Kantowski-Sachs Universe Filled with Perfect Fluid in f(R,T) Theory of Gravity

The exact solutions of the field equations in respect of Kantowski-Sachs universe filled with perfect fluid in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84:024020, 2011) is derived. A cosmological model with an appropriate choice of the function f(T) is constructed. The physical behavior of the cosmological model is studied. Some important features of astrophysical phenomena, like Hubble’s parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with red-shift are also discussed.     

Bianchi Type-V Cosmology in f(R,T) Gravity with Λ(T)

A new class of cosmological models in f(R,T) modified theories of gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011), where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar R and the trace of the stress-energy tensor T, have been investigated for a specific choice of f(R,T)=f ₁(R)+f ₂(T) by considering time dependent deceleration parameter. The concept of time dependent deceleration parameter (DP) with some proper assumptions yield the average scale factor $a(t) = \sinh^{\frac{1}{n}}(\alpha t)$ , where n and α are positive constants. For 0<n≤1, this generates a class of accelerating models while for n>1, the models of universe exhibit phase transition from early decelerating phase to present accelerating phase which is in good agreement with the results from recent astrophysical observations. Our intention is to reconstruct f(R,T) models inspired by this special law for the deceleration parameter in connection with the theories of modified gravity. In the present study we consider the cosmological constant Λ as a function of the trace of the stress energy-momentum-tensor, and dub such a model “Λ(T) gravity” where we have specified a certain form of Λ(T). Such models may display better uniformity with the cosmological observations. The statefinder diagnostic pair {r,s} parameter has been embraced to characterize different phases of the universe. We also discuss the physical consequences of the derived models.     

Bianchi Type-II String Cosmological Model with Magnetic Field in f (R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of f(R,T) gravity proposed by Harko et al. (Phys Rev D 84:024020, 2011). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=μ T. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

A New Class of Bianchi Cosmological Models in Lyra’s Geometry

The new class of cosmological model of the early Universe filled with perfect fluid in Lyra’s geometry has been considered. We obtain two classes of exact solutions of the field equations in Lyra’s geometry with a time-dependent displacement vector. The exact solutions to the corresponding field equations are obtained in quadrature form. The cosmological parameters have been discussed in detail and it is also shown that the solutions tend asymptotically to isotropic Friedmann-Robertson-Walker cosmological model. We have also discussed the well-known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance d _L and distance modulus μ(z) with redshift.     

Model-independent reconstruction of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) teleparallel cosmology

We propose a model-independent formalism to numerically solve the modified Friedmann equations in the framework of f(T) teleparallel cosmology. Our strategy is to expand the Hubble parameter around the redshift \(z=0\) up to a given order and to adopt cosmographic bounds as initial settings to determine the corresponding \(f(z)\equiv f(T(H(z)))\) function. In this perspective, we distinguish two cases: the first expansion is up to the jerk parameter, the second expansion is up to the snap parameter. We show that inside the observed redshift domain \(z\le 1\), only the net strength of f(z) is modified passing from jerk to snap, whereas its functional behavior and shape turn out to be identical. As first step, we set the cosmographic parameters by means of the most recent observations. Afterwards, we calibrate our numerical solutions with the concordance \(\Lambda \)CDM model. In both cases, there is a good agreement with the cosmological standard model around \(z\le 1\), with severe discrepancies outer of this limit. We demonstrate that the effective dark energy term evolves following the test-function: \(f(z)={\mathcal {A}}+{\mathcal {B}}{z}^2e^{{\mathcal {C}}{z}}\). Bounds over the set \(\left\{ {\mathcal {A}}, {\mathcal {B}}, {\mathcal {C}}\right\} \) are also fixed by statistical considerations, comparing discrepancies between f(z) with data. The approach opens the possibility to get a wide class of test-functions able to frame the dynamics of f(T) without postulating any model a priori. We thus re-obtain the f(T) function through a back-scattering procedure once f(z) is known. We figure out the properties of our f(T) function at the level of background cosmology, to check the goodness of our numerical results. Finally, a comparison with previous cosmographic approaches is carried out giving results compatible with theoretical expectations.     

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Properties of the Ising magnet confined in a corner geometry

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ±h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field −h acts. For temperatures T less than the critical temperature T_c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T_f(h) runs from the upper left corner to the lower right corner, while for T<T_f(h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T=T_f(h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w∝L, while for T>T_f(h) it scales as . The distribution P(?) of the interface position ? (measured along the z-direction from the corners) decays exponentially for T<T_f(h) from either corner, is essentially flat for T=T_f(h), and is a Gaussian centered at the middle of the diagonal for T>T_f(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.     

Cosmic acceleration in non-flat <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) cosmology

We study f(T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f(T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f(T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-\(\sigma \) confidence level, emphasizing the fact that \(\Omega _{k0}\) turns out to be non-compatible with zero at least at 1\(\sigma \). Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the \(\Lambda \)CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f(T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f(T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f(T) approach provides an effective de-Sitter phase, whereas the second f(T) framework shows analogous results compared with the \(\Lambda \)CDM predictions.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

The use of unitarity bounds for a stable extrapolation of low energy data

The properties of the scattering amplitude allow to define a functionf(z) satisfying the following conditions:

1. f(z) is holomorphic in a simply connected domain , which can be mapped conformally onto the unit disk;
2. |Imf(z)| is bounded by some constantM in ;
3. |Ref(z)| is known not to exceed some constantm on a certain part Γ₁ of the boundary Γ of ;f(z) is continuously extensible onto Γ.

Using these properties, constraints are derived on the real part off(z) valid at any point . The result is used for performing a stable extrapolation of low energy pion-pion scattering data to any finite energy. We derive a bound on energy averaged values of the real part of the scattering amplitude. The bound depends onm, M, on the energy variabless and on the energy average intervals ₂?s ₁. Generalizations of the method are discussed.     

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.     

The exact solution of an elimination problem in kinetic theory: I. The one-dimensional hard sphere gas

A class of initial value problems for a one-dimensional hard sphere gas is considered where a specified particle has a given distribution f⁽¹⁾(z₁; 0) and the rest are in equilibrium at t=0. An exact expansion is obtained for a certain n-particle reduced distribution function f⁽ⁿ⁾(z₁;…;z_n; t) in terms of the 1-particle reduced distribution function f⁽¹⁾(z₁; t) for the specified particle by starting with separate expressions for these functions in terms of f⁽¹⁾(z₁; 0). Expansions for the corresponding cluster functions are first obtained and then graph theoretic methods applied to obtain a solution.     

The nature of anharmonicity and anomalous piezoelectric properties of ferroelectric SbSBr crystal

The contribution of soft mode at Sb atom's sites, to the temperature dependences of Sb atom's equilibrium position's difference Δz(T) has been studied theoretically, when SbSBr crystal is deformed along a(x), b(y) and c(z)-axis in paraelectric phase and is deformed along c(z)-axis in ferroelectric phase. The largest change of Δz₃₃(T) occurs in the ferroelectric phase near the phase transition temperature in the range from 16 K to 21 K. The temperature dependence of Sb atom's equilibrium position's displacements Δz₃₃ is very similar to the temperature dependence of experimental piezoelectric modulus, when SbSBr crystal is deformed in the direction of c(z)-axis in ferroelectric phase.     

Dark-energy cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

We discuss dark-energy cosmological models in f(G) gravity. For this purpose, a locally rotationally symmetric Bianchi type I cosmological model is considered. First, exact solutions with a well-known form of the f(G) model are explored. One general solution is discussed using a power-law f(G) gravity model and physical quantities are calculated. In particular, Kasner’s universe is recovered and the corresponding f(G) gravity models are reported. Second, the energy conditions for the model under consideration are discussed using graphical analysis. It is concluded that solutions with f(G) = G^5/6 support expansion of universe while those with f(G) = G^1/2 do not favor the current expansion.     

Cosmological implications of different baryon acoustic oscillation data

In this work, we explore the cosmological implications of different baryon acoustic oscillation(BAO) data, including the BAO data extracted by using the spherically averaged one-dimensional galaxy clustering(GC) statistics(hereafter BAO1) and the BAO data obtained by using the anisotropic two-dimensional GC statistics(hereafter BAO2). To make a comparison, we also take into account the case without BAO data(hereafter NO BAO). Firstly, making use of these BAO data, as well as the SNLS3 type Ia supernovae sample and the Planck distance priors data, we give the cosmological constraints of the ΛCDM, the w CDM, and the Chevallier-Polarski-Linder(CPL) model. Then, we discuss the impacts of different BAO data on cosmological consquences, including its effects on parameter space, equation of state(Eo S), figure of merit(Fo M), deceleration-acceleration transition redshift,Hubble parameter H(z), deceleration parameter q(z), statefinder hierarchy S_3(1)(z), S_4(1)(z) and cosmic age t(z). We find that:(1)NO BAO data always give a smallest fractional matter density ?_(m0), a largest fractional curvature density ?k0and a largest Hubble constant h; in contrast, BAO1 data always give a largest ?_(m0), a smallest ?_(k0) and a smallest h.(2) For the w CDM and the CPL model, NO BAO data always give a largest Eo S w; in contrast, BAO2 data always give a smallest w.(3) Compared with the case of BAO1, BAO2 data always give a slightly larger Fo M, and thus can give a cosmological constraint with a slightly better accuracy.(4) The impacts of different BAO data on the cosmic evolution and the comic age are very small, and cannot be distinguished by using various dark energy diagnoses and the cosmic age data.     

Reconstruction of Five-Dimensional Bounce Cosmological Models from Deceleration Factor

In this paper, we consider a class of five-dimensional Ricci-flat vacuum solutions, which contain two arbitrary functions μ(t) and ν(t). It is shown that μ(t) can be rewritten as a new arbitrary function f(z) in terms of redshift z and the f(z) can be determined by choosing particular deceleration parameters q(z) which gives early deceleration and late time acceleration. In this way, the 5D cosmological model can be reconstructed and the evolution of the universe can be determined. PACS: 04.50.+h, 98.80.-k     

Anisotropic cosmological models in f (R, T) theory of gravitation

A class of non-singular bouncing cosmological models of a general class of Bianchi models filled with perfect fluid in the framework of f(R,T) gravity is presented. The model initially accelerates for a certain period of time and decelerates thereafter. The physical behaviour of the model is also studied.     

Late-time cosmological approach in mimetic <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic f(R, T) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from \(\mathcal {Q}(z)\) and the well-known particular model f(R, T), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f(R, T) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.     

五维大反弹宇宙学模型的重建及其相关宇宙学量的演化

在五维大反弹宇宙学模型框架下,通过给定三种不同的暗能量有效态方程,确定了在该模型中起重要作用的函数f(z),从而描述了五维大反弹模型中相关的宇宙学量随红移量z的演化.研究表明,与情形Ⅰ中有效态方程相对应的宇宙学量的演化规律和当前天文观测数据符合最好. 关键词： 大反弹宇宙学模型 暗能量 态方程     

Cosmology in modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>)-gravity

In the present paper we propose a further modification of f(R, T)-gravity (where T is trace of the energy-momentum tensor) by introducing higher derivatives matter fields. We discuss stability conditions in the proposed theory and find restrictions for the parameters to prevent appearance of main type of instabilities, such as ghost-like and tachyon-like instabilities. We derive cosmological equations for a few representations of the theory and discuss main differences with conventional f(R, T)-gravity without higher derivatives. It is demonstrated that in the theory presented inflationary scenarios appear quite naturally even in the dust-filled Universe without any additional matter sources. Finally, we construct an inflationary model in one of the simplest representation of the theory, calculate the main inflationary parameters and find that it may be in quite good agreement with observations.