Noether gauge symmetry approach in f(R) gravity

We discuss the f(R) gravity model in which the origin of dark energy is identified as a modification of gravity. The Noether symmetry with gauge term is investigated for the f(R) cosmological model. By utilization of the Noether Gauge Symmetry (NGS) approach, we obtain two exact forms f(R) for which such symmetries exist. Further it is shown that these forms of f(R) are stable.     

Scalar field cosmology in $$ gravity via Noether symmetry

This paper investigates the existence of Noether symmetries of isotropic universe model in \(f(R,T)\) gravity admitting minimal coupling of matter and scalar fields. The scalar field incorporates two dark energy models such as quintessence and phantom models. We determine symmetry generators and corresponding conserved quantities for two particular \(f(R,T)\) models. We also evaluate exact solutions and investigate their physical behavior via different cosmological parameters. For the first model, the graphical behavior of these parameters indicate consistency with recent observations representing accelerated expansion of the universe. For the second model, these parameters identify a transition form accelerated to decelerated expansion of the universe. The potential function is found to be constant for the first model while it becomes \(V(\phi )\approx \phi ^{2}\) for the second model. We conclude that the Noether symmetry generators and corresponding conserved quantities appear in all cases.     

The phase space of quintom cosmology

The properties of quintom model are investigated in the isotropic and homogeneous universe as a dynamical system dominated by dark energy including the phantom and quintessence fields. A general discussion about the phase space of spatially non-flat universe is presented. We study the results for the later times without assuming the specific form of the potential. Then, we exhibit an obvious structure for the dynamics of the system.     

Revisiting Noether gauge symmetry for F(R) theory of gravity

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R ⁿ (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.     

Noether gauge symmetry for f(R) gravity in Palatini formalism

In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe in the context of Palatini f(R) theory of gravity. Using the dynamical equivalence between f(R) gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying Noether gauge symmetry approach for this f(R) Lagrangian we find out the form of f(R) and the exact solution for cosmic scale factor. It is shown that the resulting form of f(R) yield a power-law expansion for the scale factor of the universe.     

A possible symmetry and role for Euclidean space-time in cosmology

In this paper, we consider conservation equation in cosmology and propose four possible forms of space-times for universe resulting from dual symmetry between scale factor and energy density in the universe with constant equation of state. We start to describe these four possible types of space-times for universe and it’s possible consequences. Due to the uniformity of the metric signature in Euclidean space-time, for the first  time, we introduce a new symmetry for Euclidean space-time and consider it as a transition unstable state between the visible 4D universe and the invisible world with an extra dimension. Finally, we schematically represent these four possible space-times in a unique scenario for the universe.     

An empirical approach to cosmology

A two-component model of the universe is proposed, based on the observations of discrete extragalactic sources and the microwave background radiation. The large scale dynamics of the universe is determined by the radiation component and it leads to a characteristic size of the universe 6×10⁵ Mpc and an age 10¹² yr. The second component, that of matter, occurs in discrete sources which group together in super-superclusters of characteristic size 6×10³ Mpc and age 10¹⁰ yr. It is suggested that our Galaxy belongs to one of these super-superclusters and that observations of discrete sources are confined to this unit. A reasonable agreement with the cosmological tests is obtained on the assumption that the geometry within a typical super-supercluster is Euclidean and that the redshifts of galaxies arise from Doppler effect due to motions originating in a local explosion which gave birth to the super-supercluster. Further observational checks on this model are proposed.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation     

An alternative approach to cosmogony and cosmology

Some problems associated with the big bang cosmological model are briefly discussed. It is shown that the quasi-steady state model (QSSC) is a viable alternative. Moreover, the cosmogony related to this theory is supported by the observations.     

Turbulence in cosmology

On the basis of the theory set out in Papers I and II (Marochniket al., 1975a, b), the kinetic equations for the spectra of classical and quantum short-wave turbulences have been obtained, taking account of the influence of the latter on the process of cosmological expansion of a homogeneous and, on average, isotropic Universe. The equilibrium and stationary spectra of the turbulence do not change the form of the cosmological solution found in II. The latter change if the spectra are non-stationary, or if the dissipation is taken into account. It is possible that a situation exists in which the primordial short-wave turbulence, having had a significant influence on the early metric, would not be observable at the present time. Quantum turbulence has been studied. Its influence on the metric may be significant only near the Planckian timet _g.     

Turbulence in cosmology

Principles of the theory of turbulence in relativistic cosmology are developed. By averaging Einstein's equations over stochastic fields a self-consistent system of equations is obtained which describes statistically: (1) the influence of the turbulence on the ‘basic state of the Universe (the background) on which the turbulence develops; (2) the behaviour of the turbulence on the background ‘distorted’ by it. By means of a qualitative study of exact equations in the region of a strong turbulence at an early stage of cosmological expansion conditions of the absence of singularity are found and the possibility of stationary solutions in the homogeneous, isotropic, on the average, Universe (the cosmological constantA=0) is shown. The rate of cosmological expansion increases if the energy density of the turbulence is positive, and decreases if it is negative. The latter alternative takes place if the absolute value of the energy density of excitations, which will change into potential motions in the future, exceeds the energy density of the remaining part of the turbulence.     

Turbulence in cosmology

The influence of short-wave turbulence on the expansion of a homogeneous and, on average, isotropic Universe was studied in Papers I–III. In the present paper we study the influence on the manner of expansion, for a complete spectrum of wavelengths, of scalar, tensor and vector perturbations. Ast»0, all waves become long (greater than the horizon); therefore, a knowledge of their influence on the averaged metric is required. It is shown that the long-wave modes of scalar and tensor perturbations which remain finite ast»0 deflect the metric for a homogeneous and, on average, isotropic Universe from the Friedmannian, giving it a form coinciding with the average quasi-isotropic solution of Lifshitz and Khalatnikov (1963). Ast»0 their contribution to the solution tends to zero. What remains to be determined is the contribution of those modes of scalar, tensor and vector perturbations which diverge ast»0. Att=0 the proposed solution for such modes becomes inapplicable. The behaviour of the metric of a homogeneous and, on average, isotropic Universe under the influence of all waves and all modes of perturbation is shown in Figure 1–3.     

Quark-Hadron transition in cosmology

The present understanding of the cosmological quark-hadron transition is briefly reviewed, trying to outline the physical questions which are related to measurable astrophysical parameters. In particular the possible impact of baryon number inhomogeneities on primeval nucleosynthesis is discussed.     

Symmetry in hierarchical cosmology

An idealized model of a hierarchy of clusters is considered, and the number-count asymmetry measure in two different directions,R ₁ |N ⁺-N ^-|/(N ⁺+N ^-), is evaluated, for values ofl _I /c _I =(distance between cluster centres)/(cluster diameter). Providedl _I /c _I 10, theory predictsR _I 0.1, in agreement with the symmetry of high-redshift radio sources.     

Stiff-matter solitons in cosmology

We study exact solutions of the Einstein field equations of the cylindrical-symmetric Einstein-Rosen type with stiff matter (p=) as a source with development and collisions of solitons associated with the metric and the fluid.Supported by a CONICET fellowship.     

Topological defects in cosmology

Topological defects in cosmology.     

Three-dimensional quantized time in cosmology

Starting from a model of 3-d time in units of the Planck energy, it is possible to model fundamental particles and forces. Masses are associated with 3-d volumes of time; forces are related to 4-d space-time structures from which the fine structure constant can be derived. Fundamental particles may then be assembled into larger objects, up to galaxies, within which special relativity is satisfied. The component parts of an object retain a common quantized temporal structure which appears to link the spatially distributed parts together. The flow of time is associated with a flow of the common temporal structure within a general 3-d temporal space. Each galaxy evolves along a 1-d timeline such that within a given galaxy standard 4-d space-time physics is satisfied. The model deviates from ordinary physics by associating different galaxies with independent timelines within a general 3-d temporal space. These timelines diverge from a common origin and can have different flow rates for different classes of objects. The common origin is consistent with standard cosmology. The radius of temporal space replaces the standard radius of curvature in describing redshifts seen when photons transfer between objects on different timelines. Redshift quantization, discordant redshifts, and other observed cosmological phenomena are natural consequences of this type of model.     

Plane-symmetric vacuum in self-creation cosmology

Vacuum field equations for the static and non-static plane-symmetric metric are obtained in self-creation theory of gravitation proposed by Barber (1982). It is shown that, in both static and non-static cases, the only plane-symmetric solution in vacuum is the empty flat space-time of Einstein's theory. It is observed that this result is quite different from that of the Brans-Dicke and other scalar-tensor theories of gravitation.     

On real-time evolution in cosmology

Real-time evolution plays an important role to understand the dynamics of the early Universe. It would be of importance to be able to investigate such typical time dependent processes like particle production, reheating, creation and evolution of fluctuations, etc. In this paper we derive the one-loop renormalized coupled einstein field equations of a scalar field with λϕ⁴ interaction in a classical curved space-time of Friedmann-Robertson-Walker type. These equations can be used to calculate quantum corrections for the dynamics in the early Universe.     

Particle creation in pre-big-bang cosmology

We present some phenomenological aspects of the pre-big-bang cosmological model inspired by the duality properties of string theory. In particular, assuming the spatial sections of the homogeneous background geometry to be isotropic, we discuss the quantum production of perturbations of the background fields (gravitons, dilatons, moduli fields), as well as the production of particles which do not contribute to the background, which we call “seeds”. As such we consider the cases of electromagnetic and axionic seeds. We also discuss their possible observational consequences, for example, we study whether they can provide the origin of primordial galactic magnetic fields, and whether they can generate the initial fluctuations leading to the formation of large-scale structure and the measured cosmic microwave background anisotropies. We finally analyze axion and photon production in four dimensional anisotropic pre-big-bang cosmological models.     

Dynamical stability in scalar-tensor cosmology

We study FRW cosmology for a double scalar-tensor theory of gravity where two scalar fields are nonminimally coupled to the geometry. In a framework to study stability and attractor solutions of the model in the phase space, we constrain the model parameters with the observational data. For an accelerating universe, the model behaves like quintom dark energy models and predicts a transition from quintessence era to phantom era.