Can Inflation, Dark Matter and Dark Energy Be Described in Terms of a Single, Real Scalar Field?

In this article, our aim is to consider inflation, dark energy and dark matter in the framework of a real scalar field. To this end, we use the quintessence approach. We have tried a real scalar field with a specific self-interaction potential in a spacially flat universe. Numerical results indicate that this potential can drive the expansion of the universe in three distinct phases. The first phase behaves as an inflationary expansion. For this stage, setting the scalar field’s initial value to ϕ ₀≥1.94 leads to N 3 68\mathcal{N}\geq 68 favored by observation. After the inflationary phase, the scalar field starts an oscillatory behavior which averages to a =0\bar{w}=0 fluid. This stage can be taken as a cold dark matter (p≈0) epoch expected from works on the structure formation issue. Observations and cosmological models indicate that t _inf ≈10⁻³⁵ s and the matter dominated lasts for t _m ≈10¹⁷ s, hence (\fract_mt_inf)_obs ? 10⁵²(\frac{t_{m}}{t_{inf}})_{obs}\approx10^{52}. We have shown that the present model can satisfy such a constraint. Finally, the scalar field leaves the oscillatory behavior and once again enters a second inflationary stage which can be identified with the recent accelerated expansion of the universe. We have also compared our model with the ΛCDM model and have found a very good agreement between the equation of state parameter of both of models during the DM and DE era.     

Energy and critical ionic-bond parameter of a 3D large-radius bipolaron

A theory of a strong-coupling large-radius bipolaron has been developed. The possibility of the formation of 3D bipolarons in high-temperature superconductors is discussed. For the bipolaron energy, the lowest variational estimate has been obtained at α > 8, where α is the electron-phonon coupling constant. The critical ionic-bond parameter η _c = ɛ_∞/ɛ₀, where ɛ_∞ and ɛ₀ are the high-frequency and static dielectric constants, has been found to be η _c = 0.2496.     

Slow Motion of Charges¶Interacting Through the Maxwell Field

We study the Abraham model for N charges interacting with the Maxwell field. On the scale of the charge diameter, R _ϕ, the charges are a distance ɛ^-1 R _ϕ apart and have a velocity with ɛ a small dimensionless parameter. We follow the motion of the charges over times of the order ɛ^-3/2 R _ϕ/c and prove that on this time scale their motion is well approximated by the Darwin Lagrangian. The mass is renormalized. The interaction is dominated by the instantaneous Coulomb forces, which are of the order ɛ². The magnetic fields and first order retardation generate the Darwin correction of the order ɛ³. Radiation damping would be of the order ɛ^7/2. Received: 13 January 2000 / Accepted: 4 February 2000     

Perfect fluid bianchi Type-I cosmological models with time varying <Emphasis Type="Italic">G</Emphasis> and Λ

Bianchi Type-I cosmological models containing perfect fluid with time varying G and Λ have been presented. The solutions obtained represent an expansion scalar θ bearing a constant ratio to the anisotropy in the direction of space-like unit vector λ ⁱ . Of the two models obtained, one has negative vacuum energy density, which decays numerically. In this model, we obtain Λ ∼ H ², Λ ∼ R ₄₄/R and Λ ∼ T ⁻² (T is the cosmic time) which is in accordance with the main dynamical laws for the decay of Λ. The second model reduces to a static solution with repulsive gravity.      

Dynamics of Multiple Scalar Fields Model of Dark Energy with Spatial Curvature

The dynamical system of multiple scalar fields in FRW universe with different spatial curvature have been analyzed in this paper. In the radiation-dominated phase, the constant curvature factor k does not work on the cosmic dynamical behaviors, including the scaling solution, energy density parameter and equation-of-state parameter. These aspects are affected by curvature factor k in the matter-dominated phase. In the special scalar field-dominated phase, the energy density parameter normalization restricts the Universe is spatial flat and the curvature factor k is not present in the dynamics. In this paper, the Universe is closed in the matter-dominated phase, and flat in the scalar field-dominated phase. The spatial flatness and the w _ϕ =−1 in the third phase are coincide with the current observations.     

The cosmological constant revisited

I briefly review the observational evidence for a small cosmological constant at the present epoch. This evidence mainly comes from high redshift observations of Type 1a supernovae, which, when combined with CMB observations strongly support a flat Universe with Ω _m + Ω_A ⋍ 1. Theoretically a cosmological constant can arise from zero point vacuum fluctuations. In addition ultra-light scalar fields could also give rise to a Universe which is accelerating driven by a time dependent Λ-term induced by the scalar field potential. Finally a Λ dominated Universe also finds support from observations of galaxy clustering and the age of the Universe.     

Pauli Operator and Aharonov–Casher Theorem¶ for Measure Valued Magnetic Fields

We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual A∈L ² _loc condition on the vector potential, which does not allow to consider such singular fields. We extend the Aharonov–Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation. One of the key technical tools is a weighted L ² estimate on a singular integral operator. Received: 14 May 2001 / Accepted: 5 September 2001     

Effect of ionizing radiation on the dielectric characteristics of TlInSe<Subscript>2</Subscript> and TlGaTe<Subscript>2</Subscript> single crystals

The temperature dependences of the electrical conductivity and the permittivity of TlInSe₂ and TlGaTe₂ crystals unirradiated and irradiated with 4-MeV electrons at a doze of 10¹⁶ cm⁻² have been investigated. It has been established that electron irradiation leads to a decrease in the electrical conductivity σ and the permittivity ɛ over the entire temperature range under study (90–320 K). It has been revealed that the TlInSe₂ and TlGaTe₂ single crystals undergo a sequence of phase transitions characteristic of crystals of this type, which manifest themselves as anomalies in the temperature dependences σ = f(T) and ɛ = f(T). Electron irradiation at a doze of 10¹⁶ cm⁻² does not affect the phase transition temperatures of the crystals under investigation.     

Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m₀ and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN ²〉/V on the particle mass m₀ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym ₀c² is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_BT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N _v〉/V but also the mean square fluctuation 〈Δ _v ² 〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino massm _v instead of the actual massm _0v .     

A Cyclic Model of Universe with Energy Exchange between Radiation,Matter and Vacuum Energy

We further extend the cosmological scenario with energy exchange by Barrow and Clifton and our previous work to the more complex case with energy exchange between three fluids: radiation, matter and vacuum energy. By prescribing the form of energy exchange function, we construct an infinitely cyclic cosmological model, in which the universe undergoes an endless sequence of cosmic epoch and each consisting of expansion and contraction, and the cosmological parameters, such as the Hubble parameter H, deceleration parameter q, transition red-shift Z _T, and densities ρ _r ,ρ _m , and ρ _Λ are consistent with the present observed values.     

Global strings in extra dimensions: The full map of solutions,matter trapping,and the hierarchy problem

We consider (d ₀ + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d ₀ dimensions, endowed with a warp factor e ^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l _c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough distances l _c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane, where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems. The text was submitted by the authors in English.     

Casimir effects near the big rip singularity in viscous cosmology

Analytical properties of the scalar expansion in the cosmic fluid are investigated, especially near the future singularity, when the fluid possesses a constant bulk viscosity ζ. In addition, we assume that there is a Casimir-induced term in the fluid’s energy-momentum tensor, in such a way that the Casimir contributions to the energy density and pressure are both proportional to 1/a ⁴, a being the scale factor. A series expansion is worked out for the scalar expansion under the condition that the Casimir influence is small. Close to the Big Rip singularity the Casimir term has however to fade away and we obtain the same singular behavior for the scalar expansion, the scale factor, and the energy density, as in the Casimir-free viscous case.     

Hydrodynamic vacuum sources of dark matter self-generation in an accelerating universe without a Big Bang

We have obtained a generalization of the hydrodynamic theory of vacuum in the context of general relativity. While retaining the Lagrangian character of general relativity, the new theory provides a natural alternative to the view that the singularity is inevitable in general relativity and the theory of a hot Universe. We show that the macroscopic source-sink motion as a whole of ordinary (dark) matter that emerges during the production of particles out of the vacuum can be a new source of gravitational vacuum polarization (determining the variability of the cosmological term in general relativity). We have removed the well-known problems of the cosmological constant by refining the physical nature of dark energy associated precisely with this hydrodynamically initiated variability of the vacuum energy density. A new exact solution of the modified general relativity equations that contains no free (fitting) parameter additional to those available in general relativity has been obtained. It corresponds to the continuous and metric-affecting production of ultralight dark matter particles (with mass m ₀ = (ħ/c ²) $ \sqrt {12\rho _0 k} $ \sqrt {12\rho _0 k} ≈ 3 × 10⁻⁶⁶ g, k is the gravitational constant) out of the vacuum, with its density ρ₀, constant during the exponential expansion of a spatially flat Universe, being retained. This solution is shown to be stable in the regime of cosmological expansion in the time interval −∞ < t < t _max, when t = 0 corresponds to the present epoch and t _max= 2/3H ₀ cΩ_0m ≈ 38 × 10⁹ yr at Ω_0m = ρ₀/ρ_c ≈ 0.28 (H ₀ is the Hubble constant, ρ_c is the critical density). For t > t _max, the solution becomes exponentially unstable and characterizes the inverse process of dark matter particle absorption by the vacuum in the regime of contraction of the Universe. We consider the admissibility of the fact that scalar massive photon pairs can be these dark matter particles. Good quantitative agreement of this exact solution with the cosmological observations of SnIa, SDSS-BAO, and the decrease in the acceleration of the expansion of the Universe has been obtained.     

The Distance Modulus Determined from Carmeli’s Cosmology Fits the Accelerating Universe Data of the High-redshift Type Ia Supernovae Without Dark Matter

The velocity of the Hubble expansion has been added to General Relativity by Moshe Carmeli and this resulted in new equations of motion for the expanding universe. For the first time the observational magnitude–redshift data derived from the high-z supernova teams has been analysed in the framework of the Carmeli theory and the fit to that theory is achieved without the inclusion of any dark matter. Best fits to the data yield an averaged matter density for the universe at the present epoch Ω_m ≈ 0.021, which falls well within the measured values of the baryonic matter density. And the best estimate of Ω_Λ+ Ω_m ≈ 1.021 at the present epoch. The analysis also clearly distinguishes that the Hubble expansion of the universe is speed-limited.     

Bianchi Type V Universe Models with Specific Expansion Anisotropy

We investigate Bianchi type V cosmological models for perfect fluid source with time varying cosmological term Λ. We examine the possibility of cosmological models assuming the expansion anisotropy (the ratio σ/θ of the shear scalar σ to the volume expansion θ) to be a function of average scale factor R. The resulting models begin with initial anisotropy and approach isotropy at late times. Our models present an initial epoch with decelerating expansion followed by late time acceleration consistent with observations.     

Magnetized Bianchi Type III Massive String Cosmological Models in General Relativity

The present study deals with Bianchi type III string cosmological models with magnetic field. The magnetic field is assumed to be along z direction. Therefore F ₁₂ is only the non-vanishing component of electromagnetic field tensor F _ij . The expansion (θ) in the model is assumed to be proportional to the shear (σ). To get determinate solution in term of cosmic time, we have solved the fields equations in two cases (i) Reddy and (ii) Nambu string. The physical and geometrical behaviour of these models is discussed.     

The influence of a magnetic field on the inelastic properties of LiF crystals

The effect of weak magnetic fields (0.1–0.8 T) on the internal friction and Young’s-modulus defect of LiF crystals is investigated over a range of relative strain amplitudes ɛ ₀ from 10⁻⁶ to 10⁻⁴ at frequencies of 40 and 80 kHz. Experiments with these fields show that the internal friction increases and the effective elastic modulus decreases, indicating an increase in the plasticity of the samples. Plots are obtained of the internal friction versus the magnitude of the magnetic field at various values of the strain amplitude ɛ ₀. Fiz. Tverd. Tela (St. Petersburg) 41, 1035–1040 (June 1999)     

Discrete Spectrum of the Deficit Angle and the Differential Structure of a Cosmic String

Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior of the cosmic string space-time and that they loose this property at the singular boundary except for the cosmic string space-times with the following deficit angles: Δ=2π(1−1/n), n=1,2,… . A connection between smoothness of fields at the conical singularity and the scalar and electromagnetic conical bremsstrahlung is discussed. It is also argued that the smoothness assumption of fields at the singularity is equivalent to the Aliev and Gal’tsov “quantization” condition leading to the above mentioned discrete spectrum of the deficit angle.     

Unraveling the f<Subscript>0</Subscript> nature by connecting KLOE and BABAR data through analyticity

We define a general procedure, based on analyticity and dispersion relations, to estimate low-energy amplitudes for processes like: φ→e ⁺ e ^- M and φ→γM, starting from cross-section data on e ⁺ e ^-→φM, where M is a generic light scalar or pseudoscalar meson. In particular this procedure is constructed to obtain predictions on the radiative decay rate which are crucially linked on the assumed quark structure for the meson M under consideration. Three cases are analyzed: M = η, M = f ₀(qˉ) and M = f ₀(qqˉ). While in the η case the estimate of the branching fraction for the radiative decay φ→ηγ is in agreement with the data, in the case of f ₀, such agreement is obtained only under the hypothesis of a tetraquark scalar meson.