arXiv subjects

Qing-Hua Zhu

Publications and source records attributed to Qing-Hua Zhu.

33 records · Page 2Linked to original sources

arXiv2023

New constraints on primordial non-Gaussianity from missing two-loop contributions of scalar induced gravitational waves

We analyze the energy density spectrum of \acp{SIGW} using the NANOGrav 15-year data set, thereby constraining the primordial non-Gaussian parameter $f_{\mathrm{NL}}$. For the first time, we calculate the seventeen missing two-loop diagrams proportional to $f_{\mathrm{NL}}A_ζ^3$ that correspond to the two-point correlation function $\langle h^{λ,(3)}_{\mathbf{k}} h^{λ',(2)}_{\mathbf{k}'} \rangle$ for local-type primordial non-Gaussianity. The total energy density spectrum of \acp{SIGW} can be significantly suppressed by these two-loop diagrams. If \acp{SIGW} dominate the \acp{SGWB} observed in \ac{PTA} experiments, the parameter interval $f_{\mathrm{NL}}\in [-5,-1]$ is notably excluded based on NANOGrav 15-year data set. After taking into account abundance of \acp{PBH} and the convergence of the cosmological perturbation expansion, we find that the only possible parameter range for $f_{\mathrm{NL}}$ might be $-1\le f_{\mathrm{NL}}< 0$.

astro-ph.CO↗

arXiv2023

Implications of Pulsar Timing Array Data for Scalar-Induced Gravitational Waves and Primordial Black Holes: Primordial Non-Gaussianity $f_{\mathrm{NL}}$ Considered

Multiple pulsar-timing-array collaborations have reported strong evidence for the existence of a gravitational-wave background. We study physical implications of this signal for cosmology, assuming that it is attributed to scalar-induced gravitational waves. By incorporating primordial non-Gaussianity $f_{\mathrm{NL}}$, we specifically examine the nature of primordial curvature perturbations and primordial black holes. We find that the signal allows for a primordial non-Gaussianity $f_{\mathrm{NL}}$ in the range of $-4.1\lesssim f_{\mathrm{NL}} \lesssim 4.1$ (68\% confidence intervals) and a mass range for primordial black holes $m_{\mathrm{pbh}}$ spanning from $\sim10^{-5}M_{\odot}$ to $\sim10^{-2}M_{\odot}$. Furthermore, we find that the signal favors a negative non-Gaussianity, which can suppress the abundance of primordial black holes. We also demonstrate that the anisotropies of scalar-induced gravitational waves serve as a powerful tool to probe the non-Gaussianity $f_{\mathrm{NL}}$. We conduct a comprehensive analysis of the angular power spectrum within the nano-Hertz band. Looking ahead, we anticipate that future projects, such as the Square Kilometre Array, will have the potential to measure these anisotropies and provide further insights into the primordial universe.

astro-ph.CO↗

arXiv2022

Overlap reduction function for gravitational wave detectors in an expanding Universe

Since it was confirmed two decades ago that the expansion of the Universe is accelerating, it would be of theoretical interests to figure out what is the influence from cosmological constant on detection of stochastic gravitational wave background. This paper studies the overlap reduction functions in de-Sitter space-time for a pair of one-way tracking gravitational wave detectors. It is shown to be non-trivial in an expanding Universe, because the propagation of light along line of sight also has effect on the response of GW detectors. It is found that the expansion of the Universe can enhance the value of magnitude of the overlap reduction functions, when the detector pairs are close to each other. For nanohertz gravitational waves, this effect can dominate the values of overlap reduction functions when the galactic pulsar pairs are separated by milliarcsecond.

gr-qc↗

arXiv2022

The Shadow of Supertranslated Schwarzschild Black Hole

The supertranslated black hole proposed by Hawking, Perry, and Strominger might provide a resolution to the information paradox, which is usually defined by a complicated space-time metric with even less space-time symmetries compared to Kerr black hole. In this paper, we figure out the shadow for the supertranslated Schwarzschild black hole by making use of supertranslated 4-velocities and the trajectories of the light rays. Based on this approach, we find that the photon sphere gets distorted due to the supertranslation hairs and the position of the shadow on the projection plane is shifted by the supertranslation vector, but the size and shape of the shadow remain the same as those of Schwarzschild black hole.

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arXiv2022

The Third Order Scalar Induced Gravitational Waves

Since the gravitational waves were detected by LIGO and Virgo, it has been promising that lots of information about the primordial Universe could be learned by further observations on stochastic gravitational waves background. The studies on gravitational waves induced by primordial curvature perturbations are of great interest. The aim of this paper is to investigate the third order induced gravitational waves. Based on the theory of cosmological perturbations, the first order scalar induces the second order scalar, vector and tensor perturbations. At the next iteration, the first order scalar, the second order scalar, vector and tensor perturbations all induce the third order tensor perturbations. We present the energy density spectrum of the third order gravitational waves for a monochromatic primordial power spectrum. The shape of the energy density spectrum of the third order gravitational waves is different from that of the second order scalar induced gravitational waves. And it is found that the third order gravitational waves sourced by the second order scalar perturbations dominate the energy density spectrum.

astro-ph.CO↗

arXiv2021

Note on gauge invariance of second order cosmological perturbations

We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are shown to be described by a finite number of bases that are gauge invariant. For the second order cosmological perturbations induced by the first order scalar perturbations, we explicitly represent the equations of motion of them in terms of the gauge invariant Newtonian, synchronous and hybrid variables, respectively.

astro-ph.CO↗

arXiv2021

The observer-dependent shadow of the Kerr black hole

Motivated by inclination of the Earth's orbit that is not located at galactic plane for observing the shadow of Sgr A*, we consider the black hole shadow for arbitrary inclinations and different velocities of observers. A surprising finding of the study is that rotation axis of a black hole might not be extracted from its shadow, since the ways of the shadow getting distorted depend not only on the spin of the black hole, but also velocities of observers. Namely, appearance of the shadow could be rotated by an angle in observers' celestial sphere due to the observer in motion. In order to further confirm this result, a formalism is presented for calculating the shadow in terms of the velocity perturbations. Besides, we also consider the Earth's orbit for the shadow of Sgr A* by making use of this formalism.

gr-qc↗

arXiv2020

Spatial variation of the fine-structure constant and Hubble's law in anisotropic coordinate of Friedmann-Lemaitre-Robertson-Walker space-time

Recent updated results of quasar spectra suggested a 3.9$σ$ significance of spatial variation of the fine-structure constant. Theoretically, it is important to examine whether the fine-structure constant, as a fundamental constant in quantum theory, is possible varying with space and time. In this paper, we explore the possibility that spatial variation of the fine-structure constant could be compatible with Einstein's general relativity. Namely, the spatially dependent fine-structure constant in the Universe could be originated in different values of the speed of light in separate local frames that are far away from us, since we have known that light rays must be bending in the present of gravity or non-inertial motions. In addition, to learn more about the anisotropic coordinate of FLRW space-time, we also study luminosity distance-redshift relation. It is found that there is a dipole structure in high redshift regime, while in low redshift regime, there is not such dipole.

gr-qc↗

arXiv2020

On the Gauge Invariance of Scalar Induced Gravitational Waves: Gauge Fixings Considered

The energy density spectrum is an observable of gravitational waves. Divergence has appeared in the energy density spectra of the scalar induced gravitational waves for different gauge fixings. To resolve the discrepancy, we investigate the gauge invariance of the scalar induced gravitational waves. It is shown that the gauge invariant induced gravitational waves can be obtained by subtracting the fictitious tensor perturbations via introducing the counter term composed of the first order scalar perturbations. The kernel function uniquely determines the energy density spectrum of the scalar induced gravitational waves. We explicitly calculate the gauge invariant kernel functions in the Newtonian gauge and the uniform density gauge, respectively. The discrepancy between the energy density spectra upon the Newtonian gauge and the uniform density gauge is shown to be eliminated in the gauge invariant framework. In fact, the gauge invariant approach is also available to other kinds of gauge fixings.

gr-qc↗

arXiv2020

Gauge Invariant Second Order Gravitational Waves

We investigate the gauge invariance of the second order gravitational waves induced by the first order scalar perturbations by following the Lie derivative method. It is shown explicitly that the second order gravitational waves are gauge invariant in the synchronous frame. In the gauge invariant framework, we derive the equation of motion of the second order gravitational waves and show that the second order gravitational waves are sourced from the first order scalar perturbations described well in the gauge invariant Newtonian frame. Since the observables of gravitational waves are measured in the synchronous frame, we define the energy density spectrum of the second order gravitational waves in terms of the gauge invariant synchronous variables. This way guarantees no fictitious tensor perturbations. It is shown that the gauge invariant energy density spectrum of the second order gravitational waves coincides with the one in the Newtonian gauge.

gr-qc↗

arXiv2020

Does the shape of the shadow of a black hole depend on motional status of an observer?

In a recent work on rotating black hole shadows [Phys. Rev. D{\bf 101}, 084029 (2020)], we proposed a new approach for calculating size and shape of the shadows in terms of astrometrical observables with respect to finite-distance observers. In this paper, we introduce a distortion parameter for the shadow shapes and discuss the appearance of the shadows of static spherical black holes and Kerr black holes in a uniform framework. We show that the shape of the shadow of a spherical black hole is circular in the view of arbitrary observers, and the size of the shadows tends to be shrunk in the view of a moving observer. The diameter of the shadows is contracted even in the direction perpendicular to the observers' motion. This seems not to be understood as length contraction effect in special relativity. The shape of Kerr black holes is dependent on motional status of observers located at finite distance. In spite of this, it is found that there is not a surrounding observer who could view the shape of the Kerr black hole shadows as circularity. These results could be helpful for observation of the Sagittarius A* in the centre of the Milky Way, as our solar system is moving around the centre black hole.

gr-qc↗

arXiv2020

Redshift drift in uniformly accelerated reference frame

We construct an alternative uniformly accelerated reference frame based on the 3+1 formalism in adapted coordinates. In this frame, time-dependent redshift drift exists between co-moving observers, which differs from that in Rindler coordinates. This phenomenon can be tested in laboratory and improve our understanding of non-inertial frames.

gr-qc↗

arXiv2020

Black hole shadow in the view of freely falling observers

First sketch of black hole from M87 galaxy was obtained by Event Horizon Telescope, recently. As appearance of black hole shadow reflects space-time geometry of black holes, observations of black hole shadow may be a promising way to test general relativity in strong field regime. In this paper, we focus on angular radius of spherical black hole shadow with respect to freely falling observers. In the framework of general relativity, aberration formulation and angular radius-gravitational redshift relation are presented. For the sake of intuitive, we consider parametrized Schwarzschild black hole and Schwarzschild-de Sitter black hole as representative examples. We find that the freely in-falling observers would observe finite size of shadow, when they go through inner horizon. For observers freely falling from the outer horizon of Schwarzschild-de Sitter black hole, we find that the angular radius of the shadows could increase even when the observers move farther from the black hole.

gr-qc↗

arXiv2020

Reference frame dependence of the local measurement of the Hubble constant

Observations recently suggest $4.4σ$ discrepancy between Hubble constant measured locally and that inferred from cosmic microwave background in standard cosmology. Either standard cosmology or local measurement might expect something new. We investigate the possibility that the value of Hubble constants might be affected by observers' motional status in the local measurement. Using adapted coordinate for geodesic observers in FLRW space-time and constraints inferred from observation of cosmic shear, we find that the motional status of reference frame could contribute to about $1.1 \pm 0.3\%$ discrepancy of these Hubble constants. Namely, the difference is $ΔH_0= 0.81\pm0.22$ km s$^{-1}$ Mpc$^{-1}$, if the locally measured Hubble constant is $ 74$ km s$^{-1}$ Mpc$^{-1}$. This effect seems not negligible as an uncertainty for local measurement of Hubble constant

gr-qc↗

arXiv2020

A revisit of rotating black hole shadow with astrometric observables

The first image of black hole in M87 galaxy taken by Event Horizon Telescope shows that directed observation of supermassive black holes would be a promising way to test general relativity in strong gravity field regime. In order to calculate shadow of rotating black holes with respect to observers located at finite distance, orthonormal tetrads have been introduced in previous works. However, it is noticed that different choice of tetrads does not lead to the same shape of shadow for observers in near regions. In this paper, we alternatively use formula of astrometric observables for calculating the shadow of a general rotating black hole with respect to these observers. For the sake of intuitive, we also consider Kerr-de Sitter black holes as a representative example. In this space-time, size and shape of Kerr-de Sitter black hole shadows are expressed as functions of distance between the black hole and observer. It is forecasted that the distortion of shadow would increase with distance.

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