to the negative cosmological constant after 44 billion years its maximal extension. Then it contracts again, and so on: An open ever-oscillating universe.     

Λ Varying Cosmological Models with Viscous Fluid

Evolution of a homogeneous, isotropic Universe with flat geometry filled with a viscous fluid is investigated in presence of a variable cosmological Λ. A non-singular solution leading to a variable deceleration parameter is obtained which reduces to the solution of Murphy in the ‘no Λ limit’ and to the recent solution of Vishwakarma in the context of ‘a Machian model of dark energy’ in the ‘no viscosity’ limit.     

An expanding Universe with constant pressure and no cosmological constant

Thanks to its fitting triumph, the ΛCDM paradigm is assumed to be the most powerful model, for describing the Universe dynamics, over much the myriad of cosmological models. Unfortunately, the quest of a self-consistent model remains not well explained, because it is not clear how to solve the problems of fine-tuning and coincidence, afflicting the ΛCDM framework; as a matter of fact, these theoretical drawbacks do not allow to consider the ΛCDM model, as the final picture of the modern cosmological scenario. Here, we show that the simplest model, which provides a constant equation of state for the pressure, leads to a generalization of ΛCDM, reducing to it in a particular case. Moreover, we highlight the physical mechanisms of this model, describing the thermodynamical reasons why a constant pressure should be negative in an expanding Universe. In addition, we fit the free parameters of our model by minimizing the chi square through the age differential method, involving a direct measurement of H.     

Bianchi type I two-fluid cosmological models with a variable G and Λ

This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.      

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.     

A new class of LRS Bianchi type-II dark energy models with variable EoS parameter

A new class of dark energy models in a Locally Rotationally Symmetric Bianchi type-II (LRS B-II) space-time with variable equation of state (EoS) parameter and constant deceleration parameter have been investigated in the present paper. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter given by Berman: Nuovo Cimento 74:182 (1983) which generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The dark energy EoS parameter ω is found to be time dependent and its existing range for both models is in good agreement with the three recent observations of (i) SNe Ia data (Knop et al.: Astrophys. J. 598:102 (2003)), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al.: Astrophys. J. 606:702 (2004)) and latest (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al.: Astrophys. J. Suppl. 180:225 (2009); Komatsu et al. Astrophys. J. Suppl. 180:330 (2009)). The cosmological constant Λ is found to be a positive decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent supernovae Ia observations. The physical and geometric behaviour of the universe have also been discussed in detail.     

Anisotropic Cosmological Models with a Perfect Fluid and a Λ Term

We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual equation of state, i.e., p = ζ, with ζ ∊ [0, 1] or a van der Waals equation of state. Role of the Λ term in the evolution of the BI Universe has been studied.     

Does the gravitational “constant” increase?

The possibility that the gravitational coupling constantG is an increasing function of the cosmic timet is discussed.In Section 1 the Maximal Power Hypothesis (MPH) stating that no power in Nature can exceed the upper boundc ⁵/G (Gunn's luminosity) is advocated.In Sections 2, 3, and 4 the MPH is employed on the cosmological scale to support the idea of an increasingG. In Section 2 the increasingG is obtained by two assumptions - the MPH and the energy conservation law - and by nothing else.In Section 3 the increasingG follows naturally from the MPH in the Einstein-Cartan theory of gravity. The arguments proposed in Sections 2 and 3 lead todG(t)/dt > 0 but cannot specify the form ofG(t). In Section 4 the MPH is applied to the energy of the vacuum and leads to a relation betweenG and the cosmological term,G S ³, valid in a matter-dominated universe (S =S(t) is the expansion factor). This relation plus the time-dependence law (suggested by many authors) t ² = constant, plustH > 2/3 (suggested by observations on the age of globular clusters;H is the Hubble parameter) implies an increasingG. One finds also GU, whereU is the mass density of the universe, in agreement with other studies.