Reconstruction of constant slow-roll inflation

Using the relations between the slow-roll parameters and the power spectra for the single field slow-roll inflation, we derive the scalar spectral tilt n_s and the tensor to scalar ratio r for the constant slow-roll inflation, and obtain the constraint on the slow-roll parameter η from the Planck 2015 results. The inflationary potential for the constant slow-roll inflation is then reconstructed in the framework of both general relativity and the scalar-tensor theory of gravity, and compared with the recently reconstructed E model potential. In the strong coupling limit, we show that the η attractor is reached.     

Impact of generalized dissipative coefficient on warm inflationary dynamics in the light of latest Planck data

The warm inflation scenario in view of the modified Chaplygin gas is studied. We consider the inflationary expansion to be driven by a standard scalar field whose decay ratio \(\Gamma \) has a generic power-law dependence with the scalar field \(\phi \) and the temperature of the thermal bath T. By assuming an exponential power-law dependence in the cosmic time for the scale factor a(t), corresponding to the intermediate inflation model, we solve the background and perturbative dynamics considering our model to evolve according to (1) weak dissipative regime and (2) strong dissipative regime. Specifically, we find explicit expressions for the dissipative coefficient, scalar potential, and the relevant inflationary observables like the scalar power spectrum, scalar spectral index, and tensor-to-scalar ratio. The free parameters characterizing our model are constrained by considering the essential condition for warm inflation, the conditions for the model evolves according to weak or strong dissipative regime, and the 2015 Planck results through the \(n_s\)–r plane.     

Warm inflation in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) theory of gravity

The aim of this paper is to explore warm inflation in the background of f(G) theory of gravity using scalar fields for the FRW universe model. We construct the field equations under slow-roll approximations and evaluate the slow-roll parameters, scalar and tensor power spectra and their corresponding spectral indices using viable power-law model. These parameters are evaluated for a constant as well as variable dissipation factor during intermediate and logamediate inflationary epochs. We also find the number of e-folds and tensor- scalar ratio for each case. The graphical behavior of these parameters proves that the isotropic model in f(G) gravity is compatible with observational Planck data.     

Dynamics of polynomial Chaplygin gas warm inflation

In the present work, we study the consequences of a recently proposed polynomial inflationary potential in the context of the generalized, modified, and generalized cosmic Chaplygin gas models. In addition, we consider dissipative effects by coupling the inflation field to radiation, i.e., the inflationary dynamics is studied in the warm inflation scenario. We take into account a general parametrization of the dissipative coefficient \(\Gamma \) for describing the decay of the inflaton field into radiation. By studying the background and perturbative dynamics in the weak and strong dissipative regimes of warm inflation separately for the positive and negative quadratic and quartic potentials, we obtain expressions for the most relevant inflationary observables as the scalar power spectrum, the scalar spectral, and the tensor-to-scalar ratio. We construct the trajectories in the \(n_\mathrm{s}\)–r plane for several expressions of the dissipative coefficient and compare with the two-dimensional marginalized contours for (\(n_\mathrm{s},r\)) from the latest Planck data. We find that our results are in agreement with WMAP9 and Planck 2015 data.     

The observational constraint on constant-roll inflation

We discuss the constant-roll inflation with constant ∈_2 and constant η. By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of ∈_1. The model with constant ∈_2 is ruled out by the observations at the 3σ confidence level, and the model with constant η is consistent with the observations at the 1σ confidence level. The potential for the model with constant η is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be the slow-roll inflation, the ns-r results from the constant-roll inflation are not the same as those from the slow-roll inflation even when η～ 0.01.     

Generalized compatibility equations for tensors of high ranks in multidimensional continuum mechanics

Compatibility equations are derived for the components of generalized strains of rank m associated with generalized displacements of rank m ? 1 by analogs of Cauchy kinematic relations in n-dimensional space (multi-dimensional continuous medium) (m ≥ 1, n ≥ 2). These relations can be written in the form of equating to zero all components of the incompatibility tensor of rank m(n ? 2) or its dual generalized Riemann–Christoffel tensor of rank 2m. The number of independent components of these tensors is found; this number coincides with that of compatibility equations in terms of generalized strains or stresses. The inequivalence of the full system of compatibility equations to any of its weakened subsystems is discussed, together with diverse formulations of boundary value problems in generalized stresses in which the number of equations in a domain can exceed the number of unknowns.     

Post-Newtonian parameter <Emphasis Type="Italic">γ</Emphasis> in generalized non-local gravity

We investigate the post-Newtonian parameter γ and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m ^2n?2 R?^?n R to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ? ⁱ in addition to the metric tensor g _μν, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters γ, we can compare our expressions and results with those in Hohmann and Järv et al. (2016), as well as current observational constraints on the values of γ in Will (2006). Hence, we draw restrictions on the nonminimal coupling terms F? around their background values.     

Limits on the scalar-leptoquark and scalar-gluon masses from the parameters <Emphasis Type="Italic">S</Emphasis>, <Emphasis Type="Italic">T</Emphasis>, and <Emphasis Type="Italic">U</Emphasis> in the minimal model based on four-color symmetry

The contributions to the parameters S, T, and U of radiative corrections from the doublets of scalar leptoquarks and scalar gluons are analyzed within the minimal model based on four-color symmetry of the Pati-Salam type. It is shown that current experimental data on the parameters S, T, and U admit the existence of relatively light scalar leptoquarks and scalar gluons (of mass lower than 1 TeV), the best fit to experimental data being attained at mass values not greater than 400 GeV. In particular, the existence of scalar leptoquarks of mass below 300 GeV is found to be compatible with data on the parameters S, T, and U at χ² < 3.1 (3.2) for m_H = 115 (300) GeV as against χ _SM ² = 3.5 (5.0) in the Standard Model. The mass of the lightest scalar gluon is then predicted to be less than 850 (720) GeV. It is emphasized that the aforementioned doublets of scalar leptoquarks and scalar gluons can play a significant role in processes involving a t quark at LHC.     

Ginzburg–Landau expansion in strongly disordered attractive Anderson–Hubbard model

We have studied disordering effects on the coefficients of Ginzburg–Landau expansion in powers of superconducting order parameter in the attractive Anderson–Hubbard model within the generalized DMFT+Σ approximation. We consider the wide region of attractive potentials U from the weak coupling region, where superconductivity is described by BCS model, to the strong coupling region, where the superconducting transition is related with Bose–Einstein condensation (ВЕС) of compact Cooper pairs formed at temperatures essentially larger than the temperature of superconducting transition, and a wide range of disorder—from weak to strong, where the system is in the vicinity of Anderson transition. In the case of semielliptic bare density of states, disorder’s influence upon the coefficients A and В of the square and the fourth power of the order parameter is universal for any value of electron correlation and is related only to the general disorder widening of the bare band (generalized Anderson theorem). Such universality is absent for the gradient term expansion coefficient C. In the usual theory of “dirty” superconductors, the С coefficient drops with the growth of disorder. In the limit of strong disorder in BCS limit, the coefficient С is very sensitive to the effects of Anderson localization, which lead to its further drop with disorder growth up to the region of the Anderson insulator. In the region of BCS–ВЕС crossover and in ВЕС limit, the coefficient С and all related physical properties are weakly dependent on disorder. In particular, this leads to relatively weak disorder dependence of both penetration depth and coherence lengths, as well as of related slope of the upper critical magnetic field at superconducting transition, in the region of very strong coupling.     

Scalar-leptoquark contributions to the neutrino magnetic moment

On the basis of astrophysical data on the neutrino magnetic moment, μ _ν < 3 × 10⁻¹² μ _B , constraints on the scalar-leptoquark masses are found within the minimal model involving four-color symmetry. It is shown that data on the neutrino magnetic moment are compatible with the mixing-parameter range that admits the existence of scalar leptoquarks whose masses are below 1 TeV, reaching experimental limits obtained from direct searches. In the case of mass degeneracy for the scalar leptoquarks S _m of electric charge Q = 2/3, the constraint m _{S m} > 330 GeV is obtained, which is independent of the mixing parameters of the model. The results are compared with the predictions of other leptoquark models. Original Russian Text ? A.V. Povarov, 2007, published in Yadernaya Fizika, 2007, Vol. 70, No. 5, pp. 905–911.     

Dominant decays of scalar leptoquarks and scalar gluons in the minimal four-color symmetry model

Fermionic and weak decays of the scalar leptoquarks S = S ₁ ⁽⁺⁾ , S ₁ ^(?) , and S _m and the scalar gluons F = F ₁ and F ₂ predicted by the minimal model involving four-color symmetry and the Higgs mechanism of quark-and lepton-mass splitting are considered. The widths and the branching ratios are calculated for these decays, and the results are analyzed versus the couplings and masses of decaying particles. It is shown that, at relatively small mass splittings Δm within scalar doublets (Δm < m _W), the fermionic decays S ₁ ⁽⁺⁾ → tl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → t \(\tilde \nu \) _j, F ₁ → t \(\tilde b\), and F ₂ → t \(\tilde t\), which are characterized by few-GeV widths for m _S, m _F < 1 TeV and decay branching ratios close to unity, are dominant, but that, for Δm > m _W, the weak decays S → S′W and F → F’W compete with the above fermionic decays. In the case of m _S < m _t, the processes S ₁ ⁽⁺⁾ → cl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → bl _j ⁺ , and S _m → c \(\tilde \nu \) _j, whose total branching ratios are Br(S ₁ ⁽⁺⁾ → cl ⁺) ≈ Br(S ₁ ^(?) → v \(\tilde b\)) ≈ 1, Br(S _m → bl ⁺) ≈ 0.9, and Br(S _m → c \(\tilde \nu \)) ≈ 0.1, appear to be dominant decays of scalar leptoquarks. Searches for these decays at LHC and the Tevatron are of interest.     

Absorption and radiation of nonminimally coupled scalar field from charged BTZ black hole

In this paper we investigate the absorption and radiation of nonminimally coupled scalar field from the charged BTZ black hole. We find the analytical expressions for the reflection coefficient, the absorption cross section and the decay rate in strong coupling case. We find that the reflection coefficient is directly governed by Hawking temperature \(T_{H}\), scalar wave frequency \(\omega \), Bekenstein–Hawking entropy \(S_{BH}\), angular momentum m and coupling constant \(\xi \).     

Anisotropic string cosmological model in Brans–Dicke theory of gravitation with time-dependent deceleration parameter

We discuss a spatially homogeneous and anisotropic string cosmological models in the Brans–Dicke theory of gravitation. For a spatially homogeneous metric, it is assumed that the expansion scalar θ is proportional to the shear scalar σ. This condition leads to A = kB^m, where k and m are constants. With these assumptions and also assuming a variable scale factor a = a(t), we find solutions of the Brans–Dicke field equations. Various phenomena like the Big Bang, expanding universe, and shift from anisotropy to isotropy are observed in the model. It can also be seen that in early stage of the evolution of the universe, strings dominate over particles, whereas the universe is dominated by massive strings at the late time. Some physical and geometrical behaviors of the models are also discussed and observed to be in good agreement with the recent observations of SNe la supernovae.     

Palatini formulation of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity theory,and its cosmological implications

We consider the Palatini formulation of f(R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f(R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type \(f=R-\alpha ^2/R+g(T)\) and \(f=R+\alpha ^2R^2+g(T)\) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

A no-hair theorem for spherically symmetric black holes in $$R^2$$ gravity

In a recent paper Cañate (Class Quantum Grav 35:025018, 2018) proved a no hair theorem to static and spherically symmetric or stationary axisymmetric black holes in general f(R) gravity. The theorem applies for isolated asymptotically flat or asymptotically de Sitter black holes and also in the case when vacuum is replaced by a minimally coupled source having a traceless energy momentum tensor. This theorem excludes the case of pure quadratic gravity, \(f(R) = R^2\). In this paper we use the scalar tensor representation of general f(R) theory to show that there are no hairy black hole in pure \(R^2\) gravity. The result is limited to spherically symmetric black holes but does not assume asymptotic flatness or de-Sitter asymptotics as in most of the no-hair theorems encountered in the literature. We include an example of a static and spherically symmetric black hole in \(R^2\) gravity with a conformally coupled scalar field having a Higgs-type quartic potential.     

The simplest non-minimal matter–geometry coupling in the <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) cosmology

f(R, T) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar R and the trace of the energy-momentum tensor T. In this way, f(R, T) models are capable of describing a non-minimal coupling between geometry (through terms in R) and matter (through terms in T). In this article we construct a cosmological model from the simplest non-minimal matter–geometry coupling within the f(R, T) gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter–geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the f(R, T) formalism in order to check its reliability in other fields, rather than cosmology.     

Dynamical Characteristics of a Non-canonical Scalar-Torsion Model of Dark Energy

In this paper, we analyze the phase-space of a model of dark energy in which a non-canonical scalar field (tachyon) non-minimally coupled to torsion scalar in the framework of teleparallelism. Scalar field potential and non-minimal coupling function are chosen as V(?) = V₀?ⁿ and f(?) = ?^N, respectively. We obtain a critical point that behaves like a stable or saddle point depending on the values of N and n. Additionally we find an unstable critical line. We have shown such a behavior of critical points using numerical computations and phase-space trajectories explicitly.     

Warm modified Chaplygin gas shaft inflation

In this paper, we examine the possible realization of a new inflation family called “shaft inflation” by assuming the modified Chaplygin gas model and a tachyon scalar field. We also consider the special form of the dissipative coefficient \(\Gamma ={a_0}\frac{T^{3}}{\phi ^{2 }}\) and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the \(n_s \)–\( \phi ,\, n_s \)–r, and \(n_s \)–\( \alpha _s\) planes (where \(n_s,\, \alpha _s,\, r\), and \(\phi \) represent the spectral index, its running, tensor-to-scalar ratio, and scalar field, respectively) are being developed, which lead to the constraints \(r< 0.11\), \(n_s=0.96 \pm 0.025\), and \(\alpha _s =-0.019 \pm 0.025\). It is quite interesting that these results of the inflationary parameters are compatible with BICEP2, WMAP \((7+9)\) and recent Planck data.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).