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.     

Spectral index and non-Gaussianity in supersymmetric hybrid inflation

We consider a supersymmetric hybrid inflation model with two inflaton fields. The superpotential during inflation is dominated by W=(κS+κ′S′)M ², where S, S′ are inflatons carrying the same U(1) _R charge, κ, κ′ are dimensionless couplings, and M (∼10¹⁵⁻¹⁶ GeV) is a dimensionful parameter associated with a symmetry breaking scale. One light mass eigenstate drives inflation, while the other heavier mass eigenstate is stuck to the origin. The smallness of the lighter inflaton mass for the scalar spectral index n _s ≈0.96, which is the center value of WMAP7, can be controlled by the ratio κ′/κ through the supergravity corrections. We also discuss the possibility of the two field inflation and large non-Gaussianity in this setup.     

An inflationary scenario taking into account of possible dark energy effects in the early universe

We investigate the possible effect of cosmological-constant type dark energy during the inflation period of the early universe. This is accommodated by a new dispersion relation in de Sitter space. The modified inflation model of a minimally coupled scalar field is still able to yield an observation-compatible scale-invariant primordial spectrum, simultaneously having the potential to generate a spectrum with lower power at large scales. A qualitative match to the WMAP 7-year data is presented. We obtain an Ω _Λ of the same order of that in the Λ-CDM model. Possible relations between the de Sitter scenario and Doubly Special Relativity (DSR) are also discussed.     

Exact Scalar Field Inflationary Solution in Rainbow Universe

Using the Friedmann equation in rainbow Universe, we obtain an exact scalar field Inflationary Solution, which is a modification of the exact scalar field with negative potential −V ₀+m ² φ ²/2. Because the rainbow metric is Finsler metric, the result in this paper implies that the research of Finsler geometry in Cosmology should lead to several new physics theories.     

A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

Inflationary scenario in the supersymmetric economical 3-3-1 model

We construct the supersymmetric economical 3-3-1 model which contains inflationary scenario and avoids the monopole puzzle. Based on the spontaneous symmetry breaking pattern (with three steps), the F-term inflation is derived. The slow-roll parameters ∈ and η are calculated. By imposing as experimental five-year WMAP data on the spectral index n, we have derived a constraint on the number of e-folding N _Q to be in the range from 25 to 50. The scenario for large-scale structure formation implied by the model is a mixed scenario for inflation and cosmic string, and the contribution to the CMBR temperature anisotropy depends on the ratio M _X /M _Pl. From the COBE data, we have obtained the constraint on the M _X to be M _X ∈ [1.22 × 10¹⁶, 0.98 × 10¹⁷] GeV. The upper value M _X ≃ 10¹⁷ GeV is a result of the analysis in which the inflationary contribution to the temperature fluctuations measured by the COBE is 90%. The coupling α varies in the range: 10⁻⁷−10⁻¹. This value is not so small, and it is a common characteristics of the supersymmetric unified models with the inflationary scenario. The spectral index n is a little bit smaller than 0.98. The SUGRA corrections are slightly different from the previous consideration. When ξ ≪ 1 and α lies in the above range, the spectral index gets the value consistent with the experimental five-year WMAP data. Comparing with string theory, one gets ξ < 10⁻⁸. Numerical analysis shows that α ≈ 10⁻⁶. To get inflation contribution to the CMBR temperature anisotropy ≈90%, the mass scale M _X < 3.5 × 10¹⁴ GeV.     

Cosmological Density Perturbations from a Quantum Gravitational Model of Inflation

We derive the implications for anisotropies in the cosmic microwave background following from a model of inflation in which a bare cosmological constant is gradually screened by an infrared process in quantum gravity. The model predicts that the amplitude of scalar perturbations is A_S = (2.0 ± 0.2) · 10^—5, that the tensor-to-scalar ratio is r ≈︂ 1.7 · 10^—3, and that the scalar and tensor spectral indices are n ≈︂ 0.97 and n_T ≈︂ —2.8 · 10^—4, respectively. By comparing the model's power spectrum with the COBE 4-year RMS quadrupole, the mass scale of inflation is determined to be M = (0.72 ± 0.03) · 10¹⁶ GeV. At this scale the model produces about 10⁸ e-foldings of inflation, so another prediction is Ω = 1. PACS numbers: 04.60.-m, 98.80.Cq     

Gravity induced particle production in earth’s gravitational field in TeV region

We discuss the production of particles via interaction with the earth’s gravitational field. Explicit calculations are done for high energy scalars passing through earth’s gravitational field. We show for example, that the width for the scalar processφ→3φ can become comparable with a typical weak decay width at an energy scale of a few TeV. (Similar conclusions can be drawn about particles that ultimately couple to some scalar field.) We speculate that similar processes may be responsible for many of the anomalies in the 10–10⁴ TeV experimental data.     

Inflationary solutions in higher-dimensional quantum cosmology

This paper studies a massive scalar field in a (n+2)-dimensional spherically symmetric space-time withR×S×S _n topology. The Hamilton-Jacobi function is constructed from the Wick-rotated action of the solution of Einstein's field equations by analytic continuation. Solutions are obtained by solving the Hamilton-Jacobi equation in the Lorentzian region, and inflation is exhibited.     

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.     

Exploring effects of strong interactions in enhancing masses of dynamical origin

A previous study of the dynamical generation of masses in massless QCD is considered from another viewpoint. The quark mass is assumed to have a dynamical origin and is substituted for by a scalar field without self-interaction. The potential for the new field background is evaluated up to two loops. Expressing the running coupling in terms of the scale parameter μ, the potential minimum is chosen to fix m _top=175 GeV when μ ₀=498 MeV. The second derivative of the potential predicts a scalar field mass of 126.76 GeV. This number is close to the value 114 GeV, which preliminary data taken at CERN suggested to be associated with the Higgs particle. However, the simplifying assumptions limit the validity of the calculations done, as indicated by the large value of a = \frac g²4p=1.077 \alpha=\frac {g^{2}}{4\pi}=1.077 obtained. However, supporting statements about the possibility of improving the scheme come from the necessary inclusion of weak and scalar field couplings and mass counterterms in the renormalization procedure, in common with the seemingly needed consideration of the massive W and Z fields, if the real conditions of the SM model are intended to be approached.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

Regge behavior of DIS structure functions in scalar theories

The Bethe-Salpeter formalism is used to incorporate the valence Regge behavior into the total DIS amplitude. For a special case of scalar quarks with massless scalar exchange, the model is solved both analytically and numerically and exact scaling is found for the valence quark contribution F ₂(x) ∼ (1/x) ^l(0)−1 which mimicks the ρ-trajectory term. The solution solves a long-standing problem by showing that the coefficient in the Regge pole expansion is indeed fine-tuned to give the expected scaling. The method allows for generalization to the region of nonzero momentum transfer and calculation of the DVCS amplitude. The text was submitted by the authors in English.     

Plane Symmetric Vacuum Bianchi Type <Emphasis Type="Italic">III</Emphasis> Cosmology in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Gravity

The main purpose of this paper is to study the exact solution of Bianchi type III spacetime in the context of metric f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives C=A ⁿ , where A and C are the metric coefficients. The physical behavior of the solution has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.     

Quantum fluid dynamics based current-density functional study of a helium atom in a strong time-dependent magnetic field

Evolution of the helium atom in a strong time-dependent (TD) magnetic field (B) of strength up to 10¹¹ G is investigated through a quantum fluid dynamics (QFD) based current-density functional theory (CDFT). The TD-QFD-CDFT computations are performed through numerical solution of a single generalized nonlinear Schr?dinger equation employing vector exchange-correlation potentials and scalar exchange-correlation density functionals that depend both on the electronic charge-density and the current-density. The results are compared with that obtained from a B-TD-QFD-DFT approach (based on conventional TD-DFT) under similar numerical constraints but employing only scalar exchange-correlation potential dependent on electronic charge-density only. The B-TD-QFD-DFT approach, at a particular TD magnetic field-strength, yields electronic charge- and current-densities as well as exchange-correlation potential resembling with that obtained from the time-independent studies involving static (time-independent) magnetic fields. However, TD-QFD-CDFT electronic charge- and current-densities along with the exchange-correlation potential and energy differ significantly from that obtained using B-TD-QFD-DFT approach, particularly at field-strengths >10⁹ G, representing dynamical effects of a TD field. The work concludes that when a helium atom is subjected to a strong TD magnetic field of order >10⁹ G, the conventional TD-DFT based approach differs “dynamically” from the CDFT based approach under similar computational constraints.     

On the stability of scalar-vacuum space-times

We study the stability of static, spherically symmetric solutions to the Einstein equations with a scalar field as the source. We describe a general methodology of studying small radial perturbations of scalar-vacuum configurations with arbitrary potentials V(ϕ), and in particular space-times with throats (including wormholes), which are possible if the scalar is phantom. At such a throat, the effective potential for perturbations V _eff has a positive pole (a potential wall) that prevents a complete perturbation analysis. We show that, generically, (i) V _eff has precisely the form required for regularization by the known S-deformation method, and (ii) a solution with the regularized potential leads to regular scalar field and metric perturbations of the initial configuration. The well-known conformal mappings make these results also applicable to scalar-tensor and f(R) theories of gravity. As a particular example, we prove the instability of all static solutions with both normal and phantom scalars and V(ϕ)≡0 under spherical perturbations. We thus confirm the previous results on the unstable nature of anti-Fisher wormholes and Fisher’s singular solution and prove the instability of other branches of these solutions including the anti-Fisher “cold black holes.”     

Nuclear fusion rates from resonant states of 3Hedμ molecular ion

We present new theoretical calculations of nuclear fusion rates λ _f ^J from the resonant states of the muonic molecular ion ³Hedμ ⁺⁺ with total angular momenta J=0,1. As a byproduct, new very accurate variational wave functions for these states have been obtained. Using these wave functions, the probability density |Ψ(R=0)|² in a fusion region has been calculated by extrapolating the variational solution to small internuclear distances by means of the multi-channel adiabatic solution. Calculated fusion rates for the states J=0 and J=1 are: λ _f ⁰ =1.9·10⁵s^-1 and λ _f ¹ =0.65·10³s^-1, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Orientational changes in the nematic liquid crystal structure on a polymer surface induced by phase separation in a magnetic field

The change in the domain texture of the 5CB nematic liquid crystal on the surface of a polyvinyl butyral gelatinous polymer solution cured in a magnetic field is studied optically. The alignment of the nematic is described by the effective order parameter S* of the polydomain cells. The anchoring energy of a liquid crystal with gelatinous polymer W _ϕ = 1 × 10⁻³ erg/cm₂ is determined.     

The dynamical mixing of light and pseudoscalar fields

We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions L _int = g _ϕ ϕε _μναβ F ^μν F ^αβ . The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.