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Liang Dai

Publications and source records attributed to Liang Dai.

At least 109 records · Page 6Linked to original sources
arXiv2016

Lensing of Fast Radio Bursts as a Probe of Compact Dark Matter

The possibility that part of the dark matter is made of massive compact halo objects (MACHOs) remains poorly constrained over a wide range of masses, and especially in the $20-100\, M_\odot$ window. We show that strong gravitational lensing of extragalactic fast radio bursts (FRBs) by MACHOs of masses larger than $\sim20\,M_\odot$ would result in repeated FRBs with an observable time delay. Strong lensing of an FRB by a lens of mass $M_L$ induces two images, separated by a typical time delay $\sim$ few $\times(M_L/30\, M_\odot)$ milliseconds. Considering the expected FRB detection rate by upcoming experiments, such as CHIME, of $10^4$ FRBs per year, we should observe from tens to hundreds of repeated bursts yearly, if MACHOs in this window make up all the dark matter. A null search for echoes with just $10^4$ FRBs, would constrain the fraction $f_{\rm DM}$ of dark matter in MACHOs to $f_{\rm DM}\lesssim 0.08$ for $M_L\gtrsim 20\,M_\odot$.

astro-ph.CO↗
arXiv2016

Sequential Monte Carlo Methods for System Identification

One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies.

stat.CO↗
arXiv2016

Antisymmetric galaxy cross-correlations as a cosmological probe

The auto-correlation between two members of a galaxy population is symmetric under the interchange of the two galaxies being correlated. The cross-correlation between two different types of galaxies, separated by a vector $\bf{r}$, is not necessarily the same as that for a pair separated by $-\bf{r}$. Local anisotropies in the two-point cross-correlation function may thus indicate a specific direction which when mapped as a function of position trace out a vector field. This vector field can then be decomposed into longitudinal and transverse components, and those transverse components written as positive- and negative-helicity components. A locally asymmetric cross-correlation of the longitudinal type arises naturally in halo clustering, even with Gaussian initial conditions, and could be enhanced with local-type non-Gaussianity. Early-Universe scenarios that introduce a vector field may also give rise to such effects. These antisymmetric cross-correlations also provide a new possibility to seek a preferred cosmic direction correlated with the hemispherical power asymmetry in the cosmic microwave background and to seek a preferred location associated with the CMB cold spot. New ways to seek cosmic parity breaking are also possible.

astro-ph.CO↗
arXiv2016

Search for Compensated Isocurvature Perturbations with Planck Power Spectra

In the standard inflationary scenario, primordial perturbations are adiabatic. The amplitudes of most types of isocurvature perturbations are generally constrained by current data to be small. If, however, there is a baryon-density perturbation that is compensated by a dark-matter perturbation in such a way that the total matter density is unperturbed, then this compensated isocurvature perturbation (CIP) has no observable consequence in the cosmic microwave background (CMB) at linear order in the CIP amplitude. Here we search for the effects of CIPs on CMB power spectra to quadratic order in the CIP amplitude. An analysis of the Planck temperature data leads to an upper bound $Δ_{\rm rms}^2 \leq 7.1\times 10^{-3}$, at the 68\% confidence level, to the variance $Δ_{\rm rms}^2$ of the CIP amplitude. This is then strengthened to $Δ_{\rm rms}^2\leq 5.0\times 10^{-3}$ if Planck small-angle polarization data are included. A cosmic-variance-limited CMB experiment could improve the $1σ$ sensitivity to CIPs to $Δ^2_{\rm rms} \lesssim 9\times 10^{-4}$. It is also found that adding CIPs to the standard $Λ$CDM model can improve the fit of the observed smoothing of CMB acoustic peaks just as much as adding a non-standard lensing amplitude.

astro-ph.CO↗
arXiv2015

Revisiting the anomalous bending elasticity of sharply bent DNA

Several recent experiments suggest that sharply bent DNA has a surprisingly high bending flexibility, but the cause of this flexibility is poorly understood. Although excitation of flexible defects can explain these results, whether such excitation can occur with the level of DNA bending in these experiments remains unclear. Intriguingly, the DNA contained preexisting nicks in most of these experiments but whether nicks might play a role in flexibility has never been considered in the interpretation of experimental results. Here, using full-atom molecular dynamics simulations, we show that nicks promote DNA basepair disruption at the nicked sites, which drastically reduces DNA bending energy. In addition, lower temperatures suppress the nick-dependent basepair disruption. In the absence of nicks, basepair disruption can also occur but requires a higher level of DNA bending. Therefore, basepair disruption inside B-form DNA can be suppressed if the DNA contains preexisting nicks. Overall, our results suggest that the reported mechanical anomaly of sharply bent DNA is likely dependent on preexisting nicks, therefore the intrinsic mechanisms of sharply bent nick-free DNA remain an open question.

physics.bio-ph↗
arXiv2015

On Separate Universes

(abridged version) The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in $Λ$CDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity $f_{\rm NL}^{\rm loc}$, and hence does not contribute to a scale-dependent galaxy bias $Δb \propto k^{-2}$ on large scales; rather, the locally measurable long-short mode coupling assumes a form essentially identical to subhorizon perturbation theory results, once the long-mode density perturbation is replaced by the synchronous-comoving gauge density perturbation. Apparent $f_{\rm NL}^{\rm loc}$-type contributions arise through projection effects on photon propagation, which depend on the specific large-scale structure tracer and observable considered, and are in principle distinguishable from the local mode coupling induced by gravity. We conclude that any observation of $f_{\rm NL}^{\rm loc}$ beyond these projection effects signals a departure from standard single-clock inflation.

astro-ph.CO↗
arXiv2015

Conformal Fermi Coordinates

Fermi Normal Coordinates (FNC) are a useful frame for isolating the locally observable, physical effects of a long-wavelength spacetime perturbation. Their cosmological application, however, is hampered by the fact that they are only valid on scales much smaller than the horizon. We introduce a generalization that we call Conformal Fermi Coordinates (CFC). CFC preserve all the advantages of FNC, but in addition are valid outside the horizon. They allow us to calculate the coupling of long- and short-wavelength modes on all scales larger than the sound horizon of the cosmological fluid, starting from the epoch of inflation until today, by removing the complications of the second order Einstein equations to a large extent, and eliminating all gauge ambiguities. As an application, we present a calculation of the effect of long-wavelength tensor modes on small scale density fluctuations. We recover previous results, but clarify the physical content of the individual contributions in terms of locally measurable effects and "projection" terms.

gr-qc↗
arXiv2015

On the exponential convergence of the Kaczmarz algorithm

The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a way that its solution path can be interpreted as the output from a particular dynamical system. The asymptotic stability results of the corresponding dynamical system can then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds.

eess.SY↗
arXiv2015

Detecting the integrated Sachs-Wolfe effect with high-redshift 21-cm surveys

We investigate the possibility to detect the integrated Sachs-Wolfe (ISW) effect by cross-correlating 21-cm surveys at high redshifts with galaxies, in a way similar to the usual CMB-galaxy cross-correlation. The high-redshift 21-cm signal is dominated by CMB photons that travel freely without interacting with the intervening matter, and hence its late-time ISW signature should correlate extremely well with that of the CMB at its peak frequencies. Using the 21-cm temperature brightness instead of the CMB would thus be a further check of the detection of the ISW effect, measured by different instruments at different frequencies and suffering from different systematics. We also study the ISW effect on the photons that are scattered by HI clouds. We show that a detection of the unscattered photons is achievable with planned radio arrays, while one using scattered photons will require advanced radio interferometers, either an extended version of the planned Square Kilometre Array or futuristic experiments such as a lunar radio array.

astro-ph.CO↗
arXiv2014

Spectral distortions from the dissipation of tensor perturbations

Spectral distortions of the cosmic microwave background (CMB) may become a powerful probe of primordial perturbations at small scales. Existing studies of spectral distortions focus almost exclusively on primordial scalar metric perturbations. Similarly, vector and tensor perturbations should source CMB spectral distortions. In this paper, we give general expressions for the effective heating rate caused by these types of perturbations, including previously neglected contributions from polarization states and higher multipoles. We then focus our discussion on the dissipation of tensors, showing that for nearly scale invariant tensor power spectra, the overall distortion is some six orders of magnitudes smaller than from the damping of adiabatic scalar modes. We find simple analytic expressions describing the effective heating rate from tensors using a quasi-tight coupling approximation. In contrast to adiabatic modes, tensors cause heating without additional photon diffusion and thus over a wider range of scales, as recently pointed out by Ota et. al 2014. Our results are in broad agreement with their conclusions, but we find that small-scale modes beyond k< 2x10^4 Mpc^{-1} cannot be neglected, leading to a larger distortion, especially for very blue tensor power spectra. At small scales, also the effect of neutrino damping on the tensor amplitude needs to be included.

astro-ph.CO↗
arXiv2014

The redshift-space galaxy two-point correlation function and baryon acoustic oscillations

Future galaxy surveys will measure baryon acoustic oscillations (BAOs) with high significance, and a complete understanding of the anisotropies of BAOs in redshift space will be important to exploit the cosmological information in BAOs. Here we describe the anisotropies that arise in the redshift-space galaxy two-point correlation function (2PCF) and elucidate the origin of features that arise in the dependence of the BAOs on the angle between the orientation of the galaxy pair and the line of sight. We do so with a derivation of the configuration-space 2PCF using streaming model. We find that, contrary to common belief, the locations of BAO peaks in the redshift-space 2PCF are anisotropic even in the linear theory. Anisotropies in BAO depend strongly on the method of extracting the peak, showing maximum 3 % angular variation. We also find that extracting the BAO peak of $r^2ξ(r,μ)$ significantly reduces the anisotropy to sub-percent level angular variation. When subtracting the tilt due to the broadband behavior of the 2PCF, the BAO bump is enhanced along the line of sight because of local infall velocities toward the BAO bump. Precise measurement of the angular dependence of the redshift-space 2PCF will allow new geometrical tests of dark energy beyond the BAO.

astro-ph.CO↗
arXiv2014

Reheating constraints to inflationary models

Evidence from the BICEP2 experiment for a significant gravitational-wave background has focussed attention on inflaton potentials $V(ϕ) \propto ϕ^α$ with $α=2$ ("chaotic" or "$m^2ϕ^2$" inflation) or with smaller values of $α$, as may arise in axion-monodromy models. Here we show that reheating considerations may provide additional constraints to these models. The reheating phase preceding the radiation era is modeled by an effective equation-of-state parameter $w_{\rm re}$. The canonical reheating scenario is then described by $w_{\rm re}=0$. The simplest $α=2$ models are consistent with $w_{\rm re} = 0$ for values of $n_s$ well within the current $1σ$ range. Models with $α=1$ or $α=2/3$ require a more exotic reheating phase, with $-1/3 1/3$, unless $n_s$ is close to the lower limit of the $2σ$ range. For $m^2ϕ^2$ inflation and canonical reheating as a benchmark, we derive a relation $\log_{10}\left(T_{\rm re}/10^6\,{\rm GeV} \right) \simeq 2000\,(n_s-0.96)$ between the reheat temperature $T_{\rm re}$ and the scalar spectral index $n_s$. Thus, if $n_s$ is close to its central value, then $T_{\rm re}\lesssim 10^6$~GeV, just above the electroweak scale. If the reheat temperature is higher, as many theorists may prefer, then the scalar spectral index should be closer to $n_s\simeq0.965$ (at the pivot scale $k=0.05\,{\rm Mpc}^{-1}$), near the upper limit of the $1σ$ error range. Improved precision in the measurement of $n_s$ should allow $m^2ϕ^2$, axion-monodromy, and $ϕ^4$ models to be distinguished, even without precise measurement of $r$, and to test the $m^2ϕ^2$ expectation of $n_s\simeq0.965$.

astro-ph.CO↗
arXiv2014

New operator approach to the CMB aberration kernels in harmonic space

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 $\ell$ and $m$, and the spin weight $s$. Further recursion relations express kernels of other Doppler weights $d \neq 1$ 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 non-linear 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 formulae 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.

astro-ph.CO↗
arXiv2014

Tensor-induced B modes with no temperature fluctuations

The recent indications for a tensor-to-scalar ratio $ r \simeq 0.2$ from BICEP2 measurements of the cosmic microwave background (CMB) B-mode polarization present some tension with upper limits $r \lesssim 0.1$ from measurements of CMB temperature fluctuations. Here we point out that tensor perturbations can induce B modes in the CMB polarization without inducing any temperature fluctuations nor E-mode polarization whatsoever, but only, at the expense of violating the Copernican principle. We present this mathematical possibility as a new ingredient for the model-builder's toolkit in case the tension between B modes and temperature fluctuations cannot be resolved with more conventional ideas.

astro-ph.CO↗
arXiv2014

Sparse Estimation From Noisy Observations of an Overdetermined Linear System

This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed estimator performs more efficiently than a traditional approach. The method consists of three steps: (1) a classical Least Squares Estimate (LSE), (2) the support is recovered through a Linear Programming (LP) optimization problem which can be computed using a soft-thresholding step, (3) a de-biasing step using a LSE on the estimated support set. The main contribution of this note is a formal derivation of an associated ORACLE property of the final estimate. That is, when the number of samples is large enough, the estimate is shown to equal the LSE based on the support of the {\em true} parameters.

eess.SY↗
arXiv2014

Linking the BICEP2 result and the hemispherical power asymmetry through spatial variation of $r$

For the simplest inflation models, the recent detection of a large primordial B-mode polarization signal by the BICEP2 experiment indicates a slight tension with the upper limit on the tensor-to-scalar ratio, $r$, from the Planck satellite. Here, we discuss spatially varying $r$ as a possible explanation for this discrepancy. This idea seems attractive since it may also explain part of the hemispherical temperature power asymmetry seen by WMAP and Planck at large angular scales. If these two aspects are indeed connected, the model suggests that in the Northern hemisphere $r$ should be much smaller, a hypothesis that could be confirmed with future B-mode experiments, providing a test for the stationarity of primordial tensor contributions across the sky. The BICEP2 measurement furthermore rules out that a simple dipolar modulation of $r$ alone can be responsible for the full hemispherical power asymmetry.

astro-ph.CO↗
arXiv2014

On the Nuclear Norm heuristic for a Hankel matrix Recovery Problem

This note addresses the question if and why the nuclear norm heuristic can recover an impulse response generated by a stable single-real-pole system, if elements of the upper-triangle of the associated Hankel matrix were given. Since the setting is deterministic, theories based on stochastic assumptions for low-rank matrix recovery do not apply here. A 'certificate' which guarantees the completion is constructed by exploring the structural information of the hidden matrix. Experimental results and discussions regarding the nuclear norm heuristic applied to a more general setting are also given.

eess.SY↗