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Two models that unify warm inflation with dark matter and dark energy are proposed. In the models, a single scalar field is responsible for the early expansion of the universe through the process of dissipative warm inflation and then acts as both dark matter and dark energy in subsequent stages. The first model is based on a noncanonical field with the Lagrangian density $\mathcal{L}=F(X)-V(\phi)$, where the potential is dominant at the slow-roll inflationary epoch and negligible in subsequent stages. The second model takes advantage of a $k$-essence Lagrangian density having the coupled form $\mathcal{L}=F(X)V(\phi)$. For both models, equations of the evolution for the fields and observational constraints are presented, and an evolution law describing how the energy density $\rho$ and state parameter $w$ scale with the scale factor $a$ is obtained., Comment: 8 pages, 0 figures

The framework of a kind of noncanonical warm inflation is introduced, and the dynamical equations of this scenario are presented. We propose the slow roll approximations and give some redefining slow roll parameters in this scenario which remain dimensionless. Performing systemic stability analysis, we calculate the slow roll conditions to guarantee that slow roll approximations hold. The slow roll conditions suggest slow roll inflation in general noncanonical warm inflationary scenario can still exist, and in addition, the slow roll approximations are more easily to be satisfied. Then, a concrete Dirac-Born-Infeld warm inflationary model is studied., Comment: 6 pages, 0figures

The general kind noncanonical warm inflation is introduced and its total non-Gaussianity of perturbation on uniform energy density hypersurfaces is studied. The total non-Gaussianity contains two complementary parts: the three- and the four-point correlations. The three-point correlation part denoted by $f^{int}_{NL}$, comes from the three-point correlation of inflaton field, while the four-point correlation part, denoted by $f_{NL}^{\delta N}$, is the contribution due to the four-point correlation function of the inflaton field. The aforementioned two parts of non-Gaussianity in general noncanonical warm inflation are calculated and analysed respectively, and the comparisons and discussions of the two parts are finally carried out in this study., Comment: 8pages,0figures

Deep learning method develops very fast as a tool for data analysis these years. Such a technique is quite promising to treat gravitational wave detection data. There are many works already in the literature which used deep learning technique to process simulated gravitational wave data. In this paper we apply deep learning to LIGO O1 data. In order to improve the weak signal recognition we adjust the convolutional neural network (CNN) a little bit. Our adjusted convolutional neural network admits comparable accuracy and efficiency of signal recognition as other deep learning works published in the literature. Based on our adjusted CNN, we can clearly recognize the eleven confirmed gravitational wave events included in O1 and O2. And more we find about 2000 gravitational wave triggers in O1 data., Comment: 7 pages; 5 figures

We study the two-field warm inflation models with a double quadratic potential and a linear temperature dependent dissipative coefficient. We derived the evolution equation of all kinds of perturbations without assuming slow-roll approximation, and obtained the curvature power spectrum at the end of inflation with a fully numerical method. Then we compute the scalar spectral index $n_s$, tensor-to-scalar ratio $r$ for several representative potentials, and compare our results with observational data. At last, we use Planck data to constrain the parameters in our models. This work is a natural extension of single-field warm inflation, and the aim of this work is to present some features of multi-field warm inflation using a simple two-field model., Comment: 13 pages, 6 figures. Accepted for publication in Physical Review D

We attempt a new scheme to combine the Higgs field in the minimal standard model and the statistic physics with thermal effect together. By introducing the stochastic differential equation in FRW metric frame which is something like the warm inflation model but not exactly the same. By using the previous researches on Fokker-Planck equation with double-well potential, we find the abundance of primordial black holes (PBHs) dominate at a special mass and the PBHs with extremely large or extremely small mass could be almost excluded. In addition, two perturbed model within this frame are employed, one is the model with symmetry breaking and another is stochastic resonance. The former may increase the probability to the generation of PBHs, while the latter may both increase and decrease the probability. Finally, we also discuss the possibility on extension this scenario to other models., Comment: 9 pages, 3 figures

We study the power spectra and entropy of two-field warm inflationary scenario with canonical condition which is described by many-dimensional stochastic differential equations. The field perturbations are analytically calculated via a Volterra integral equation of the second kind, based on which we obtain a spectra with leading order and first order of slow-roll parameters. We also find the evolutions of background are not independent but relying on dissipative coefficients, which is distinguished from that in cold inflation. Then, we calculate the entropy on the basis of statistical physics theory by introducing an entropy matrix. On super-horizon scale, the entropy matrix follows the fluctuation-dissipation relation consistent with the scale-invariance of spectra or the stationarity of field perturbations. The entropy perturbation vanishes at both super-horizon and sub-horizon scale, while narrow peaks generate at a specific scale which could be considered as horizon. In addition, the second law of thermodynamics is followed as well., Comment: 12 pages, 5 figures. Accepted for publication in Physical Review D

In this paper, we discuss the warm inflation model with both a Langevin equation and a generalized Langevin equation scenario. As a brief picture to illustrate the basic properties of stochastic differential equation in warm inflation, this paper is started from a simple condition with constant dissipative coefficient. In this model, we prove the perturbed inflaton field exhibits a stationary process on large scale, so the perturbed field has a scale-invariant power spectrum. Then we study the warm inflation with a generalized Langevin equation scenario. The perturbed field in such model also shows a stationary process and the power spectrum is quite similar to the one in cold inflation. If choosing an appropriate fluctuation-dissipation relation, we can get a spectrum same as the cold inflation. In a word, we attempt to show the rationality of warm inflationary scenario via statistical physics method., Comment: 11 pages, 1 figure

We study and analyze the dynamic properties of both canonical and noncanonical warm inflationary models with dissipative effects. We consider different models of canonical warm inflation with different dissipative coefficients and prove that the behavior at infinity of quadratic dissipative model distinctly differs from that of the constant dissipative model, which means that quadratic dissipative coefficient increases the possibility of the occurrence of inflation. We also show that the different choice of combination of the parameters in noncanonical warm inflation exhibits dramatically different global phase portraits on the Poincar\'{e} disk. We try to illustrate that the noncanonical field will not expand the regime of inflation, but it will increase the possibility of the occurrence of inflation as well and the duration of inflation. Then, by dynamic analysis, we can exclude several inflationary models, like the warm inflation model, with negative dissipative coefficients, and explain that the model without potential is almost impossible. With relevant results, we give the condition when reheating occurs., Comment: 13 pages, 11 figures

Warm inflation is extended from the canonical field to the noncanonical field with a general Lagrangian density having coupling form of kinetic and potential terms. We develop the motion equation of the noncanonical inflaton field, and notice the motion equation has an annoying coupling term $\mathcal{L}_{X\varphi}\dot\varphi^2$, which makes the inflation difficult to solve. It is found that a special field redefinition exists, making the motion equation of inflaton uncoupled. Then we can solve inflation in the special field representation for convenience. The relation of field redefinition between the special uncoupled field and general noncanonical field is obtained. The motion equations and slow roll approximations of noncanonical warm inflation in the special field representation are developed. Then we give two examples to show how to translate a general noncanonical Lagrangian density in the coupled $\varphi$ representation, to the uncoupled $\phi$ representation. Finally, the cosmological perturbations generated by the new kind of warm inflation is calculated., Comment: 15 pages,0 figures

A fundamental prediction of inflation is a nearly scale-invariant spectrum of gravitational wave. The features of such a signal provide extremely important information about the physics of the early universe. In this paper, we focus on several topics about warm inflation. First, we discuss the stability property about warm inflation based on nonequilibrium statistical mechanics, which gives more fundamental physical illustrations to thermal property of such model. Then, we calculate the power spectrum of gravitational waves generated during warm inflation, in which there are three components contributing to such spectrum: thermal term, quantum term and cross term combining the both. We also discuss some interesting properties about these terms and illustrate them in different panels. As a model different from cold inflation, warm inflation model has its individual properties in observational practice, so we finally give a discussion about the observational effect to distinguish it from cold inflation., Comment: 11 pages, 2 figures

We explore the homogeneous background dynamics and the evolution of generated perturbations of cosmological inflation that is driven by multiple scalar fields interacting with a perfect fluid.Then we apply the method to warm inflation driven by two scalar fields and a radiation fluid, and present general results about the evolution of the inflaton and radiation. After decomposing the perturbations into adiabatic and entropy modes, we give the equation of motion of adiabatic and entropy perturbations on large scales. Then, we give numerical results of background and perturbation equations in a concrete model (the dissipative coefficient $\Gamma \propto H$). At last, we use the most recent observational data to constrain our models and give the observationally allowed regions of parameters. This work is a natural extension of warm inflation to multi-field cases., Comment: 10 pages, 4 figures

We investigate the cosmological perturbation theory and calculate the perturbation spectra in the warm $k$-inflation. Unlike the scalar perturbations of $k$-inflation in the cold inflationary scenario, entropy perturbations should be considered in our model. We study how the entropy perturbations affect the evolution of curvature perturbation $\mathcal{R}$ on the comoving hypersurfaces and find the dissipation coefficient $\Gamma$ plays a central role in the entropy perturbations and the evolution equation of $\mathcal{R}$. In the weak dissipation condition, entropy perturbations on the large scale can be neglected such that the primordial spectrum of cosmological perturbations is due only to adiabatic perturbations. Like general warm inflationary models, density fluctuations also mainly originated from the thermal fluctuations of the inflaton field rather than the vacuum fluctuations in our model. Finally, we calculate the perturbation spectra and the tensor-to-scalar ratio, then find the tensor-to-scalar ratio is smaller than that in the $k$-inflation or the general potential-driven cold inflationary models., Comment: 7 pages

Non-Gaussianity generated in inflation can be contributed by two parts. The first part, denoted by $f_{NL}^{\delta N}$, is the contribution from four-point correlation of inflaton field which can be calculated using $\delta N$ formalism, and the second part, denoted by $f_{NL}^{int}$, is the contribution from the three-point correlation function of the inflaton field. We consider the two contributions to the non-Gaussianity in noncanonical warm inflation throughout (noncanonical warm inflation is a new inflationary model which is proposed in \cite{Zhang2014}). We find the two contributions are complementary to each other. The four-point correlation contribution to the non-Gaussianity is overwhelmed by the three-point one in strong noncanonical limit, while the conclusion is opposite in the canonical case. We also discuss the influence of the field redefinition, thermal dissipative effect and noncanonical effect to the non-Gaussianity in noncanonical warm inflation., Comment: 7 pages. Accepted for publication in Physical Review D

We extend the k-inflation which is a type of kinetically driven inflationary model under the standard inflationary scenario to a possible warm inflationary scenario. The dynamical equations of this warm k-inflation model are obtained. We rewrite the slow-roll parameters which are different from the usual potential driven inflationary models and perform a linear stability analysis to give the proper slow-roll conditions in the warm k-inflation. Two cases, a power-law kinetic function and an exponential kinetic function, are studied, when the dissipative coefficient $\Gamma=\Gamma_0$ and $\Gamma=\Gamma(\phi)$, respectively. A proper number of e-folds is obtained in both concrete cases of warm k-inflation. We find a constant dissipative coefficient ($\Gamma=\Gamma_0$) is not a workable choice for these two cases while the two cases with $\Gamma=\Gamma(\phi)$ are self-consistent warm inflationary models., Comment: 8 pages. Accepted for publication as a Regular Article in Physical Review D

Anomaly-free perturbations of loop quantum cosmology with holonomy corrections reveal an $\Omega$ -deformed spacetime structure, $\Omega:=1-2\rho/\rho_c$, where $\Omega<0$ indicates a Euclidean-like space and $\Omega>0$ indicates a Lorentz-like space. It would be reasonable to give the initial value at the spacetime transition point, $\rho=\rho_c/2$, but we find that it is impossible to define a Minkowski-like vacuum even for large $k$ modes at that time. However, if we loosen the condition and give the initial value slightly after $\Omega=0$, e.g., $\Omega\simeq 0.2$, the vacuum state can be well defined and, furthermore the slow roll approximation also works well in that region. Both scalar and tensor spectra are considered in the framework of loop quantum cosmology with holonomy corrections. We find that if the energy density is not too small in relation to $\rho_c/2$ when the considered $k$ mode crossing the horizon, effective theory can give a much smaller scalar power spectrum than classical theory and the spectrum of tensor perturbations could blueshift. But when compared to other observations, since the energy densities when the modes crossed the horizon were significantly smaller than $\rho_c$,the results we get agree with previous work in the literature and with the classical inflation theory., Comment: 7 pages,the final version published in PRD

A $\delta N$ formalism is used to study the non-Gaussianity of the primordial curvature perturbation on an uniform density hypersurfaces generated by the warm inflation for the first time. After introducing the framework of the warm inflation and the $\delta N$ formalism, we obtain an analytic expression for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in slow roll approximation, and find that the $\delta N$ formalism gives a very good result. We analyse the magnitude of $f_{NL}$ and compare our result with those of the standard inflation. Then we discuss two concrete examples: the quartic chaotic model and the hilltop model. The quartic potential model can again be in very good agreement with the Planck results in the warm inflationary scenario, and we give out the concrete results of how the nonlinear parameter depends on the dissipation strength of the warm inflation and the amounts of expansion. We find that the range of the nonlinear parameters in these two cases are both well inside of the allowed region of Planck., Comment: 9 pages, 5 figures

Anomaly-free perturbations of loop quantum cosmology reveal a deformed space-time structure, in which the signature changes when the energy density is $\rho=\rho_c/2$. Furthermore, in loop quantum cosmology, one can obtain an effective causal structure only for a low density region ($\rho\leq\rho_c/2$), which gives a natural initial condition to consider the horizon problem. Choosing the initial value at $\rho(0)=\rho_c/2$ in this paper, we investigate the horizon problem and the probability of inflation in the framework of loop quantum cosmology. Two models are considered: the quadratic inflation and the natural inflation. We use the Liouville measure to calculate the probability of inflation which solves the horizon problem, and find that, for the quadratic inflation model, the probability is very close to unity, while for the natural inflation model, the probability is about $35\$., Comment: 8 pages, 2 figure, 2 tables, final published version

We study the bispectrum of the primordial curvature perturbation on uniform-density hypersurfaces generated by a kind of the noncanonical warm inflation, wherein the inflation is provided by a noncanonical scalar inflaton field that is coupled to radiation through a thermal dissipation effect. We obtain an analytic form for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in first-order cosmological perturbation theory and analyse the magnitude of this nonlinear parameter. We make a comparison between our result and those of the standard inflation and the canonical warm inflation. We also discuss when the contribution to the non-Gaussianity due to the second-order perturbation theory becomes more important and what effect can be observed. We take the Dirac-Born-Infeld (DBI) inflation as a concrete example to find how the sound speed and the thermal dissipation strength to decide the non-Gaussianity and to get a lower bound of the sound speed constrained by PLANCK., Comment: 7 pages, 2 figures

Assuming that the e-folding number is just determined by the change of the scale factor, the tachyonic inflation theory in LQC has been discussed. Considering the tachyon field with exponential potential and inverse quadratic potential, we find that the evolutionary pictures of super inflation are affected by the potentials and the initial conditions. However it cannot provide enough e-folding number, no matter which condition is chosen. Therefore a slow-rolling inflation is necessary. The e-folding number for slow-rolling inflation depends on the values of the parameter $\alpha$ of the exponential potential and the initial conditions. To get enough e-folding number, $\alpha$ should be small. Based on the slow-rolling inflation happens immediately when the super inflation ends, and the scale factor is continuously growing during the whole inflation stage, we consider an e-folding number provided by the whole inflationary stage, and we find that it is easier to get enough e-folding number when the scale factor increases during all the inflation phase., Comment: 8 pages, 6 figures

We extend the warm inflationary scenario to the case of the noncanonical scalar fields. The equation of motion and the other basic equations of this new scenario are obtained. The Hubble damped term is enhanced in noncanonical inflation. A linear stability analysis is performed to give the proper slow-roll conditions in warm noncanonical inflation. We study the density fluctuations in the new picture and obtain an approximate analytic expression of the power spectrum. The energy scale at the horizon crossing is depressed by both noncanonical effect and thermal effect, and so is the tensor-to-scalar ratio. Besides the synergy, the noncanonical effect and the thermal effect are competing in the case of the warm noncanonical inflation., Comment: 7 pages, 0 figures, accepted by Physical Review D

Phenomenological effect of the super-inflation in loop quantum cosmology (LQC) is discussed. We investigate the case that the Universe is filled with the interacting field between massive scalar field and radiation. Considering the damping coefficient $\Gamma$ as a constant, the changes of the scale factor during super-inflation with four different initial conditions are discussed, and we find that the changes of the scale factor depends on the initial values of energy density of the scalar field and radiation at the bounce point. But no matter which initial condition is chosen, the radiation always dominated at the late time. Moreover, we investigate whether the super-inflation can provide enough e-folding number. For the super-inflation starts from the quantum bounce point, the initial value of Hubble parameter $H(t_i)\sim0$, then it is possible to solve the flatness problem and horizon problem. As an example, following the method of \cite{Amoros-prd} to calculate particle horizon on the condition that the radiation dominated at bounce point, and we find that the Universe has had enough time to be homogeneous and isotopic., Comment: 9 pages, 4 figures. Physics Letters B, online publication complete: 13-NOV-2013

This study concerns the consistency of the tachyon warm inflationary models. A linear stability analysis is performed to find the slow-roll conditions, characterized by the potential slow-roll (PSR) parameters, for the existence of a tachyon warm inflationary attractor in the system. The PSR parameters in the tachyon warm inflationary models are redefined. Two cases, an exponential potential and an inverse power-law potential, are studied, when the dissipative coefficient $\Gamma=\Gamma_0$ and $\Gamma=\Gamma(\phi)$, respectively. A crucial condition is obtained for a tachyon warm inflationary model characterized by the Hubble slow-roll (HSR) parameter $\epsilon_{_H}$, and the condition is extendable to some other inflationary models as well. A proper number of e-folds is obtained in both cases of the tachyon warm inflation, in contrast to existing works. It is also found that a constant dissipative coefficient $(\Gamma=\Gamma_0)$ is usually not a suitable assumption for a warm inflationary model., Comment: 10 pages, 0 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP)

The detailed formulation of loop quantum cosmology with higher order holonomy corrections has been constructed recently in the homogeneous and isotropic spacetime, yet it is important to extend the higher order holonomy corrections to include the effects of anisotropy which typically grow during the collapsing phase. In this paper we investigate the Bianchi I model in $\bar{\mu}'$ scheme which truly captures the regularization of the Hamiltonian constraint. To compare with the earlier works and provide a comparison with the $\bar{\mu}'$ scheme, we also investigate the $\bar{\mu}$ scheme although it has many disadvantages. First we construct the effective dynamics with higher order holonomy corrections in a massless scalar field, then we extend it to the inclusion of arbitrary matter. Besides that, we also analyze the behavior of the anisotropy during the evolution of the universe. We find that in the $\bar{\mu}'$ scheme, the singularity is never approached and the quantum bounce is generic as in the isotropic case, regardless of the order of the holonomy corrections. Some differences in the bouncing phase of the two schemes are also found out. It is also shown that in the two schemes the behavior of the anisotropy is not the same before and after the bounce., Comment: 16 pages, 3 figures

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., Comment: 6 pages, 2 figures, accepted for publication in General Relativity and Gravitation

A general form of warm inflation with the dissipative coefficient $\Gamma=\Gamma_0(\phi /\phi_0) ^n(T/\tau_0) ^m$ in loop quantum cosmology is studied. In this case, we obtain conditions for the existence of a warm inflationary attractor in the context of loop quantum cosmology by using the method of stability analysis. The two cases when the dissipative coefficient is independent $(m=0)$ and dependent $(m\neq0)$ on temperature are analyzed specifically. In the latter case, we use the new power spectrum which should be used when considering temperature dependence in the dissipative coefficient. We find that the thermal effect is enhanced in the case $m>0$. As in the standard inflation in loop quantum cosmology, we also reach the conclusion that quantum effect leaves a tiny imprint on the cosmic microwave background (CMB) sky., Comment: 12 pages, accepted for publication in Rhys. Rev. D

We investigate the scalar mode of perturbation of super inflation in the version of loop quantum cosmology in which the gauge invariant holonomy corrections are considered. Given a background solution, we calculate the power spectrum of the perturbation in the classical and LQC conditions. Then we compute the anisotropy originated from the perturbation. It is found that in the presence of the gauge invariant holonomy corrections the power spectrum is exponentially blue and the anisotropy also grows exponentially in the epoch of super inflation., Comment: 12 pages,4 figures,Published version

A path integral formulation of the Bianchi I models containing a massless scalar field in loop quantum cosmology is constructed. Following the strategy used in the homogenous and isotropic case, the calculation is extended to the simplest non-isotropic models according to the $\bar{\mu}$ and $\bar{\mu}^{\prime}$ scheme. It is proved from the path integral angle that the quantum dynamic lacks the full invariance with respect to fiducial cell scaling in the $\bar{\mu}$ scheme, but it does not in the $\bar{\mu}^{\prime}$ scheme. The investigation affirms the equivalence of the canonical approach and the path integral approach in loop quantum cosmology., Comment: 11 pages,revised version, accepted for publication in Class. Quantum Grav

The dynamical behavior of tachyon field with an inverse potential is investigated in loop quantum cosmology. It reveals that the late time behavior of tachyon field with this potential leads to a power-law expansion. In addition, an additional barotropic perfect fluid with the adiabatic index $0<\gamma<2$ is added, and the dynamical system is shown to be an autonomous one. The stability of this autonomous system is discussed using phase plane analysis. There exist up to five fixed points with only two of them possibly stable. The two stable node (attractor) solutions are specified, and their cosmological indications are discussed. For the tachyon dominated solution, the further discussion is stretched to the possibility of considering tachyon field as a combination of two parts which respectively behave like dark matter and dark energy., Comment: 7 pages, 3 figures, conference or other essential info

We generalize the perturbations theory of loop quantum cosmology to a hydrodynamical form and define an effective curvature perturbation on an uniform density hypersurfaces $\zeta_e$. As in the classical cosmology, $\zeta_e$ should be gauge-invariant and conservation on the large scales. The evolutions of both the adiabatic and the non-adiabatic perturbations for a multi-fluids model are investigated in the framework of the effective hydrodynamical theory of loop quantum cosmology with the inverse triad correction. We find that, different from the classical cosmology, the evolution of the large-scales non-adiabatic entropy perturbation can be driven by an adiabatic curvature perturbation and this adiabatic source for the non-adiabatic perturbation is a quantum effect. As an application of the related formalism, we study a decay model and give out the numerical results., Comment: 10 pages, 3 figures

We investigate the warm inflation condition in loop quantum cosmology. In our consideration, the system is described by a tachyon field interacted with radiation. The exponential potential function, $V(\phi)=V_0 e^{-\alpha\phi}\label{exp-p}$, with the same order parameters $V_0$ and $\alpha$, is taken as an example of this tachyon warm inflation model. We find that, for the strong dissipative regime, the total number of e-folds is less than the one in the classical scenario, and for the weak dissipative regime, the beginning time of the warm inflation will be later than the tachyon (cool) inflation., Comment: 7 pages,accepted for publication in Physics Letters B

Applying the higher order holonomy corrections to the perturbation theory of cosmology, the lattice power law of Loop Quantum Cosmology, $\tilde{\mu}\propto p^{\beta}$, is analysed and the range of $\beta$ is decided to be [-1,0] which is different from the conventional range $-0.1319>\beta\geq-5/2$ \cite{lqct}. At the same time, we find that there is a anomaly free condition in this theory, and we obtain this condition in the vector and tensor mode. We also find that the nonzero mass of gravitational wave essentially results from the quantum nature of Riemannian geometry of loop quantum gravity., Comment: 7 pages, 1 figures

We investigate the convergence behaviors of the scalar and the vector perturbations for a big bounce phase in loop quantum cosmology. Two models are discussed: one is the universe filled by a massless scalar field; the other is a toy model which is radiation-dominated in the asymptotic past and future. We find that the behaviors of the Bardeen potential of the scalar mode near both the bounce point and the transition point of the null energy condition are good, moreover, the unlimited growth of the vector perturbation can be avoided in our bounce model. This is different from the bounce models in pure general relativity. And we also find that the maximum of an observable vector mode is inversely proportional to the square of the minimum scalar factor $a_{bounce}$. This conclusion is independent with the bounce model, and we may conclude that the bounce in loop quantum cosmology is reasonable., Comment: 8 pages, 2 figures

We discuss the stability properties of an autonomous system in loop quantum cosmology. The system is described by a self-interacting scalar field $\phi$ with positive potential $V$, coupled with a barotropic fluid in the Universe. With $\Gamma=VV"/V'^2$ considered as a function of $\lambda=V'/V$, the autonomous system is extended from three dimensions to four dimensions. We find that the dynamic behaviors of a subset, not all, of the fixed points are independent of the form of the potential. Considering the higher-order derivatives of the potential, we get an infinite-dimensional autonomous system which can describe the dynamical behavior of the scalar field with more general potential. We find that there is just one scalar-field-dominated scaling solution in the loop quantum cosmology scenario., Comment: 9 pages

The dynamical behaviors of interacting dark energy in loop quantum cosmology are discussed in this paper. Based on defining three dimensionless variables, we simplify the equations of the fixed points. The fixed points for interacting dark energy can be determined by the Friedmann equation coupled with the dynamical equations {in Einstein cosmology}. But in loop quantum cosmology, besides the Friedmann equation, the conversation equation also give a constrain on the fixed points. The difference of stability properties for the fixed points in loop quantum cosmology and the ones in Einstein cosmology also have been discussed., Comment: 7 pages, 5 figures

Along with the development of interferometric gravitational wave detector, we enter into an epoch of gravitational wave astronomy, which will open a brand new window for astrophysics to observe our universe. Almost all of the data analysis methods in gravitational wave detection are based on matched filtering. Gravitational wave detection is a typical example of weak signal detection, and this weak signal is buried in strong instrument noise. So it seems attractable if we can take advantage of stochastic resonance. But unfortunately, almost all of the stochastic resonance theory is based on Fourier transformation and has no relation to matched filtering. In this paper we try to relate stochastic resonance to matched filtering. Our results show that stochastic resonance can indeed be combined with matched filtering for both periodic and non-periodic input signal. This encouraging result will be the first step to apply stochastic resonance to matched filtering in gravitational wave detection. In addition, based on matched filtering, we firstly proposed a novel measurement method for stochastic resonance which is valid for both periodic and non-periodic driven signal., Comment: 5 pages, 3 figures

There are many different proposals for a theory of quantum gravity. Even leaving aside the fundamental difference among theories such as the string theory and the non-perturbative quantum gravity, we are still left with many ambiguities (and/or parameters to be determined) with regard to the choice of variables, the choice of related groups, etc. Loop quantum gravity is also in such a state. It is interesting to search for experimental observables to distinguish these quantum schemes. This paper investigates the loop quantum gravity effect on luminosity-redshift relation. The quantum bounce behavior of loop quantum cosmology is found to result in multivalued correspondence in luminosity-redshift relation. And the detail multivalued behavior can tell the difference of different quantum parameters. The inverse volume quantum correction does not result in bounce behavior in this model, but affects luminosity-redshift relation also significantly., Comment: 11 pages, 3 figures; revised version

Considering an arbitrary, varying equation of the state parameter, the thermodynamic properties of the dark energy fluid in a semiclassical loop quantum cosmology scenario, which we consider the inverse volume modification, is studied. The equation of the state parameters are corrected as a semiclassical one during considering the effective behavior. Assuming that the apparent horizon has Hawking temperature, the modified entropy-area relation is obtained, we find that this relation is different from the one which is obtained by considering the holonomy correction. Considering the dark energy is a thermal equilibrium fluid, we get the expressions for modified temperature, chemical potential and entropy. The temperature, chemical potential and entropy are well-defined in the semiclassical regions., Comment: 7 pages, no figures, revised version

Antal et al. [Phys. Rev. E \textbf{72}, 036121 (2005)] have studied the balance dynamics on the social networks. In this paper, based on the model proposed by Antal et al., we improve it and generalize the binary social networks to the ternary social networks. When the social networks get dynamically balanced, we obtain the distributions of each relation and the time needed for dynamic balance. Besides, we study the self-organized criticality on the ternary social networks based on our model. For the ternary social networks evolving to the sensitive state, any small disturbance may result in an avalanche. The occurrence of the avalanche satisfies the power-law form both spatially and temporally. Numerical results verify our theoretical expectations., Comment: 11 pages, 12 figures

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, S. He and H. Zhang proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected., Comment: 4 pages, 2 figures, revised version

Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. And the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but are actually also found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid., Comment: 4 pages

Wormhole and time machine are very interesting objects in general relativity. However, they need exotic matters which are impossible in classical level to support them. But if we introduce the quantum effects of gravity into the stress-energy tensor, these peculiar objects can be constructed self-consistently. Fortunately, loop quantum cosmology (LQC) has the potential to serve as a bridge connecting the classical theory and quantum gravity. Therefore it provides a simple way for the study of quantum effect in the semiclassical case. As is well known, loop quantum cosmology is very successful to deal with the behavior of early universe. In the early stage, if taken the quantum effect into consideration, inflation is natural because of the violation of every kind of local energy conditions. Similar to the inflationary universe, the violation of the averaged null energy condition is the necessary condition for the traversable wormholes. In this paper, we investigate the averaged null energy condition in LQC in the framework of effective Hamiltonian, and find out that LQC do violate the averaged null energy condition in the massless scalar field coupled model., Comment: 5 pages

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly, which is different from the classical big bang singularity. So this singularity is only a week singularity., Comment: 7 pages, 3 figures. Accepted for publication in Physical Review D

In the context of a gravity's rainbow, the asymptotic quasinormal modes of the scalar perturbation in the quantum modified Schwarzschild black holes are investigated. By using the monodromy method, we calculated and obtained the asymptotic quasinormal frequencies, which are dominated not only by the mass parameter of the spacetime, but also by the energy functions from the modified dispersion relations. However, the real parts of the asymptotic quasinormal modes is still $T_H\ln 3$, which is consistent with Hod's conjecture. In addition, for the quantum corrected black hole, the area spacing is calculated and the result is independent of the energy functions, in spite of the area itself is energy dependence. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole.

Planck scale corrections arising from deformed special relativity on Hawking radiation in Parikh and Wilczk's tunneling framework are studied. We calculate the emission rate of massless particles tunneling though the corrected horizon of modified black holes from gravity's rainbow. In the tunneling process, when a particle get across the quantum horizon, the metric fluctuation not only due to the energy conservation but also quantum effects of the space-time are taken into account. Our results show that, the emission rate is related to the changes of the black hole's quantum corrected entropy and consistent with an underlying unitary theory. In the modified black hole, by using black hole thermodynamics, a series of quantum correction terms including a logarithmic term to the Bekenstein-Hawking entropy are obtained. Correspondingly, the Planck scale corrected emission spectrum is obtained and it deviates from the thermal spectrum.

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. We show that this is always true in tachyon matter LQC. Different from the classical Friedman-Robertson-Walker (FRW) cosmology, the super inflation can appear in the tachyon matter LQC; furthermore, the inflation can be extended to the region where classical inflation stops. Using numerical method, we give an evolution picture of the tachyon field with an exponential potential in the context of LQC. It indicates that the quantum dynamical solutions have the attractive behavior as the classical solutions do. The whole evolution of the tachyon field is that in the distant past, the tachyon field--being in the contracting cosmology--is accelerates to climb up the potential hill with a negative velocity; then at the boundary the tachyon field is bounced into an expanding universe with positive velocity rolling down to the bottom of the potential. In the slow roll limit, we compare the quantum inflation with the classical case in both an analytic and numerical way., Comment: 8 pages, 3 figures, the version published in Phys.Rev.D

It is known that in loop quantum cosmology (LQC) the universe avoids the singularity by a bounce when the matter density approaches the critical density $\rho_c$ (the order of Planck density). After incorporating the inverse volume modifications both in the gravitational and matter part in the improved framework of LQC, we find that the inverse volume modification can decrease the bouncing energy scale, and the presence of nonsingular bounce is generic. For the backward evolution in the expanding branch, in terms of different initial states the evolution trajectories classify into two classes. One class with larger initial energy density leads to the occurrence of bounce in the region $a>a_{ch}$ where $a_{ch}$ marks the different inverse volume modification region. The other class with smaller initial energy density evolves back into the region $a

In quantum gravity, we study the evolution of a two-dimensional planar open frozen spin network, in which the color (i.e. the twice spin of an edge) labeling edge changes but the underlying graph remains fixed. The mainly considered evolution rule, the random edge model, is depending on choosing an edge randomly and changing the color of it by an even integer. Since the change of color generally violate the gauge invariance conditions imposed on the system, detailed propagation rule is needed and it can be defined in many ways. Here, we provided one new propagation rule, in which the involved even integer is not a constant one as in previous works, but changeable with certain probability. In random edge model, we do find the evolution of the system under the propagation rule exhibits power-law behavior, which is suggestive of the self-organized criticality (SOC), and it is the first time to verify the SOC behavior in such evolution model for the frozen spin network. Furthermore, the increase of the average color of the spin network in time can show the nature of inflation for the universe., Comment: 5 pages, 5 figures

This paper investigates the particle radiation from Gibbons-Maeda black hole. Taking into account the self-gravitation of the particle, we calculate the tunnelling rate of the massless particle across the horizon, then we promote the work to the radiation of the charged particle. The calculations prove that the rate of tunnelling equals precisely the exponent of the difference of the black hole entropy before and after emission and the radiation spectrum deviates from exact thermal. The conclusion supports the viewpoint of information conservation., Comment: 15 pages, no figures