Exploring bouncing cosmologies with cosmological surveys

From recent observational data two significant directions have been made in the field of theoretical cosmology recently.First,we are now able to make use of present observations,such as the Planck and BICEP2 data,to examine theoretical predictions from the standard inflationaryΛCDM which were made decades of years ago.Second,we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm.In particular,a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the big bang singularity.These models have achieved a series of considerable developments in recent years,in particular in their perturbative frameworks,which made brand-new predictions of cosmological signatures that could be visible in current and forthcoming observations.Herein we present two representative paradigms of early universe physics.The first is the reputed new matter(or matter-ekpyrotic)bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase.In the setting of this paradigm,we have proposed some possible mechanisms of generating a red tilt for primordial curvature perturbations and confront the general predictions with recent cosmological observations.The second is the matter-bounce inflation scenario which can be viewed as an extension of inflationary cosmology with a matter contraction before inflation.We present a class of possible model constructions and review the implications on the current CMB experiments.Lastly a review of significant achievements of these paradigms beyond the inflationaryΛCDM model is made,which is expected to shed new light on the future direction of observational cosmology.     

Influence of dark energy on time-like geodesic motion in Schwarzschild spacetime

In this paper we investigate the influence of the dark energy on the time-like geodesic motion of a particle in Schwarzschild spacetime by analysing the behaviour of the effective potential which appears in an equation of motion. For the non-radial time-like geodesics, we find a bound orbit when the particle energy is in an appropriate range, and also find another possible orbit, which is that the particle drops straightly into the singularity of a black hole or escapes to infinity. For the radial time-like geodesics, we find an unstable circular orbit when the particle energy is the critical value, in which case it is possible for the particle to escape to infinity.     

Friedmann Cosmology with a Generalized Equation of State and Bulk Viscosity

The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state (endowed some deviation from the conventionally assuned cosmic perfect fluid model).We assume the bulk viscosity is a linear combination of two termsone is constant,and the other is proportional to the scalar expansion θ = 3a/a.The equation of state is described as p = (γ - 1)p p0,where p0 is a parameter.In this framework we demonstrate that this model can be used to explain the dark energy dominated universe,and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolutionno future singularity,big rip,or Type-Ⅲ singularity as presented in [S.Nojiri,S.D.Odintsov,and S.Tsujikawa,Phys.Rev.D 71 (2005) 063004].     

Editorial

正The hot big bang model is an amazing idea to explain the origin and the evolution of our universe. The Hubble constant (H_0)characterizing the current expansion rate of the universe is one of the key parameters in the hot big bang model. A lot of efforts have been made to measure its value, and now an around 1% measurement accuracy is already available. For example, recently     

A New Solution to Einstein's Field Equations

We construct a new exact solution to the vacuum Einstein field equations. This solution possesses a naked physical singularity. The norm of the Riemann curvature tensor of the solution takes infinity at some points and the solution does not have any event horizon around the singularity. A detailed analysis of this new singularity is also presented.     

Constrained instanton and black hole creation

It is generally accepted that the Einstein theory of general relativity governs the evolution of the universe. However, the singularity theorem of Hawking and Penrose[1] shows that under the most reasonable physical conditions, a spacetime singularity, where physics laws and even causality are broken down, is unavoidable. One has to impose the boundary or initial conditions at the edge of spacetime for the evolution of the universe. This is the so-called first cause problem. The no-boundary …     

Primordial black hole mass functions as a probe of cosmic origin

We discuss a novel window to probe the origin of our universe via the mass functions of primordial black holes(PBHs).The mass functions of PBHs are simply estimated using the conventional Press-Schechter formalism for two paradigms of cosmic origin,including inflationary ΛCDM and bounce cosmology.The standard inflationary ΛCDM model cannot generate an appreciable number of massive PBHs;however,non-trivial inflation models with blue-tilted power spectra at small scales and matter bounce cosmology...     

Bianchi Type-III Cosmological Models with Gravitational Constant G and the Cosmological Constant ∧

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅲ universe by assuming conservation law for the energy-momentum tensor. Exact solutions of the field equations are obtained by using the scalar of expansion proportional to the shear scalar θ∝σ, which leads to a relation between metric potential B = Cn, where n is a constant. The corresponding physical interpretation of the cosmological solutions are also discussed.     

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

Quantum Creation of Closed Universe with Both Effects of Tunnelling and Well

A new “twice loose shoe“ method in the Wheeler-DeWitt equation of the universe wavefunction on the cosmic scale factor a and a scalar field φ is suggested,We analyze both the affections coming from the tunnelling effect of α and the potential well effect of φ,and obtain the initial values α0 about a primary closed universe which is born with the largest probability in the quantum manner,Our result is able to overcome the “large field difficulty“ of the universe quantum creation probabiltiy with only tunnelling effect.This new born universe has to suffer a startup of inflation,and then comes into the usual slow rolling inflation.The universe with the largest probalility maybe has a “gentle“ inflation of an eternal chaotic infltion.this depends on a new parameter q which describes the tunnelling character.     

Dark Energy Density in Brane World

We present a possible explanation to the tiny positive cosmological constant under the frame of AdS5 spacetime embedded by a dS4 brahe. We calculate the dark energy density by summing the zero point energy of massive scalar fields in AdS5 spacetime. Under the assumption that the radius of AdS5 spacetime is of the same magnitude as the radius of observable universe, the dark energy density in dS4 brahe is obtained, which is smaller than the observational value. The reasons are also discussed.     

Exact solution of phantom dark energy model

We investigate the phantom dark energy model derived from the scalar field with a negative kinetic term.By assuming a particular relation between the time derivative of the phantom field and the Hubble function,an exact solution of the model is constructed.Absence of the ’big rip’ singularity is shown explicitly.We then derive special features of phantom dark energy model and show that its predictions are consistent with all astrophysical observations.     

Elastic analysis of a mode II crack in a decagonal quasi—crystal

The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.     

Viscous Modified Chaplygin Gas in Classical and Loop Quantum Cosmology

We investigate the cosmological model of viscous modified Chaplygin gas(VMCG) in classical and loop quantum cosmology(LQC). Firstly, we constrain its equation of state parameters in the framework of standard cosmology from Union 2.1 SNe Ia data. Then, we probe the dynamical stability of this model in a universe filled with VMCG and baryonic fluid in LQC background. It is found that the model is very suitable with(X~(2/d.o.f)= 0.974) and gives a good prediction of the current values of the deceleration parameter q_0 =∈(-0.60,-0.57) and the effective state parameter ω_(eff)∈(-0.76,-0.74) that is consistent with the recent observational data. The model can also predict the time crossing when(ρ_(DE) ≈ρmatter) at z = 0.75 and can solve the coincidence problem. In LQC background, the Big Bang singularity found in classical cosmology ceases to exist and is replaced by a bounce when the Hubble parameter vanishes at ρtot≈ρc.     

Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model

We investigate a 6 D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant.Each stress-energy tensor T_(ab)~i on the brane is shown to be similar to a constant vacuum energy.This is consistent with the Randall-Sundrum model,in which each 3-brane Lagrangian yielded a constant vacuum energy.By adopting an anisotropic metric ansatz,we obtain the 5 D Friedmann-Robertson-Walker field equations.In a slightly later period,the expansion of the universe is proportional to the square root of time,t~(1/2),which is similar to the period of the radiation-dominated regime.Moreover,we investigate the case with two a(t) and two b(t).In a large range of t,we obtain the 3 D effective cosmological constant Λ_(eff)=-2Ω/30,which is independent of the integral constant.Here,the scale factor is an exponential expansion,which is consistent with our present observation of the universe.Our results demonstrate that it is possible to construct a model that solves the dark energy problem,while guaranteeing a positive brane tension.     

Oscillating Quintom Model with Time Periodic Varying Deceleration Parameter

We propose a new law for the deceleration parameter that varies periodically with time. According to the law we give a model of the oscillating universe with quintom matter in the framework of a 4-dimensional Friedmann Ftobertson Walker background. We find that, in the model, the Hubble parameter oscillates and keeps positive The universe undergoes decelerating expansion and accelerating expansion alternately without singularity.     

De Broglie–Bohm Interpretation of Canonical Quantum Cosmology Implies Early Stages of the Universe Dominated by Radiation

The Einstein＇s genera/relativity is formulated in the Hamiltonian form for a spatia/ly Bat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obtain the Wheeler-DeWitt equation. Solving the Wheeler-DeWitt equation and employing the de Broglie-Bohm interpretation to the wave function of the universe, we obtain a new version of spatia/ly fiat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufilcientlv small.     

Creation from Nothing：A New Model

We try to propose a new model of the creation of Universe.First,the de Sitter spacetime is created from nothing and then we obtain an anti-de Sitter spacetime which has closed time-like curves by analytical continuation.We know that the anti-de Sitter spacetime is classically unstable,so it is easier to create an inflationary bubble universe as that we live in.     

Nonsingularity in two-dimensional cylindrical invisible cloaks

The method of designing electromagnetic invisible cloaks is usually based on the form-invariance of Maxwell's equations in coordinate transformation. The exterior boundary of a cylindrical invisible cloak is unchanged and the interior boundary is extended from that of a point to that of a cylindrical region in coordination transformation. This transformation process makes perfect cloaks, but it causes singularity in the constitutive material parameters of cloaks. This singularity makes the cloaks impossible to realize in practice. In order to remove this singularity, this paper sets a small cylindrical region replacing a point in the space transformation. The cylindrical region is so small that it does not affect the invisibility effects, but it can remove the singularity for material parameters. Full wave simulations based on the finite element method were used to verify the designed cloaks.     

Multiple Darboux–B?cklund transformations via truncated Painleve′ expansion and Lie point symmetry approach

For a given truncated Painleve′ expansion of an arbitrary nonlinear Painleve′ integrable system, the residue with respect to the singularity manifold is known as a nonlocal symmetry, called the residual symmetry, which is proved to be localized to Lie point symmetries for suitable prolonged systems. Taking the Korteweg–de Vries equation as an example, the n-th binary Darboux–Ba¨cklund transformation is re-obtained by the Lie point symmetry approach accompanied by the localization of the n-fold residual symmetries.