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Wen Zhao

Publications and source records attributed to Wen Zhao.

At least 217 records · Page 12Linked to original sources
arXiv2010

Separating E and B types of polarization on an incomplete sky

Detection of magnetic-type ($B$-type) polarization in the Cosmic Microwave Background (CMB) radiation plays a crucial role in probing the relic gravitational wave (RGW) background. In this paper, we propose a new method to deconstruct a polarization map on an incomplete sky in real space into purely electric and magnetic polarization type maps, ${\mathcal{E}}(\hatγ)$ and ${\mathcal{B}}(\hatγ)$, respectively. The main properties of our approach are as follows: Firstly, the fields ${\mathcal{E}}(\hatγ)$ and ${\mathcal{B}}(\hatγ)$ are constructed in real space with a minimal loss of information. This loss of information arises due to the removal of a narrow edge of the constructed map in order to remove various numerical errors, including those arising from finite pixel size. Secondly, this method is fast and can be efficiently applied to high resolution maps due to the use of the fast spherical harmonics transformation. Thirdly, the constructed fields, ${\mathcal{E}}(\hatγ)$ and ${\mathcal{B}}(\hatγ)$, are scalar fields. For this reason various techniques developed to deal with temperature anisotropy maps can be directly applied to analyze these fields. As a concrete example, we construct and analyze an unbiased estimator for the power spectrum of the $B$-mode of polarization $C_{\ell}^{BB}$. Basing our results on the performance of this estimator, we discuss the RGW detection ability of two future ground-based CMB experiments, QUIET and POLARBEAR.

astro-ph.CO↗
arXiv2010

Improved calculation of relic gravitational waves

In this paper, we improve the calculation of the relic gravitational waves (RGW) in two aspects: First, we investigate the transfer function after considering the redshift-suppression effect, the accelerating expansion effect, the damping effect of free-streaming relativistic particles, and the damping effect of cosmic phase transition, and give a simple approximate analytic expression, which clearly illustrates the dependent relations on the cosmological parameters. Second, we develop a numerical method to calculate the primordial power spectrum of RGW at a very wide frequency range, where the observed constraints on $n_s$ (the scalar spectral index) and $P_S(k_0)$ (the amplitude of primordial scalar spectrum) and the Hamilton-Jacobi equation are used. This method is applied to two kinds of inflationary models, which all satisfy the current constraints on $n_s$, $α$ (the running of $n_s$) and $r$ (the tensor-scalar ratio). We plot them in the $r-Ω_g$ diagram, where $Ω_g$ is the strength of RGW, and study their detection by the CMB experiments and laser interferometers.

gr-qc↗
arXiv2010

Quintessence models with an oscillating equation of state and their potentials

In this paper, we investigate the quintessence models with an oscillating equation of state (EoS) and their potentials. From the constructed potentials, which have the EoS of $ω_ϕ=ω_0+ω_1\sin z$, we find they are all the oscillating functions of the field $ϕ$, and the oscillating amplitudes are decreasing (or increasing) with $ϕ$. From the evolutive equation of the field $ϕ$, we find this is caused by the expansion of the universe. This also makes that it is very difficult to build a model whose EoS oscillates forever. However one can build a model with EoS oscillating for a period. Then we discuss three quintessence models, which are the combinations of the invert power law functions and the oscillating functions of the field $ϕ$. We find they all follow the oscillating EoS.

astro-ph↗
arXiv2010

Numeric Spectrum of Relic Gravitational Waves in Accelerating Universe

The accelerating expansion of the Universe at the present stage is a process that will change the spectrum of relic gravitational waves. Here we present a numerical calculation for the power spectrum of relic gravitational waves in the accelerating Universe. The results show that although the overall features of the power spectrum is similar to that in the non-accelerating models, the amplitude is smaller by an order of $10^{-1}$. We also find that the spectrum is very sensitive to the index $β$ of the inflationary expansion with the scale factor $a(τ) \propto |τ|^{1+β}$. With increase of $β$, the resulting spectrum is tilted to be flatter with more power on high frequencies, and the sensitivity of the second science run of the LIGO detectors puts a restriction on the parameter $β< -1.8$. The influence of reheating following the inflation has been examined.

astro-ph↗
arXiv2009

Attractor Solution in Coupled Yang-Mills Field Dark Energy Models

We investigate the attractor solution in the coupled Yang-Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows that, if the attractor solution exists, the equation-of-state of the dark energy must evolve from $w_y>0$ to $w_y\le-1$, which is slightly suggested by the observation. At the same time, the total equation-of-state in the attractor solution is $w_{tot}=-1$, the universe is a de Sitter expansion, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.

gr-qc↗
arXiv2009

Perturbations of the Yang-Mills field in the universe

It has been suggested that the Yang-Mills (YM) field can be a kind of candidate for the inflationary field at high energy scales or the dark energy at very low energy scales, which can naturally give the equation of state $-1<ω<0$ or $ω<-1$. We discuss the zero order and first order Einstein equations and YM field kinetic energy equations of the free YM field models. From the zero order equations, we find that $ω+1\propto a^{-2}$, from which it follows that the equation of state of YM field always goes to -1, independent of the initial conditions. By solving the first order Einstein equations and YM field equations, we find that in the YM field inflationary models, the scale-invariant primordial perturbation power spectrum cannot be generated. Therefore, only this kind of YM field is not enough to account for inflationary sources. However, as a kind of candidate of dark energy, the YM field has the `sound speed' $c_s^2=-1/3<0$, which makes the perturbation $ϕ$ have a damping behavior at the large scale. This provides a way to distinguish the YM field dark energy models from other kinds of models.

astro-ph↗
arXiv2009

New method to constrain the relativistic free-streaming gas in the Universe

We discuss a method to constrain the fraction density $f$ of the relativistic gas in the radiation dominant stage, by their impacts on a relic gravitational waves and the cosmic microwave background (CMB) $B$ polarization power spectrum. We find that the uncertainty of $f$ strongly depends on the noise power spectra of the CMB experiments and the amplitude of the gravitational waves. Taking into account of the CMBPol instrumental noises, an uncertainty $Δf=0.046$ is obtained for the model with tensor-to scalar ratio $r=0.1$. For an ideal experiment with only the reduced cosmic lensing as the contamination of $B$-polarization, $Δf=0.008$ is obtained for the model with $r=0.1$. So the precise observation of the CMB $B$-polarization provides a great opportunity to study the relativistic components in the early Universe.

astro-ph.CO↗
arXiv2008

The State Equation of the Yang-Mills field Dark Energy Models

In this paper, we study the possibility of building Yang-Mills(YM) field dark energy models with equation of state (EoS) crossing -1, and find that it can not be realized by the single YM field models, no matter what kind of lagrangian or initial condition. But the states of $-1<ω<0$ and $ω<-1$ all can be naturally got in this kind of models. The former is like a quintessence field, and the latter is like a phantom field. This makes that one can build a model with two YM fields, in which one with the initial state of $-1<ω<0$, and the other with $ω<-1$. We give an example model of this kind, and find that its EoS is larger than -1 in the past and less than -1 at the present time. We also find that this change must be from $ω>-1$ to $<-1$, and it will go to the critical state of $ω=-1$ with the expansion of the Universe, which character is same with the single YM field models, and the Big Rip is naturally avoided.

astro-ph↗
arXiv2008

An exact analytic spectrum of relic gravitational waves in an accelerating universe

An exact analytic calculation is presented for the spectrum of relic gravitational waves in the scenario of accelerating Universe $Ω_Λ+Ω_m = 1$. The spectrum formula contains explicitly the parameters of acceleration, inflation, reheating, and the (tensor/scalar) ratio, so that it can be employed for a variety of cosmological models. We find that the spectrum depends on the behavior of the present accelerating expansion. The amplitude of gravitational waves for the model $Ω_Λ=0.65$ is about $\sim 50 %$ greater than that of the model $Ω_Λ=0.7$, an effect accessible to the designed sensitivities of LIGO and LISA. The spectrum sensitively depends on the inflationary models with $a(τ) \propto |τ|^{1+β}$, and a larger $β$ yields a flatter spectrum, producing more power. The current LIGO results rule out the inflationary models of $β\geq -1.8$. The LIGO with its design sensitivity and the LISA will also be able to test the model of $β=-1.9$. We also examine the constraints on the spectral energy density of relic gravitational waves. Both the LIGO bound and the nucleosynthesis bound point out that the model $β=-1.8$ is ruled out, but the model $β=-2.0$ is still alive. The exact analytic results also confirm the approximate spectrum and the numerical one in our previous work.

astro-ph↗
arXiv2008

Evolution of magnetic component in Yang-Mills condensate dark energy models

The evolution of the electric and magnetic components in an effective Yang-Mills condensate dark energy model is investigated. If the electric field is dominant, the magnetic component disappears with the expansion of the Universe. The total YM condensate tracks the radiation in the earlier Universe, and later it becomes $w_y\sim-1$ thus is similar to the cosmological constant. So the cosmic coincidence problem can be avoided in this model. However, if the magnetic field is dominant, $w_y>1/3$ holds for all time, suggesting that it cannot be a candidate for the dark energy in this case.

gr-qc↗
arXiv2008

Statefinder diagnostic for Yang-Mills dark energy model

We study the statefinder parameters in the Yang-Mills condensate dark energy models, and find that the evolving trajectories of these models are different from those of other dark energy models. We also define two eigenfunctions of the Yang-Mills condensate dark energy models. The values of these eigenfunctions are quite close to zero if the equation-of-state of the Yang-Mills condensate is not far from -1, which can be used to simply differentiate between the Yang-Mills condensate models and other dark energy models.

gr-qc↗
arXiv2008

Coincidence Problem in YM Field Dark Energy Model

The coincidence problem is studied in the effective Yang-Mills condensate dark energy model. As the effective YM Lagrangian is completely determined by quantum field theory, there is no adjustable parameter in this model except the energy scale, and the cosmic evolution only depends on the initial conditions. For generic initial conditions with the YM condensate subdominant to the radiation and matter, the model always has a tracking solution, the Universe transits from matter-dominated into the dark energy dominated stage only recently $z\sim 0. 3$, and evolve to the present state with $Ω_{y}\sim 0.73$ and $Ω_m\sim 0.27$.

astro-ph↗
arXiv2008

Quintom models with an equation of state crossing -1

In this paper, we investigate a kind of special quintom model, which is made of a quintessence field $ϕ_1$ and a phantom field $ϕ_2$, and the potential function has the form of $V(ϕ_1^2-ϕ_2^2)$. This kind of quintom fields can be separated into two kinds: the hessence model, which has the state of $ϕ_1^2>ϕ_2^2$, and the hantom model with the state $ϕ_1^2<ϕ_2^2$. We discuss the evolution of these models in the $ω$-$ω'$plane ($ω$ is the state equation of the dark energy, and $ω'$ is its time derivative in unites of Hubble time), and find that according to $ω>-1$ or $<-1$, and the potential of the quintom being climbed up or rolled down, the $ω$-$ω'$ plane can be divided into four parts. The late time attractor solution, if existing, is always quintessence-like or $Λ$-like for hessence field, so the Big Rip doesn't exist. But for hantom field, its late time attractor solution can be phantom-like or $Λ$-like, and sometimes, the Big Rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the $ω$-$ω'$ plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation of state function $ω(z)$. We apply our method to five kinds of parametrizations of equation of state parameter, where $ω$ crossing -1 can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom $δ_Q$ and the metric $Φ$ are all finite even if at the state of $ω=-1$ and $ω'\neq0$.

astro-ph↗
arXiv2008

Relic gravitational waves and their detection

As the strong evidence for inflation, the relic gravitational waves (RGW) have been extensively studied. Although, it has not been detected, yet some constraints have been achieved by the observations. Future experiments for the RGW detection are mainly two kinds: the CMB experiments and the laser interferometers. In this paper, we study these current constraints and the detective abilities of future experiments. We calculate the strength of RGW $Ω_g(k)$ in two methods: the analytic method and the numerical method by solving the inflationary flow equations. By the first method we obtain a bound $Ω_g<3.89\times10^{-16}$ at $ν=0.1$Hz, where we have used the current constraints on the scalar spectral index, the tensor-scalar ratio, furthermore, we have taken into account of the redshift-suppression effect, the accelerating expansion effect, the neutrino damping effect on the RGW. But the analytic expression of $Ω_g(k)$ depends on the specific inflationary models and not well applies for the waves with very high frequencies. The numerical method is more precise for the waves with high frequencies and applies to any single-field inflationary model. It gives a bound $Ω_g<8.62\times10^{-14}$, which is independent of the inflationary parameters, and applies to any single-field slow-roll inflationary model. After considering the current constraints on the inflationary parameters, this bound becomes $Ω_g<2\times10^{-17}$ (see text).

astro-ph↗
arXiv2008

Analytic approach to the CMB polarizations generated by relic gravitational waves

By Polnarev's method we analytically calculate the polarization spectra of the cosmic microwave background radiation (CMB) generated by cosmic relic gravitational waves (RGW). In this analytic approach the physics involved in this generating process is more transparent. Consequently, the effects due to various elements of physics can be isolated easily. In solving the equation for evolution of RGW in the expanding universe, both the sudden transition and the WKB approximation for the scale factor during the radiation-matter transition have been taken. To describe more precisely the decoupling process, we have introduced an analytic expression for the visibility function, consisting of two pieces of half-Gaussian curves. We also include the damping on polarizations due to the photon diffusion up to the second order of the tight coupling. Analytic polarization spectra $C_l^{XX}$ have been obtained with the following several improvements over the previous results. 1. The approximate analytic result is quite close to the numerical one evaluated from the cmbfast code, especially, for the first three peaks of the spectrum that are observable (see the text).

astro-ph↗
arXiv2008

Holographic hessence models

We discuss the evolution of holographic hessence model, which satisfies the holographic principle and can naturally realizes the equation of state crossing -1. By discussing the evolution of the models in the $w w'$ plane, we find that, if $c\geq1$, $w_{he}\geq-1$ and $\dot{V}<0$ keep for all time, which are quintessence-like. However, if $c<-1$, which mildly favors the current observations, $w_{he}$ evolves from $w_{he}>-1$ to $w_{he}<-1$, and the potential is a nonmonotonic function. In the earlier time, the potential must be rolled down, and then be climbed up. Considered the current constraint on the parameter $c$, we reconstruct the potential of the holographic hessence model.

astro-ph↗