C-Field Cosmological Model for Barotropic Fluid Distribution with Varying Λ in FRW Space Time

A cosmological model for barotropic fluid distribution in creation field cosmology with varying cosmological constant (Λ) in FRW space-time is investigated. To get the deterministic model satisfying conservation equation, we have assumed $\varLambda = \frac{1}{R^{2}}$ as considered by Chen and Wu (in Phys. Rev. D 41:695, 1990) where R is scale factor. We find that creation field (C) increases with time, which matches with the result of HN Theory (in Hoyle and Narlikar, Proc. R. Astron. Soc. A 282:178, 1964), $\varLambda\sim\frac{1}{t^{2}}$ , the spatial volume increases with time and deceleration parameter q<0 which shows that universe is accelerating. This result matches with recent observations. The inflationary scenario exists in the models and the results so obtained match with astronomical observations. The various special cases of the model (21) viz. dust filled universe (γ=0) and radiation dominated era (ρ=3p), ρ=p (stiff fluid universe) are also discussed. The models are free from horizon.     

Thermodynamics and holography of tachyon cosmology

Recently, we have investigated the dynamics of the universe in tachyon cosmology with non-minimal coupling to matter (Farajollahi et al. in Mod Phys Lett A 26(15):1125–1135, 2011; Phys Lett B 711(3–4)15:225–231,2012; Phys Rev D 83:124042, 2011; JCAP 10:014, 20112011; JCAP 05:017, 2011). In particular, for the interacting holographic dark energy (IHDE), the model is studied in Farajollahi et al. (Astrophys Space Sci 336(2):461–467, 2011). In the current work, a significant observational program has been conducted to unveil the model’s thermodynamic properties. Our result shows that the IHDE version of our model better fits the observational data than $\Lambda $ CDM model. The first and generalized second thermodynamics laws for the universe enveloped by cosmological apparent and event horizon are revisited. From the results, both first and generalized second laws, constrained by the observational data, are satisfied on cosmological apparent horizon.In addition, the total entropy is verified with the observation only if the horizon of the universe is taken as apparent horizon. Then, due to validity of generalized second law, the current cosmic acceleration is also predicted.     

Critical collapse of scalar fields beyond axisymmetry

We display a simple solution to the Penrose CCC scenario. For this solution we chose for the late stages of the previous aeon a FRW, $\hbox {k}=0$ , universe with both a cosmological constant and radiation (no mass) while for the early stages of the ‘present’ aeon we have again a FRW universe, $\hbox {k}=0$ , with the same cosmological constant and again with radiation but with mass not yet present. The Penrose conditions force the parameters describing the radiation of the former and present aeons to be equal and the transition metric in the overlap region turns out to be flat. We further study how different rest-mass zero fields transition between the different conformally related regions. These (test) fields appears to easily allow perturbations of the geometry within the CCC scenario.     

Warm-intermediate inflationary universe model with viscous pressure in high dissipative regime

Warm inflation model with bulk viscous pressure in the context of “intermediate inflation” where the cosmological scale factor expands as $a(t)=a_0\exp (At^f)$ , is studied. The characteristics of this model in slow-roll approximation and in high dissipative regime are presented in two cases: 1—Dissipative parameter $\Gamma $ as a function of scalar field $\phi $ and bulk viscous coefficient $\zeta $ as a function of energy density $\rho $ . 2— $\Gamma $ and $\zeta $ are constant parameters. Scalar, tensor perturbations and spectral indices for this scenario are obtained. The cosmological parameters appearing in the present model are constrained by recent observational data (WMAP7).     

Higher dimensional cylindrical or Kasner type electrovacuum solutions

We consider a $D$ D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or cosmological Einstein–Maxwell vacuum spacetimes. We mainly focus on electrovacuum solutions and four different types of solutions are obtained in which one of them has no four dimensional counterpart. We also consider the properties of the general solution corresponding to the exterior field of a charged line mass and discuss its several properties. Although it resembles the same form with four dimensional one, there is a difference on the range of the solutions for fixed signs of the parameters. General magnetic field vacuum solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic universe for a special choice of the parameters. The Kasner forms of the general solution are also presented for the cylindrical or cosmological cases.     

Asymptotic analysis of perturbed dust cosmologies to second order

Nonlinear perturbations of Friedmann–Lemaitre cosmologies with dust and a cosmological constant $\Lambda >0$ Λ > 0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if $\Lambda >0$ Λ > 0 but logarithmic if $\Lambda =0$ Λ = 0 and $K<0$ K < 0 . Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if $\Lambda >0$ Λ > 0 the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein–de Sitter universe ( $K=\Lambda =0$ K = Λ = 0 ) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein–de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.     

A four-dimensional \Lambda CDM-type cosmological model induced from higher dimensions using a kinematical constraint

A class of cosmological solutions of higher dimensional Einstein field equations with the energy-momentum tensor of a homogeneous, isotropic fluid as the source are considered with an anisotropic metric that includes the direct sum of a 3-dimensional (physical, flat) external space metric and an $n$ -dimensional (compact, flat) internal space metric. A simple kinematical constraint is postulated that correlates the expansion rates of the external and internal spaces in terms of a real parameter $\lambda $ . A specific solution for which both the external and internal spaces expand at different rates is given analytically for $n=3$ . Assuming that the internal dimensions were at Planck length scales when the external space starts with a Big Bang ( $t=0$ ), they expand only 1.49 times and stay at Planck length scales even in the present age of the universe (13.7 Gyr). The effective four dimensional universe would exhibit a behavior consistent with our current understanding of the observed universe. It would start in a stiff fluid dominated phase and evolve through radiation dominated and pressureless matter dominated phases, eventually going into a de Sitter phase at late times.     

Dynamics of Anisotropic Bianchi Type-III Bulk Viscous String Model with Magnetic Field

In this paper, we discuss the dynamics of spatially homogeneous and anisotropic Bianchi type-III string cosmological model in presence of bulk viscous fluid and electromagnetic field. Exact solutions of Einstein’s field equations are obtained by assuming (i) a special form of the deceleration parameter and (ii) the component \(\sigma^{1}_{1}\) of the shear scalar tensor is proportional to mean Hubble parameter. The source of magnetic field is due to an electric current produced along z-axis. The role of bulk viscosity and magnetic field in establishing string phase of universe is presented. The physical and kinematical features of solutions are also discussed in detail.     

Renormalization aspects of \mathcal {N}=1 Super Yang–Mills theory in the Wess–Zumino gauge

The generalized $f(R)$ gravity with curvature–matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal space-like Killing vector field of 5D spacetime, and it can be reduced to the 4D formalism of FRW universe. This theory is quite general and can give the corresponding results for Einstein gravity, and $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give some new results besides previous ones given by Huang et al. in Phys Rev D 81:064003, 2010. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho $ , we not only discuss the constraints on the model parameters $m,n$ , but also illustrate the evolutionary trajectories of the scale factor $a(t)$ , the deceleration parameter $q(t)$ , and the scalar field $\epsilon (t),\phi (t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.     

Semiclassical strings in supergravity PFT

In this paper, we introduce the bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function \(f(R,T)\) , where \(R\) and \(T\) denote the curvature scalar and the trace of the energy–momentum tensor, respectively, within the framework of a flat Friedmann–Robertson–Walker model. As an equation of state for a prefect fluid, we take \(p=(\gamma -1)\rho \) , where \(0 \le \gamma \le 2\) and a viscous term as a bulk viscosity due to the isotropic model, of the form \(\zeta =\zeta _{0}+\zeta _{1}H\) , where \(\zeta _{0}\) and \(\zeta _{1}\) are constants, and \(H\) is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non-viscous and viscous fluids, respectively, by assuming a simplest particular model of the form of \(f(R,T) = R+2f(T)\) , where \(f(T)=\alpha T\) ( \(\alpha \) is a constant). A big-rip singularity is also observed for \(\gamma <0\) at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of \(\alpha \) to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits a transition from a decelerated phase to an accelerated phase under certain constraints of \(\zeta _0\) and \(\zeta _1\) . We compare the viscous models with the non-viscous one through the graph plotted between the scale factor and cosmic time and find that the bulk viscosity plays a major role in the expansion of the universe. A similar graph is plotted for the deceleration parameter with non-viscous and viscous fluids and we find a transition from decelerated to accelerated phase with some form of bulk viscosity.     

Parameter estimation of a nonlinear magnetic universe from observations

The cosmological model consisting of a nonlinear magnetic field obeying the Lagrangian \(\mathcal {L}= \gamma F^{\alpha },\, F\) being the electromagnetic invariant, coupled to a Robertson-Walker geometry is tested with observational data of Type Ia Supernovae, Long Gamma-Ray Bursts and Hubble parameter measurements. The statistical analysis show that the inclusion of nonlinear electromagnetic matter is enough to produce the observed accelerated expansion, with not need of including a dark energy component. The electromagnetic matter with abundance \(\varOmega _B\) , gives as best fit from the combination of all observational data sets \(\varOmega _B=0.562^{+0.037}_{-0.038}\) for the scenario in which \(\alpha =-1, \varOmega _B=0.654^{+0.040}_{-0.040}\) for the scenario with \(\alpha =-1/4\) and \(\varOmega _B=0.683^{+0.039}_{-0.043}\) for the one with \(\alpha =-1/8\) . These results indicate that nonlinear electromagnetic matter could play the role of dark energy, with the theoretical advantage of being a mensurable field.     

An interacting dark energy model in a non-flat universe

In this paper, an interacting dark energy model in a non-flat universe is studied, with taking interaction form $C=\alpha H\rho _{de}$ C = α H ρ d e . And in this study a property for the mysterious dark energy is aforehand assumed, i.e. its equation of state $w_{\Lambda }=-1$ w Λ = - 1 . After several derivations, a power-law form of dark energy density is obtained $\rho _{\Lambda } \propto a^{-\alpha }$ ρ Λ ∝ a - α , here $a$ a is the cosmic scale factor, $\alpha $ α is a constant parameter introducing to describe the interaction strength and the evolution of dark energy. By comparing with the current cosmic observations, the combined constraints on the parameter $\alpha $ α is investigated in a non-flat universe. For the used data they include: the Union2 data of type Ia supernova, the Hubble data at different redshifts including several new published datapoints, the baryon acoustic oscillation data, the cosmic microwave background data, and the observational data from cluster X-ray gas mass fraction. The constraint results on model parameters are $\Omega _{K}=0.0024\,(\pm 0.0053)^{+0.0052+0.0105}_{-0.0052-0.0103}, \alpha =-0.030\,(\pm 0.042)^{+0.041+0.079}_{-0.042-0.085}$ Ω K = 0.0024 ( ± 0.0053 ) - 0.0052 - 0.0103 + 0.0052 + 0.0105 , α = - 0.030 ( ± 0.042 ) - 0.042 - 0.085 + 0.041 + 0.079 and $\Omega _{0m}=0.282\,(\pm 0.011)^{+0.011+0.023}_{-0.011-0.022}$ Ω 0 m = 0.282 ( ± 0.011 ) - 0.011 - 0.022 + 0.011 + 0.023 . According to the constraint results, it is shown that small constraint values of $\alpha $ α indicate that the strength of interaction is weak, and at $1\sigma $ 1 σ confidence level the non-interacting cosmological constant model can not be excluded.     

Dark energy, cosmic coincidence and future singularity of the universe

Dark energy model with the equation of state $p_{DE} =-\rho _{DE} -A\rho _{DE}^\alpha $ , is characterised by four finite life time future singularity of the universe for different values of the parameter $A$ and $\alpha $ [Nojiri et al. in Phys Rev D 71:063004, 2005]. Since from the matter dominated era to the dark energy dominated era the ratio of the dark energy density to the matter energy density increases as the universe expand for these future singularities, the universe passes through a significant time when the dark energy density and the matter energy density are nearly comparable. Considering $\frac{1}{r_0 }<r=\frac{\rho _{DE} }{\rho _M }<r_0 $ , where $r_0$ is any fixed ratio, we calculate the fraction of total life time of the universe when the universe passes through the coincidental stage for these singularities. It has been found that the fractional time varies as $\alpha $ varies within the range for which these finite life time future singularities occur and the fraction is smaller for smaller values of $r_0 $ . Importance of the fractional time and observational limits onto the values of the parameter $A$ and $\alpha $ has also been discussed.     

Non-singular model universe from a perfect fluid scalar-metric cosmology

To seek for a singularity free model universe from a perfect fluid scalar-metric cosmology, we work in the “Emergent Cosmology” (EC) paradigm which is a non-singular alternative for cosmological inflation. By using two methods including Linear Stability Theory and Effective Potential Formalism, we perform a classical analysis on the possible static solutions (that are called usually as Einstein Static Universes (ESU)in literature) in order to study EC paradigm in a FRW background. Our model contains a kinetic term of the scalar field minimally coupled to the background geometry without a potential term. The matter content of the model consists of a perfect fluid plus a cosmological constant \(\Lambda \) as a separate source. In the framework of a local dynamical system analysis, we show that in the absence or presence of \(\Lambda \), depending on some adopted values for the free parameters of the underlying cosmological model with flat and non-flat spatial geometries, one gets some static solutions which are viable under classical linear perturbations. By extending our study to a global dynamical system analysis, we show that in the presence of \(\Lambda \) with non-flat spatial geometries there is a future global de Sitter attractor in this model. Following the second method, we derive a new static solution that represents a stable ESU but this time without dependence on the free parameters of the cosmological model at hand. As a whole, our analysis suggests the possibility of graceful realization of a non-singular EC paradigm (i.e. leaving the initial static phase and entering the inflation period as the universe is evolving) through either preserving or violation of the strong energy condition.     

Cosmological Constraints on Polytropic Gas Model

We study the polytropic gas scenario as the unification of dark matter and dark energy. We fit the model parameters by using the latest observational data including type Ia supernovae, baryon acoustic oscillation, cosmic microwave background, and Hubble parameter data. At 68.3 % and 95.4 % confidence levels, we find the best fit values of the model parameters as $\tilde{K}=0.742_{-0.024}^{+0.024}(1\sigma)_{-0.049}^{+0.048}(2\sigma)$ and $n=-1.05_{-0.08}^{+0.08}(1\sigma)_{-0.16}^{+0.15}(2\sigma)$ . Using the best fit values of the model, we obtain the evolutionary behaviors of the equation of state parameters of the polytropic gas model and dark energy, the deceleration parameter of the universe, the dimensionless density parameters of dark matter and dark energy as well as the growth factor of structure formation. Then, we investigate different energy conditions in the polytropic gas model and obtain that only the strong energy condition is violated for the special ranges of the redshift. We also conclude that in the this model, the universe starts from the matter dominated epoch and approaches a de Sitter phase at late times, as expected. Further, the universe begins to accelerate at redshift z _t=0.74. Furthermore, in contrary to the ΛCDM model, the cosmic coincidence problem is solved naturally in the polytropic gas scenario. Moreover, this model fits the data of the growth factor well as the ΛCDM model.     

Remarks on nonlinear electrodynamics

Dark energy models with a slowly rolling cosmological scalar field provide a popular alternative to the standard, time-independent cosmological constant model. We study the simultaneous evolution of background expansion and growth in the scalar field model with the Ratra–Peebles self-interaction potential. We use recent measurements of the linear growth rate and the baryon acoustic oscillation peak positions to constrain the model parameter \(\alpha \) that describes the steepness of the scalar field potential.     

Dark energy reconstruction based on the Padé approximation; an expansion around the $$\varLambda $$CDM

We study the dynamical properties of dark energy based on a large family of Padé parameterizations for which the dark energy density evolves as the ratio between two polynomials in the scale factor of the universe. Using the latest cosmological data we perform a standard likelihood analysis in order to place constraints on the main cosmological parameters of different Padé models. We find that the basic cosmological parameters, namely \(({\varOmega _{m0}},h,{\sigma _{8}})\) are practically the same for all Padé parametrizations explored here. Concerning the free parameters which are related to dark energy we show that the best-fit values indicate that the equation of state parameter at the present time is in the phantom regime (\(w<-1\)); however, we cannot exclude the possibility of \(w>-1\) at \(1\sigma \) level. Finally, for the current family of Padé parametrizations we test their ability, via AIC, BIC and Jeffreys’ scale, to deviate from \(\varLambda \)CDM cosmology. Among the current Padé parametrizations, the model which contains two dark energy parameters is the one for which a small but non-zero deviation from \(\varLambda \)CDM cosmology is slightly allowed by the AIC test. Moreover, based on Jeffreys’ scale we show that a deviation from \(\varLambda \)CDM cosmology is also allowed and thus the possibility of having a dynamical dark energy in the form of Padé parametrization cannot be excluded.     

Periodicity and area spectrum of the three dimensional BTZ black hole

Very recently, a new scheme to quantize the horizon area of a black hole has been proposed by Zeng and Liu et?al. In this paper, we further apply the analysis to investigate area spectrum of three dimensional BTZ black hole with the cosmological constant ${\Lambda=-1/l^{2}}$ . The results show that the area spectrum and entropy spectrum are independent of the cosmological constant. The area spectrum of the black hole is ${\Delta A=8\pi l_{P}^{2}}$ , which confirms the initial proposal of Bekenstein that the area spectrum is independent of the black hole parameters and the spacing is ${8\pi l_{P}^{2}}$ . This result also confirms the speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization. In addition, for the rotating and non-rotating BTZ black holes, we obtain the same entropy spectrum ${\triangle S=2\pi}$ , which is consistent with the result for other black holes. This implies that the entropy spectrum is more fundamental than the area spectrum.     

Cosmological meaning of the gravitational gauge group

It is shown that among the \(R+\beta S^{abc}S_{abc}\) models, only the one with \(\beta =1/2\) has nonvanishing torsion effect in the Robertson–Walker universe filled with a spin fluid, where \(S_{abc}\) denotes torsion. Moreover, the torsion effect in that model is found to be able to replace the big-bang singularity by a big bounce. Furthermore, we find that the model can be obtained under a Kaluza–Klein-like ansatz, by assuming that the gravitational gauge group is the de Sitter group.     

Dynamical behaviors of FRW universe containing a positive/negative potential scalar field in loop quantum cosmology

The dynamical behaviors of FRW Universe containing a posivive/negative potential scalar field in loop quantum cosmology scenario are discussed. The method of the phase-plane analysis is used to investigate the stability of the Universe. It is found that the stability properties in this situation are quite different from the classical cosmology case. For a positive potential scalar field coupled with a barotropic fluid, the cosmological autonomous system has five fixed points and one of them is stable if the adiabatic index $\gamma $ satisfies $0<\gamma <2$ . This leads to the fact that the universe just have one bounce point instead of the singularity which lies in the quantum dominated area and it is caused by the quantum geometry effect. There are four fixed points if one considers a scalar field with a negative potential, but none of them is stable. Therefore, the universe has two kinds of bounce points, one is caused by the quantum geometry effect and the other is caused by the negative potential, the Universe may enter a classical re-collapse after the quantum bounce. This hints that the spatially flat FRW Universe containing a negative potential scalar field is cyclic.