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With the advent of gravitational-wave astronomy and the discovery of more compact binary coalescences, data quality improvement techniques are desired to handle the complex and overwhelming noise in gravitational wave (GW) observational data. Though recent studies have shown promising results for data denoising, they are unable to precisely recover both the GW signal amplitude and phase. To address such an issue, we develop a deep neural network centered workflow, WaveFormer, for significant noise suppression and signal recovery on observational data from the Laser Interferometer Gravitational- Wave Observatory (LIGO). The WaveFormer has a science-driven architecture design with hierarchical feature extraction across a broad frequency spectrum. As a result, the overall noise and glitch are decreased by more than 1 order of magnitude and the signal recovery error is roughly 1% and 7% for the phase and amplitude, respectively. Moreover, we achieve state-of-the-art accuracy on reported binary black hole events of existing LIGO observing runs and substantial 1386 years inverse false alarm rate improvement on average. Our work highlights the potential of large neural networks and can be extended to the data processing analyses of upcoming observing runs.

Physical review / D 107(2), 023021 (2023). doi:10.1103/PhysRevD.107.023021, Published by APS, Woodbury, NY

Gravitational waves (GWs) from tens of millions of compact binaries in our Milky Way enter the milli-Hertz band of space-based detection. The majority of them cannot be resolved individually, resulting in a foreground confusion noise for Laser Interferometer Space Antenna (LISA). The concept of Taiji mission is similar to LISA's with slightly better sensitivity, which means that the galactic GW signals will also affect the detection with Taiji. Here we generate the GW signals from 29.8 million galactic binaries for Taiji and subtract the `resolvable' sources. The confusion noise is estimated and fitted in an analytic form with 6-month, 1-year, 2-year and 4-year observation time. We find that the full sensitivity curve is slightly lower for Taiji than for LISA at frequencies of $\leq 0.8$ mHz and around 2~mHz. For a 4-year lifetime, more than 29 thousand sources are resolvable with Taiji. Compared to LISA, Taiji can subtract $\sim 20 \%$ more sources and the distribution of them in our Milky Way is consistent with that of the resolvable sources with LISA. At frequencies around 2~mHz or with the chirp masses ranging from $0.2 M_\odot$ to $0.4 M_\odot$, more sources become resolvable with Taiji., Comment: 7 pages, 5 figures. Version accepted by PRD

We investigate gravitational waves (GWs) generated in a two-field inflationary model with a non-canonical kinetic term, in which the gravitational Chern-Simons term is coupled to a heavy dynamical field. In such a model, primordial GWs experience a period of resonant amplification for some modes. In addition, isocurvature perturbations suffer from a temporary tachyonic instability due to an effective negative mass, which source curvature perturbations, resulting in large induced GWs. These two stochastic gravitational wave backgrounds correspond to different frequency bands, which are expected to be detected by future GW detectors such as SKA, LISA and Taiji.

The Hubble tension seems to be a crisis with $\sim5\sigma$ discrepancy between the most recent local distance ladder measurement from type Ia supernovae calibrated by Cepheids and the global fitting constraint from the cosmic microwave background data. To narrow down the possible late-time solutions to the Hubble tension, we have used in a recent study [Phys. Rev. D 105, L021301 (2022)] an improved inverse distance ladder method calibrated by the absolute measurements of the Hubble expansion rate at high redshifts from the cosmic chronometer data, and found no appealing evidence for new physics at the late time beyond the $\Lambda$CDM model characterized by a parametrization based on the cosmic age. In this paper, we further investigate the perspective of this improved inverse distance ladder method by including the late-time matter perturbation growth data. Independent of the dataset choices, model parametrizations, and diagnostic quantities ($S_8$ and $S_{12}$), the new physics at the late time beyond the $\Lambda$CDM model is strongly disfavored so that the previous late-time no-go guide for the Hubble tension is further strengthened., Comment: v1, 15 pages, 4 figures, 6 tables; v2, 16 pages, 5 figures, 6 tables, covariance matrix added for the cosmic chronometer data, accepted for publication in Physical Review D; v3, to match the published version

In this perspective, we outline that a space borne gravitational wave detector network combining LISA and Taiji can be used to measure the Hubble constant with an uncertainty less than 0.5% in ten years, compared with the network of the ground based gravitational wave detectors which can measure the Hubble constant within a 2% uncertainty in the next five years by the standard siren method. Taiji is a Chinese space borne gravitational wave detection mission planned for launch in the early 2030 s. The pilot satellite mission Taiji-1 has been launched in August 2019 to verify the feasibility of Taiji. The results of a few technologies tested on Taiji-1 are presented in this paper. Gravitational wave astronomy has opened the door to test general relativity and the effect of gravity in the Universe. The authors present the capabilities of an overlap between space gravitational wave detectors LISA and Taiji to constrain the Hubble constant to 0.5%, in 10 years, and what can be learned from the satellite pilot Taiji-1 launched in 2019.

The nonattractor evolution in ultra-slow-roll (USR) inflation results in the amplification of superhorizon curvature perturbations and then induces a strong and detectable stochastic gravitational wave background. In this letter, we search for such a stochastic gravitational wave background in data from the third LIGO-Virgo observing run and place constraints on the USR inflationary models. The $e$-folding number of the USR phase are constrained to be $\Delta N \lesssim 2.9$ at the 95% confidence level and the power spectrum of curvature perturbations amplified during the USR phase is constrained to be $\log_{10}P_{R\mathrm{p}}, Comment: 6 pages, 3 figures

Extending the electromagnetic and gravitational radiations from binary black holes with electric and magnetic charges in circular orbits in Phys. Rev. D {\bf 102}, 103520 (2020), we calculate the total emission rates of energy and angular momentum due to gravitational and electromagnetic radiations from dyonic binary black holes in precessing elliptical orbits. It is shown that the emission rates of energy and angular momentum due to gravitational and electromagnetic radiations have the same dependence on the conic angle for different orbits. Moreover, we obtain the evolutions of orbits and find that a circular orbit remains circular while an elliptic orbit becomes quasi-circular due to electromagnetic and gravitational radiations. Using the evolution of orbits, we derive the waveform models for dyonic binary black hole inspirals and show the amplitudes of the gravitational waves for dyonic binary black hole inspirals differ from those for Schwarzschild binary black hole inspirals, which can be used to test electric and magnetic charges of black holes., Comment: 10 pages, 2 figures, a new section added

It has been a half-decade since the first direct detection of gravitational waves, which signifies the coming of the era of the gravitational-wave astronomy and gravitational-wave cosmology. The increasing number of the detected gravitational-wave events has revealed the promising capability of constraining various aspects of cosmology, astronomy, and gravity. Due to the limited space in this review article, we will briefly summarize the recent progress over the past five years, but with a special focus on some of our own work for the Key Project ``Physics associated with the gravitational waves'' supported by the National Natural Science Foundation of China. In particular, (1) we have presented the mechanism of the gravitational-wave production during some physical processes of the early Universe, such as inflation, preheating and phase transition, and the cosmological implications of gravitational-wave measurements; (2) we have put constraints on the neutron star maximum mass according to GW170817 observations; (3) we have developed a numerical relativity algorithm based on the finite element method and a waveform model for the binary black hole coalescence along an eccentric orbit., v1, 93 pages, 18 figures, prepared as a status review of project report for Sci. China Phys. Mech. Astron.; v2, 95 pages, minor revision, references added, accepted for publication in Sci. China Phys. Mech. Astron; v3, to match the published version

The Hubble tension, if not caused by any systematics, could be relieved or even resolved from modifying either the early-time or late-time Universe. The early-time modifications are usually in tension with either galaxy clustering or galaxy lensing constraints. The late-time modifications are also in conflict with the constraint from the inverse distance ladder, which, however, is weakened by the dependence on a sound-horizon prior and some particular approximation for the late-time expansion history. To achieve a more general no-go argument for the late-time scenarios, we propose to use a global parametrizationbased on the cosmic age (PAge) to consistently use the cosmic chronometers data beyond the Taylor expansion domain and without the input of a sound-horizon prior. Both the early-time and late-time scenarios are therefore largely ruled out, indicating the possible ways out of the Hubble tension from either exotic modifications of our concordance Universe or some unaccounted systematics., v1, 5 pages + appendices, 4 figures, 4 tables; v2, references added; v3, version accepted for publication as a Letter in Phys. Rev. D; v4, to match the published version

Parametric resonance in a single-field inflationary model with a periodic structure on the potential gives rise to curvature perturbations with large amplitudes on small scales, which could result in observable primordial black holes (PBHs) and concomitant gravitational waves (GWs) induced by curvature perturbations in the radiation-dominated era. In such a model, GWs associated with the PBH formation were investigated in Ref. [1]. In this paper, we consider a stochastic GW background sourced by inflaton perturbations resonantly amplified during inflation. We compute the energy spectra of induced GWs produced both during inflation and in the radiation-dominated era, and find that the peak of the energy spectrum of the former is much higher than that of the latter, but is located at a lower frequency. Moreover, the energy spectrum of induced GWs produced during inflation exhibits a unique oscillating character in the ultraviolet region. Both the stochastic GW backgrounds are expected to be detected by future space-based laser interferometers., 13 pages,1 figure

We investigate the stochastic gravitational wave background (SGWB) from cosmic domain walls (DWs) caused by quantum fluctuations of a light scalar field $\phi$ during inflation. Perturbations of $\phi$ remain almost constant after leaving the Hubble horizon. The probabilities of the two domains depend on the averaged value of $\phi$ at each large scale region, leading to large scale perturbations of DW energy density and large anisotropies in the SGWB. We find that the angular power spectrum is scale-invariant and at least of the order of $10^{-2}$, which is expected to be detected by future gravitational-wave (GW) detectors. Since we have not detected primordial GWs yet, anisotropies of the SGWB could help us to verify the rationality of inflation and determine the energy scale of inflation., Comment: 6 pages, 2 figures

Values of the Hubble constant between the direct measurements from various independent local observations and that inferred from the cosmic microwave background with the $\Lambda$-cold-dark-matter model are in tension with persistent significance. We propose a late-time inhomogeneous resolution suggesting that a chameleon field coupled to a local overdensity of matter could be trapped at a higher potential energy density as an effective cosmological constant driving the local expansion rate faster than that of the background with lower matter density. We illustrate this mechanism in a toy model in which a region with only $20\%$ overdensity of matter is sufficient to resolve the Hubble tension, and the Hubble constant measured by the local distance ladders could be accommodated by the chameleon coupled to the observed overdensities from the large-scale structure surveys., Comment: v4, to match the published version in Physical Review D as a Letter

Stochastic gravitational wave backgrounds (SGWBs) receive increasing attention and provide a new possibility to directly probe the early Universe. In the preheating process at the end of inflation, parametric resonance can generate large energy density perturbations and efficiently produce gravitational waves (GWs) which carry unique information about inflation. Since the peak frequency of such GWs is approximately proportional to the inflationary energy scale, $\Lambda_{\mathrm{inf}}$, GWs from preheating are expected to be observed by interferometer GW detectors in low-scale inflationary models. We investigate the dependence of the amplitude of such GWs on $\Lambda_{\mathrm{inf}}$, and find that the present energy spectrum of these GWs does not depend on $\Lambda_{\mathrm{inf}}$ only in the case of $\Lambda_{\mathrm{inf}}$ is above a critical value $\Lambda_{c}$, a parameter depending on the resonance strength. We numerically obtain $\Lambda_{c}$ in terms of the model parameters in linear approximation and then conduct lattice simulations to verify this result. For $\Lambda_{\mathrm{inf}}\lesssim\Lambda_{c}$, the amplitude of GWs quickly decreases with $\Lambda_{\mathrm{inf}}$ and becomes challenging to observe. In turn, observing such GWs in interferometer detectors also helps to determine $\Lambda_{\mathrm{inf}}$ and the resonance strength during the preheating., Comment: 9 pages, 7 figures

Primordial curvature perturbations with a large enough amplitude on small scales can lead to two kinds of gravitational waves which are expected to be detected by multiband gravitational-wave observations. One is induced due to the nonlinear coupling of the curvature perturbation to tensor perturbation while the other is produced by coalescences of binary primordial black holes formed when the scalar perturbations reenter the horizon in the radiation dominant era. In this letter, we identify the relation of peak frequency for the spectra of such two stochastic gravitational-wave backgrounds. This peak frequency relation offers a new criterion for the existence of primordial black holes. Moreover, the relation provides a new method for measuring the Hubble constant $H_0$ through multiband observations of stochastic gravitational-wave backgrounds. Such a method does not need the redshift information which is necessary in the standard siren method., 6 pages, 2 figures; modified title, updated references

Primordial black holes (PBHs) produced in the early Universe have attracted wide interest for their ability to constitute dark matter and explain the compact binary coalescence. We propose a new mechanism of PBH production during first-order phase transitions (PTs) and find that PBHs are naturally produced during PTs model-independently. Because of the randomness of the quantum tunneling, there always exists some probability that the vacuum decay is postponed in a whole Hubble volume. Since the vacuum energy density remains constant while radiation is quickly redshifted in the expanding Universe, the postponed vacuum decay then results in overdense regions, which finally collapse into PBHs as indicated by numerical simulations. Utilizing this result one can obtain mutual predictions and constraints between PBHs and GWs from PTs. The predicted mass function of PBHs is nearly monochromatic. We investigate two typical cases and find that 1) PBHs from a PT constitute all dark matter and GWs peak at $1$Hz, 2) PBHs from a PT can explain the coalescence events observed by LIGO-Virgo collaboration, and meanwhile GWs can explain the common-spectrum process detected by NANOGrav collaboration., Comment: 7 pages, 2 figures

The Hubble parameter is one of the central parameters in modern cosmology, which describes the present expansion rate of the universe. Their values inferred from the late-time observations are systematically higher than those from the early-time measurements by about $10\%$. To come to a robust conclusion, independent probes with accuracy at percent levels are crucial. Gravitational waves from compact binary coalescence events can be formulated into the standard siren approach to provide an independent Hubble parameter measurement. The future space-borne gravitational wave observatory network, such as the LISA-Taiji network, will be able to measure the gravitational wave signals in the Millihertz bands with unprecedented accuracy. By including several statistical and instrumental noises, we show that within 5 years operation time, the LISA-Taiji network is able to constrain the Hubble parameter within $1\%$ accuracy, and possibly beats the scatters down to $0.5\%$ or even better., 15 pages, 6 figures

We derive the equations of motion of dyonic black hole binaries with electric and magnetic charges and explore features of static orbits. By using a Newtonian method with the inclusion of radiation reaction, we calculate the total emission rate of energy and angular momentum due to gravitational radiation and electromagnetic radiation for circular orbits. Moreover, we obtain the evolutions of orbits and calculate merger times of dyonic binaries. We show that electric and magnetic charges significantly suppress the merger times of dyonic binaries. Our results provide rich information about dyonic binaries and can be used to test black holes with magnetic charges., V1,11 pages, 8 figures; V2, 13pages, 8 figures, title changed, PRD version

The ultra-slow-roll (USR) inflationary models predict large-amplitude scalar perturbations at small scales which can lead to the primordial black hole production and scalar-induced gravitational waves. In general scalar perturbations in the USR models can only be obtained using numerical method because the usual slow-roll approximation breaks. In this work, we propose an analytical approach to estimate the scalar spectrum which is consistent with the numerical result. We find that the USR inflationary models predict a peak with power-law slopes in the scalar spectrum and energy spectrum of gravitational waves, and we derive the expression of the spectral indexes in terms of the inflationary potential. In turn, the inflationary potential near the USR regime can be reconstructed from the negative spectral index of the gravitational wave energy spectrum., Comment: 7 pages, 3 figures

Both LISA and Taiji, planned space-based gravitational-wave detectors in orbit around the Sun, are expected to launch in 2030-2035. Assuming a one-year overlap, we explore a potential LISA-Taiji network to fast and accurately localize the gravitational-wave sources., 6 pages. 2 figures

We investigate the formation of primordial black holes (PBHs) from the collapse of spherically symmetric domain wall bubbles, which spontaneously nucleate via quantum tunneling during inflation. Since the tension of domain walls changes with time and so domain walls nucleate in a short time interval, the mass function of PBHs in general has a spike-like structure. In contrast to models in which PBHs produced from overdense regions, our model avoids the uncertainties of PBHs production mechanism. PBHs from domain walls with mass around $10^{20}\mathrm{g}$ may constitute all dark matter, those with mass around $10^{34}\mathrm{g}$ can explain the merger events of binary black holes detected by LIGO., Comment: 7 pages, 4 figures

We study the production of gravitational waves from primordial scalar perturbations in double-inflection-point inflation, in which one of the inflection points leads to a primordial power spectrum consistent with CMB observations at large scales and the other generates a large peak in the power spectrum of scalar perturbations at small scales. We calculate the energy spectrum of the reduced gravitational waves and find that the gravitational-wave signal can be detected by future space-based laser interferometers.

Space-based gravitational-wave detectors consist of a triangle of three spacecraft, which makes it possible to detect polarization modes of gravitational waves due to the motion of the detectors in space. In this paper we explore the ability of Taiji to detect the polarization modes in the parametrized post-Einsteinian framework. Assuming massive black hole binaries with the total mass of $M=4\times10^5\,M_{\odot}$ at redshift of $z=1$, we find that Taiji can measure the dipole and quadruple emission ($\Delta\alpha_D/\alpha_D$ and $\Delta\alpha_Q/\alpha_Q$) with the accuracy of up to $\sim 0.04\%$, with the fiducial value of $\alpha_D=0.001$, the scalar transverse and longitudinal modes ($\Delta\alpha_B$ and $\Delta\alpha_L$) up to $\sim 0.01$, and the vector modes ($\Delta\alpha_V$) up to $\sim 0.0005$., Comment: 17 pages, 3 figures. v2: published version

The increasing tension between the different local direct measurements of the Hubble expansion rate and that inferred from the Cosmic Microwave Background observation by $\Lambda$-Cold-Dark-Matter model could be a smoking gun of new physics, if not caused by either observational systematics or local bias. We generalize previous investigation on the local bias from a local void by globally fitting the Pantheon sample over all parameters in the radial profile function of a local void described by an inhomogeneous but isotropic Lema\^{i}tre-Tolman-Bondi metric with a cosmological constant. Our conclusion strengths the previous studies that the current tension on Hubble constant cannot be saved by a local void alone., Comment: 9 pages, 5 figures, to match the published version

We investigate the effect of the cuspiness of scalar potentials on the production of gravitational waves during oscillon formation after inflation. We consider a more general form of potentials with a mass parameter $M$, which repoduce cuspy potentials for fields much larger than $M$, and smooth potentials in the opposite limit. For cuspy potentials, nonsmooth oscillations of the inflaton induce an amplification of the inflaton fluctuations at the bottom of the potential, so that oscillons copiously form, which leads to a significant stochastic gravitational wave background with a double-peak spectrum. By varying the parameter $M$, we find that cuspy potentials yield stronger signals of gravitational waves and the generation of gravitational waves disappears for smooth potentials. Moreover, we calculate the equation of state after inflation and find the presence of a quasi matter-dominated stage right before the transition to the radiation-dominated stage., 13 pages, 9 figures

We develop a formalism to calculate the merger rate density of primordial black hole binaries with a general mass function, by taking into account the merger history of primordial black holes. We apply the formalism to three specific mass functions, monochromatic, power-law and log-normal cases. In the former case, the merger rate density is dominated by the single-merger events, while in the latter two cases, the contribution of the multiple-merger events on the merger rate density can not be ignored. The effects of the merger history on the merger rate density depend on the mass function., Comment: 9 pages, 7 figures; V2, references added, discussion added, title changed. v3, a new subsection added

We develop an analytic formalism for computing the merger rate of primordial black hole binaries with a general mass function by taking into account the torques by the surrounding primordial black holes and linear density perturbations. We find that $\alpha=-(m_{i}+m_{j})^2\partial^{2} \ln {\mathcal R}(m_{i},m_{j})/\partial m_{i} \partial m_{j}=36/37$ is independent of the mass function. Moreover, the ratio of the merger rate density of primordial black hole binaries by taking into account the torques by the surrounding primordial black holes to by the nearest primordial black hole is independent of the masses of binaries., Comment: V1,7 pages, 2 figures; V2, references added, submitted to Phys.Rev.D; V3, Phys.Rev.D; V4. Journal reference and DOI added

We review potential low-frequency gravitational-wave sources, which are expected to be detected by Taiji, a Chinese space-based gravitational-wave detector, estimate the detection rates of these gravitational-wave sources and present the parameter estimation of massive black hole binaries., Comment: 15 pages, for the strain sensitivity of Taiji please send an email to

The space gravitational wave (GW) antennae is more sensitive to the lower frequency GW signals compare with the ground-based GW detectors. The space mission Taiji is designed to detect the GW sources within frequencies between 0.1 mHz and 1 Hz. A preliminary study of Taiji was started in 2008. Up to now, a sophisticated mission design of Taiji have gradually taken shape. The research and development of the key technologies for Taiji is now officially launched. A brief introduction to the analysis and the pre-work of the Taiji technology are given here.

We propose a double inflection points inflationary model in supergravity with a single chiral superfield. Such a model allows for the generation of primordial black holes (PBHs) at small scales, which can account for a significant fraction of dark matter. Moreover, in vacuum it is possible to give a small and adjustable supersymmetry breaking with a tiny cosmological constant.

In this paper, we simulate Super-Eddington accreting massive black holes (SEAMBHs) as the candles to probe cosmology for the first time. SEAMBHs have been demonstrated to be able to provide a new tool for estimating cosmological distance. Thus, we create a series of mock data sets of SEAMBHs, especially in the high redshift region, to check their abilities to probe the cosmology. To fulfill the potential of the SEAMBHs on the cosmology, we apply the simulated data to three projects. The first is the exploration of their abilities to constrain the cosmological parameters, in which we combine different data sets of current observations such as the cosmic microwave background from {\it Planck} and type Ia supernovae from Joint Light-curve Analysis (JLA). We find that the high redshift SEAMBHs can help to break the degeneracies of the background cosmological parameters constrained by {\it Planck} and JLA, thus giving much tighter constraints of the cosmological parameters. The second uses the high redshift SEAMBHs as the complements of the low redshift JLA to constrain the early expansion rate and the dark energy density evolution in the cold dark matter frame. Our results show that these high redshift SEAMBHs are very powerful on constraining the early Hubble rate and the evolution of the dark energy density; thus they can give us more information about the expansion history of our Universe, which is also crucial for testing the $\Lambda$CDM model in the high redshift region. Finally, we check the SEAMBH candles' abilities to reconstruct the equation of state of dark energy at high redshift. In summary, our results show that the SEAMBHs, as the rare candles in the high redshift region, can provide us a new and independent observation to probe cosmology in the future., Comment: 11 pages, 7 figures. The version published in PRD

We investigate the constraints on the reionization history of the Universe from a joint analysis of the cosmic microwave background and neutral hydrogen fraction data. The $\tanh$ parametrization and principal component analysis methods are applied to the reionization history respectively. The commonly used $\tanh$ parametrization is oversimplistic when the neutral hydrogen fraction data are taken into account. Using the principal component analysis method, the reconstructed reionization history is consistent with the neutral hydrogen fraction data. With the principal component analysis method, we reconstruct the neutral hydrogen fraction at $z=9.75$ as $x_{\text{HI}}=0.69^{+0.30}_{-0.32}$ for $6, Comment: 11 pages, 9 figures

We study the production of gravitational waves during oscillations of the inflaton around the minimum of a cuspy potential after inflation. We find that a cusp in the potential can trigger copious oscillon formation, which sources a characteristic energy spectrum of gravitational waves with double peaks. The discovery of such a double-peak spectrum could test the underlying inflationary physics., Comment: 5 pages,4 figures Accepted for publication in Phys. Rev. Lett

We investigate constraints on Lorentz invariance violation in the neutrino sector from a joint analysis of big bang nucleosynthesis and the cosmic microwave background. The effect of Lorentz invariance violation during the epoch of big bang nucleosynthesis changes the predicted helium-4 abundance, which influences the power spectrum of the cosmic microwave background at the recombination epoch. In combination with the latest measurement of the primordial helium-4 abundance, the Planck 2015 data of the cosmic microwave background anisotropies give a strong constraint on the deformation parameter since adding the primordial helium measurement breaks the degeneracy between the deformation parameter and the physical dark matter density., 10 pages, 8 figure

The direct detection of gravitational wave by Laser Interferometer Gravitational-Wave Observatory indicates the coming of the era of gravitational-wave astronomy and gravitational-wave cosmology. It is expected that more and more gravitational-wave events will be detected by currently existing and planned gravitational-wave detectors. The gravitational waves open a new window to explore the Universe and various mysteries will be disclosed through the gravitational-wave detection, combined with other cosmological probes. The gravitational-wave physics is not only related to gravitation theory, but also is closely tied to fundamental physics, cosmology and astrophysics. In this review article, three kinds of sources of gravitational waves and relevant physics will be discussed, namely gravitational waves produced during the inflation and preheating phases of the Universe, the gravitational waves produced during the first-order phase transition as the Universe cools down and the gravitational waves from the three phases: inspiral, merger and ringdown of a compact binary system, respectively. We will also discuss the gravitational waves as a standard siren to explore the evolution of the Universe., v1, 37 pages, 7 figures, invited review for National Science Review; v2, revised version to match the online publication version

We consider the process of magnetogenesis in the context of nonsingular bounce cosmology. We show that large primordial magnetic fields can be generated during contraction without encountering strong coupling and backreaction issues. The fields may seed large-scale magnetic fields with observationally interesting strengths. This result leads to a theoretical constraint on the relation of the energy scale of the bounce cosmology to the number of effective $e$-foldings of the contracting phase in the case of scale invariance for the power spectrum of primordial magnetic fields. We show that this constraint can be satisfied in a sizable region of the parameter space for the nonsingular bounce cosmology.

We introduce a model-independent approach to the null test of the cosmic curvature which is geometrically related to the Hubble parameter $H(z)$ and luminosity distance $d_L(z)$. Combining the independent observations of $H(z)$ and $d_L(z)$, we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and determine the cosmic curvature $\Omega_K^{(0)}$ in the null test relation. The null test is totally geometrical and without assuming any cosmological model. We show that the cosmic curvature $\Omega_K^{(0)}=0$ is consistent with current observational data sets, falling within the $1\sigma$ limit. To demonstrate the effect on the precision of the null test, we produce a series of simulated data of the models with different $\Omega_K^{(0)}$. Future observations in better quality can provide a greater improvement to constrain or refute the flat universe with $\Omega_K^{(0)}=0$., Comment: To match the published version

We develop a new model-independent method to probe the constancy of the speed of light $c$. In our method, the degeneracy between the cosmic curvature and the speed of light can be eliminated, which makes the test more natural and general. Combining the independent observations of Hubble parameter $H(z)$ and luminosity distance $d_L(z)$, we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and then detect variation of the speed of light. We find no signal of deviation from the present value of the speed of light $c_0$. Moreover, to demonstrate the improvement in probing the constancy of the speed of light from future experiments, we produce a series of simulated data. The Dark Energy Survey will be able to detect $\Delta c /c_0 \sim 1\%$ at $\sim 1.5\sigma$ confidence level and $\Delta c /c_0 \sim 2\%$ at $\sim 3\sigma$ confidence level. If the errors are reduced to one-tenth of the expected DES ones, it can detect a $\Delta c /c_0 \sim 0.1\%$ variation at $\sim 2\sigma$ confidence level., Comment: 10 pages, several corrections and updates to match the published version

We study cosmological solutions in the low-energy effective heterotic string theory, which is the Einstein gravity with Gauss-Bonnet term and the dilaton. We show that the field equations are cast into an autonomous system for flat internal and external spaces, and derive all the fixed points in the system. We also examine the time evolution of the solutions and whether the solutions can give (transient) accelerated expansion of our four-dimensional space in the Einstein frame., Comment: 18 pages, 10 figures, PTPTeX, accepted for publication in PTP

We consider a new generalized Chaplygin gas model that includes the original Chaplygin gas model as a special case. In such a model the generalized Chaplygin gas evolves as from dust to quiessence or phantom. We show that the background evolution for the model is equivalent to that for a coupled dark energy model with dark matter. The constraints from the current type Ia supernova data favour a phantom-like Chaplygin gas model., 8 pages, 3 figures, LaTeX2e, Accepted for publication in Phys. Lett. B