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When gravitational waves (GWs) pass by a massive object on its way to Earth, a strong gravitational lensing effect will happen. Thus, the GW signal will be amplified, deflected, and delayed in time. Through analyzing the lensed GW waveform, physical properties of the lens can be inferred. On the other hand, neglecting lensing effects in the analysis of GW data may induce systematic errors in the estimating of source parameters. As a space-borne GW detector, TianQin will be launched in the 2030s. It is expected to detect dozens of mergers of massive black hole binaries (MBHBs) as far as z=15 and thus will have high probability to detect at least one lensed event during the mission lifetime. In this article, we discuss the capability of TianQin to detect lensed MBHB signals. Three lens models are considered in this work: the point mass model, the singular isothermal sphere (SIS) model, and the Navarro-Frenk-White (NFW) model. The sensitive frequency band for space-borne GW detectors is around millihertz, and the corresponding GW wavelength could be comparable to the lens gravitational length scale, which requires us to account for wave diffraction effects. In calculating lensed waveforms, we adopt the approximation of geometric optics at high frequencies to accelerate computation, while precisely evaluating the diffraction integral at low frequencies. Through a Fisher analysis, we analyze the accuracy to estimate the lens parameters. We find that the accuracy can reach to the level of 10-3 for the mass of point mass and SIS lens and to the level of 10-5 for the density of the NFW lens. We also assess the impact on the accuracy of estimating the source parameters and find that the improvement of the accuracy is dominated by the increasing of signal-to-noise ratio.

Compensated isocurvature perturbations (CIPs) are perturbations to the primordial baryon density that are accompanied by dark-matter-density perturbations so that the total matter density is unperturbed. Such CIPs, which may arise in some multifield inflationary models, can be long-lived and only weakly constrained by current cosmological measurements. Here we show that the CIP-induced modulation of the electron number density interacts with the electron-temperature fluctuation associated with primordial adiabatic perturbations to produce, via the Biermann-battery mechanism, a magnetic field in the post-recombinaton Universe. Assuming the CIP amplitude saturates the current BBN bounds, this magnetic field can be stronger than 10-15 nG at z≃20 and stronger by an order of magnitude than that (produced at second order in the adiabatic-perturbation amplitude) in the standard cosmological model, and thus can serve as a possible seed for galactic dynamos.

Correlated red noise recently reported from pulsar timing observations may be an indication of stochastic gravitational waves emitted by cosmic strings that formed during a primordial phase transition near the grand unification energy scale. Unfortunately, known probes of cosmic strings, namely the cosmic microwave background anisotropies and string lensing of extragalactic galaxies, are not sensitive enough for low dimensionless string tensions of Gμc-2=10-10-10-7 (where the tension μ is the string energy per unit length) that are needed to explain this putative signal. We show that strong gravitational lensing of fast radio bursts (FRBs) by cosmic strings is a potentially unambiguous avenue to probe that range of string tension values. The image pair of string lensing are expected to have identical magnification factor and parity, and have a typical time delay of ∼102(G μ c-2/10-8)2 s. The unique spectral fingerprint of each FRB, as well as the possibility to detect correlations in the time series of the electric field of the radio waves, will enable verification of the string lensing interpretation. Very-long-baseline interferometry observations can spatially resolve the image pair and provide a lower bound on the string tension based on the image separation. We calculate the FRB lensing rate as a function of the FRB detection number for several different models of the FRB redshift distribution. We find that a survey detecting ∼105 FRBs, in line with estimates for the detection rate of the forthcoming survey CHORD, can uncover a strong lensing event for a string tension of Gμ c-2≃10-7. Larger FRB surveys, such as Phase 2 of the Square Kilometre Array, have the potential to significantly improve the sensitivity on the string tension to Gμ c-2≃10-9.

We present a reanalysis of GW151226, the second binary black hole merger discovered by the LIGO-Virgo Collaboration. Previous analysis showed that the best-fit waveform for this event corresponded to the merger of a ∼14 M⊙ black hole with a ∼7.5 M companion, and the posterior distribution in mass ratio (q≤1) is rather flat. In this work, we perform parameter estimation using a waveform model that includes the effects of orbital precession and higher-order radiative multipole modes, and we find that the source parameters of GW151226 shift toward the low q and high effective spin (χeff) region and that q is better measured. The new solution has a log likelihood roughly two points higher than when either higher multipoles or orbital precession is neglected and can alter the astrophysical interpretation of GW151226. Additionally, we find it useful to use a flat-in-χeff prior, which does not penalize the large |χeff| region, in order to uncover the higher likelihood region for GW151226. Our solution has several interesting properties: (a) the secondary black hole mass is close to the upper limit of the hypothesized lower mass gap of astrophysical black hole population; and (b) orbital precession is driven by the primary black hole spin, which has a dimensionless magnitude as large as ∼0.85 and is tilted away from the orbital angular momentum at an angle of ∼57°. Since GW151226 is a relatively weak signal, an unambiguous claim of the detection of these effects in the signal cannot be made.

Faster likelihood evaluation enhances the efficiency of gravitational wave signal analysis. We present mode-by-mode relative binning, a new method designed for obtaining fast and accurate likelihoods for advanced waveform models that include spin-orbit precession effects and multiple radiation harmonics from compact binary coalescence. Leveraging the "twisting-up"procedure of constructing precessing waveform modes from nonprecessing ones, the new method mitigates degrade of relative binning accuracy due to interference from superimposed modes. Additionally, we supplement algorithms for optimizing the choice of frequency bins specific to any given strain signal under analysis. Using the new method, we are able to evaluate the likelihood with up to an order of magnitude reduction in the number of waveform model calls per frequency compared to the previously used relative binning scheme, and achieve better likelihood accuracy than is sufficient for obtaining source parameter posterior distributions that are indistinguishable from the exact ones.

We introduce a new technique to search for gravitational wave events from compact binary mergers that produce a clear signal only in a single gravitational wave detector, and marginal signals in other detectors. Such a situation can arise when the detectors in a network have different sensitivities, or when sources have unfavorable sky locations or orientations. We start with a short list of loud single-detector triggers from regions of parameter space that are empirically unaffected by glitches (after applying signal-quality vetoes). For each of these triggers, we compute evidence for astrophysical origin from the rest of the detector network by coherently combining the likelihoods from all detectors and marginalizing over extrinsic geometric parameters. We report the discovery of two new binary black hole (BBH) mergers in the second observing run of Advanced LIGO and Virgo (O2), in addition to the ones that were reported in [B. P. Abbott (LIGO Scientific and Virgo Collaborations), Phys. Rev. X 9, 031040 (2019)PRXHAE2160-330810.1103/PhysRevX.9.031040 and [T. Venumadhav, Phys. Rev. D 101, 083030 (2020)PRVDAQ2470-001010.1103/PhysRevD.101.083030]. We estimate that the two events have false alarm rates of one in 19 years (60 O2) and one in 11 years (36 O2). One of the events, GW170817A, has primary and secondary masses m1src=56-10+16 M⊙ and m2src=40-11+10 M⊙ in the source frame. The existence of GW170817A should be very informative about the theoretically predicted upper mass gap for stellar mass black holes. Its effective spin parameter is measured to be χeff=0.5±0.2, which is consistent with the tendency of the heavier detected BBH systems to have large and positive effective spin parameters. The other event, GWC170402, will be discussed thoroughly in future work.

Searches for gravitational waves crucially depend on exact signal processing of noisy strain data from gravitational wave detectors, which are known to exhibit significant nonstationary and non-Gaussian behavior. In this paper, we study two distinct effects in the LIGO/Virgo data that reduce the sensitivity of searches: first, variations in the noise power spectral density (PSD) on timescales of more than a few seconds; and second, loud and abrupt transient "glitches"of terrestrial or instrumental origin. We derive a simple procedure to correct, at first order, the effect of the variation in the PSD on the search background. Given the knowledge of the existence of localized glitches, in particular segments of data, we also develop a method to insulate statistical inference from these glitches, so as to cleanly excise them without affecting the search background in neighboring seconds. We show the importance of applying these methods on the publicly available LIGO data and estimate an increase in the detection volume of at least 15% from the PSD-drift correction alone, due to the improved background distribution.

The intergalactic medium is expected to be at its coldest point before the formation of the first stars in the Universe. Motivated by recent results from the EDGES experiment, we revisit the standard calculation of the kinetic temperature of the neutral gas through this period. When the first ultraviolet (UV) sources turn on, photons redshift into the Lyman lines of neutral hydrogen and repeatedly scatter within the Lyman-α line. They heat the gas via atomic recoils, and, through the Wouthuysen-Field effect, set the spin temperature of the 21-cm hyperfine (spin-flip) line of atomic hydrogen in competition with the resonant cosmic microwave background (CMB) photons. We show that the Lyman-α photons also mediate energy transfer between the CMB photons and the thermal motions of the hydrogen atoms. In the absence of x-ray heating, this new mechanism is the major correction to the temperature of the adiabatically cooling gas (∼10% at z=17), and is several times the size of the heating rate found in previous calculations. We also find that the effect is more dramatic in nonstandard scenarios that either enhance the radio background above the CMB or invoke new physics to cool the gas in order to explain the EDGES results. The coupling with the radio background can reduce the depth of the 21-cm absorption feature by almost a factor of 2 relative to the case with no sources of heating, and prevent the feature from developing a flattened bottom. As an inevitable consequence of the UV background that generates the absorption feature, this heating should be accounted for in any theoretical prediction.

Gravitational waves emitted from compact binary coalescence can be subject to wave diffraction if they are gravitationally lensed by an intervening mass clump whose Schwarzschild time scale matches the wave period. Waves in the ground-based frequency band f∼10-103 Hz are sensitive to clumps with masses ME∼102-103 M enclosed within the impact parameter. These can be the central parts of low mass ML∼103-106 M dark matter halos, which are predicted in cold dark matter scenarios but are challenging to observe. Neglecting finely-tuned impact parameters, we focus on lenses aligned generally on the Einstein scale for which multiple lensed images may not form in the case of an extended lens. In this case, diffraction induces amplitude and phase modulations whose sizes ∼10%-20% are small enough so that standard matched filtering with unlensed waveforms do not degrade, but are still detectable for events with high signal-to-noise ratio. We develop and test an agnostic detection method based on dynamic programming, which does not require a detailed model of the lensed waveforms. For pseudo-Jaffe lenses aligned up to the Einstein radius, we demonstrate that a pair of fully upgraded aLIGO/Virgo detectors can extract diffraction imprints from binary black hole mergers out to zs∼0.2-0.3. The prospect will improve dramatically for a third-generation detector for which binary black hole mergers out to zs∼2-4 will all become valuable sources.

The recent detection of gravitational waves indicates that stellar-mass black hole binaries are likely to be a key population of sources for forthcoming observations. With future upgrades, ground-based detectors could detect merging black hole binaries out to cosmological distances. Gravitational-wave bursts from high redshifts (z≳1) can be strongly magnified by gravitational lensing due to intervening galaxies along the line of sight. In the absence of electromagnetic counterparts, the mergers' intrinsic mass scale and redshift are degenerate with the unknown magnification factor μ. Hence, strongly magnified low-mass mergers from high redshifts appear as higher-mass mergers from lower redshifts. We assess the impact of this degeneracy on the mass-redshift distribution of observable events for generic models of binary black hole formation from normal stellar evolution, Pop III star remnants, or a primordial black hole population. We find that strong magnification (μ≳3) generally creates a heavy tail of apparently massive mergers in the event distribution from a given detector. For LIGO and its future upgrades, this tail may dominate the population of intrinsically massive, but unlensed mergers in binary black hole formation models involving normal stellar evolution or primordial black holes. Modeling the statistics of lensing magnification can help account for this magnification bias when testing astrophysical scenarios of black hole binary formation and evolution.

Aberration kernels describe how harmonic-space multipole coefficients of cosmic microwave background (CMB) observables transform under Lorentz boosts of the reference frame. For spin-weighted CMB observables, transforming like the CMB temperature (i.e., Doppler weight d=1), we show that the aberration kernels are the matrix elements of a unitary boost operator in harmonic space. Algebraic properties of the rotation and boost generators then give simple, exact recursion relations that allow us to raise or lower the multipole quantum numbers ? and m and the spin weight s. Further recursion relations express kernels of other Doppler weights d≠1 in terms of the d=1 kernels. From those we show that on the full sky, to all orders in β=v/c, E- and B-mode polarization observables do not mix under aberration if and only if d=1. The new relations, fully nonlinear in the boost velocity β, form the basis of a practical recursive algorithm to accurately compute any aberration kernel. In addition, we develop a second, fast algorithm in which aberration kernels are obtained using a set of ordinary differential equations. This system can also be approximately solved at small scales, providing simple asymptotic formulas for the aberration kernels. The results of this work will be useful for further studying the effect of aberration on future CMB temperature and polarization analysis and might provide a basis for relativistic radiative transfer schemes. © 2014 American Physical Society.

Inflationary models predict a correlation between primordial density perturbations (scalar metric perturbations) and gravitational waves (tensor metric perturbations) in the form of a scalar-scalar-tensor three-point correlation, or bispectrum in Fourier space. The squeezed limit of this bispectrum implies a quadrupolar asymmetry in the observed local power spectrum for matter and galaxies. Here we show (like others before) that an infrared divergence in the amplitude of this power asymmetry predicted in single-field slow-roll models is canceled by projection effects when considering the observed power spectrum. We then further evaluate the nonzero, but finite, residual quadrupolar power asymmetry that remains after the divergences are canceled. While the quadrupolar power asymmetry is small, it is conceptually important. Our calculation moreover clarifies how the predictions for this power asymmetry may change in models with different scalar-scalar-tensor bispectra, and shows that convincing detection of the quadrupolar power asymmetry would rule out the single-field slow-roll models of inflation. © 2013 American Physical Society.

Most calculations in cosmological perturbation theory, including those dealing with the inflationary generation of perturbations, their time evolution, and their observational consequences, decompose those perturbations into plane waves (Fourier modes). However, for some calculations, particularly those involving observations performed on a spherical sky, a decomposition into waves of fixed total angular momentum (TAM) may be more appropriate. Here we introduce TAM waves-solutions of fixed total angular momentum to the Helmholtz equation-for three-dimensional scalar, vector, and tensor fields. The vector TAM waves of given total angular momentum can be decomposed further into a set of three basis functions of fixed orbital angular momentum, a set of fixed helicity, or a basis consisting of a longitudinal (L) and two transverse (E and B) TAM waves. The symmetric traceless rank-2 tensor TAM waves can be similarly decomposed into a basis of fixed orbital angular momentum or fixed helicity, or a basis that consists of a longitudinal (L), two vector (VE and VB, of opposite parity), and two tensor (TE and TB, of opposite parity) waves. We show how all of the vector and tensor TAM waves can be obtained by applying derivative operators to scalar TAM waves. This operator approach then allows one to decompose a vector field into three covariant scalar fields for the L, E, and B components and symmetric-traceless-tensor fields into five covariant scalar fields for the L, VE, VB, TE, and TB components. We provide projections of the vector and tensor TAM waves onto vector and tensor spherical harmonics. We provide calculational detail to facilitate the assimilation of this formalism into cosmological calculations. As an example, we calculate the power spectra of the deflection angle for gravitational lensing by density perturbations and by gravitational waves. We comment on an alternative approach to cosmic microwave background fluctuations based on TAM waves. An accompanying paper will work out three-point functions in terms of TAM waves and their relation to the usual Fourier-space bispectra. Our work may have applications elsewhere in field theory and in general relativity. © 2012 American Physical Society.