arXiv subjects

Matias Zaldarriaga

Publications and source records attributed to Matias Zaldarriaga.

At least 91 records · Page 5Linked to original sources

arXiv2019

Constraints on Binary Black Hole Populations from LIGO-Virgo Detections

We reanalyse the LIGO-Virgo strain data of the 10 binary black hole mergers reported to date and compute the likelihood function in terms of chirp mass, mass ratio and effective spin. We discuss the strong degeneracy between mass ratio and spin for the three lighter events. We use this likelihood and an estimate of the horizon volume as a function of intrinsic parameters to constrain the properties of the population of merging binary black holes. The data disfavour large spins. Typical spins are constrained to $\overline a \lesssim 0.4$, even if the underlying population has randomly-oriented spins. For aligned spins the constraints are tighter, with typical spins required to be around $\overline a\sim 0.1$ and have comparable dispersion. We detect no statistically significant tendency towards a positive average spin in the direction of the orbital angular momentum. We put an upper limit on the fraction of systems where the secondary could have been tidally locked prior to the formation of the black holes (corresponding to merger times shorter than $10^8$ years) $f \lesssim 0.3$. Four events are consistent with having a maximally-spinning secondary, although one only marginally. We confirm previous findings that there is a hint of a cutoff at high mass. The data favour distributions of mass ratios with an average $\overline q \gtrsim 0.7$.

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arXiv2018

Beyond the traditional Line-of-Sight approach of cosmological angular statistics

We present a new efficient method to compute the angular power spectra of large-scale structure observables that circumvents the numerical integration over Bessel functions, expanding on a recently proposed algorithm based on FFTlog. This new approach has better convergence properties. The method is explicitly implemented in the CLASS code for the case of number count $C_\ell$'s (including redshift-space distortions, weak lensing, and all other relativistic corrections) and cosmic shear $C_\ell$'s. In both cases our approach speeds up the calculation of the exact $C_\ell$'s (without the Limber approximation) by a factor of order 400 at a fixed precision target of 0.1%.

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arXiv2018

Exploring the posterior surface of the large scale structure reconstruction

The large scale structure (LSS) of the universe is generated by the linear density gaussian modes, which are evolved into the observed nonlinear LSS. The posterior surface of the modes is convex in the linear regime, leading to a unique global maximum (MAP), but this is no longer guaranteed in the nonlinear regime. In this paper we investigate the nature of posterior surface using the recently developed MAP reconstruction method, with a simplified but realistic N-body simulation as the forward model. The reconstruction method uses optimization with analytic gradients from back-propagation through the simulation. For low noise cases we recover the initial conditions well into the nonlinear regime ($k\sim 1$ h/Mpc) nearly perfectly. We show that the large scale modes can be recovered more precisely than the linear expectation, which we argue is a consequence of nonlinear mode coupling. For noise levels achievable with current and planned LSS surveys the reconstruction cannot recover very small scales due to noise. We see some evidence of non-convexity, specially for smaller scales where the non-injective nature of the mappings: several very different initial conditions leading to the same near perfect final data reconstruction. We investigate the nature of these phenomena further using a 1-d toy gravity model, where many well separated local maximas are found to have identical data likelihood but differ in the prior. We also show that in 1-d the prior favors some solutions over the true solution, though no clear evidence of these in 3-d. Our main conclusion is that on very small scales and for a very low noise the posterior surface is multi-modal and the global maximum may be unreachable with standard methods, while for realistic noise levels in the context of the current and next generation LSS surveys MAP optimization method is likely to be nearly optimal.

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arXiv2018

Implication of the Shape of the EDGES Signal for the 21 cm Power Spectrum

We revisit the 21 cm power spectrum from the epoch of cosmic dawn in light of the recent EDGES detection of the 21 cm global signal at frequencies corresponding to $z\sim20$. The shape of the signal suggests that the spin temperature of neutral hydrogen was coupled to the kinetic temperature of the gas relatively rapidly ($19\lesssim z \lesssim 21$). We therefore consider models in which the UV photons were dominantly produced in the rarest and most massive halos ($M\gtrsim 10^9M_\odot$), since their abundance grows fast enough at those redshifts to account for this feature of the signal. We show that these models predict large power spectrum amplitudes during the inhomogeneous coupling, and then inhomogeneous heating by CMB and Lyman-$α$ photons due to the large shot noise associated with the rare sources. The power spectrum is enhanced by more than an order of magnitude compared to previous models which did not include the shot noise contribution, making it a promising target for upcoming radio interferometers that aim to detect high-redshift 21 cm fluctuations.

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arXiv2018

Heating of the intergalactic medium by the cosmic microwave background during cosmic dawn

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 ($\sim 10 \%$ 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 non-standard 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 two 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.

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arXiv2017

Efficient Evaluation of Cosmological Angular Statistics

Angular statistics of cosmological observables are hard to compute. The main difficulty is due to the presence of highly-oscillatory Bessel functions which need to be integrated over. In this paper, we provide a simple and fast method to compute the angular power spectrum and bispectrum of any observable. The method is based on using an FFTlog algorithm to decompose the momentum-space statistics onto a basis of power-law functions. For each power law, the integrals over Bessel functions have a simple analytical solution. This allows us to efficiently evaluate these integrals, independently of the value of the multipole $\ell$. In particular, this method significantly speeds up the evaluation of the angular bispectrum compared to existing methods. To illustrate our algorithm, we compute the galaxy, lensing and CMB temperature angular power spectrum and bispectrum.

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arXiv2017

Dynamical Tides Reexpressed

Zahn (1975) first put forward and calculated in detail the torque experienced by stars in a close binary systems due to dynamical tides. His widely used formula for stars with radiative envelopes and convective cores is expressed in terms of the stellar radius, even though the torque is actually being applied to the convective core at the core radius. This results in a large prefactor, which is very sensitive to the global properties of the star, that multiplies the torque. This large factor is compensated by a very small multiplicative factor, $E_{2}$. Although this is mathematically accurate, depending on the application this can lead to significant errors. The problem is even more severe, since the calculation of $E_{2}$ itself is non-trivial, and different authors have obtained inconsistent values of $E_{2}$. Moreover, many codes (e.g. BSE, StarTrack, MESA) interpolate (and sometimes extrapolate) a fit of $E_{2}$ values to the stellar mass, often in regimes where this is not sound practice. We express the torque in an alternate form, cast in terms of parameters at the envelope-core boundary and a dimensionless coefficient, $β_{2}$. Previous attempts to express the torque in such a form are either missing an important factor, which depends on the density profile of the star, or are not easy to implement. We show that $β_{2}$ is almost independent of the properties of the star and its value is approximately unity. Our formula for the torque is simple to implement and avoids the difficulties associated with the classic expression.

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arXiv2017

Cosmological Perturbation Theory Using the FFTLog: Formalism and Connection to QFT Loop Integrals

We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a $Λ$CDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

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arXiv2017

Phases of New Physics in the BAO Spectrum

We show that the phase of the spectrum of baryon acoustic oscillations (BAO) is immune to the effects of nonlinear evolution. This suggests that any new physics that contributes to the initial phase of the BAO spectrum, such as extra light species in the early universe, can be extracted reliably at late times. We provide three arguments in support of our claim: First, we point out that a phase shift of the BAO spectrum maps to a characteristic sign change in the real space correlation function and that this feature cannot be generated or modified by nonlinear dynamics. Second, we confirm this intuition through an explicit computation, valid to all orders in cosmological perturbation theory. Finally, we provide a nonperturbative argument using general analytic properties of the linear response to the initial oscillations. Our result motivates measuring the phase of the BAO spectrum as a robust probe of new physics.

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arXiv2017

The Effective Field Theory of Large-Scale Structure in the presence of Massive Neutrinos

We develop a formalism to analytically describe the clustering of matter in the mildly non-linear regime in the presence of massive neutrinos. Neutrinos, whose free streaming wavenumber ($k_{\rm fs}$) is typically longer than the non-linear scale ($k_{\rm NL}$) are described by a Boltzmann equation coupled to the effective fluid-like equations that describe dark matter. We solve the equations expanding in the neutrino density fraction $(f_ν)$ and in $k/ k_{\rm NL}$, and add suitable counterterms to renormalize the theory. This allows us to describe the contribution of short distances to long-distance observables. Equivalently, we construct an effective Boltzmann equation where we add additional terms whose coefficients renormalize the contribution from short-distance physics. We argue that neutrinos with $k_{\rm fs}\gtrsim k_{\rm NL}$ require an additional counterterm similar to the speed of sound ($c_s$) for dark matter. We compute the one-loop total-matter power spectrum, and find that it is roughly equal to $16f_ν$ times the dark matter one for $k$'s larger that the typical $k_{\rm fs}$. It is about half of that for smaller $k$'s. The leading contribution results from the back-reaction of the neutrinos on the dynamics of the dark matter. The counterterms contribute in a hierarchical way: the leading ones can either be computed in terms of $c_s$, or can be accounted for by shifting $c_s$ by an amount proportional to $f_ν$.

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arXiv2017

Research Note: The Expected Spins of Gravitational Wave Sources With Isolated Field Binary Progenitors

We explore the consequences of dynamical evolution of field binaries composed of a primary black hole (BH) and a Wolf-Rayet (WR) star in the context of gravitational wave (GW) source progenitors. We argue, from general considerations, that the spin of the WR-descendent BH will be maximal in a significant number of cases due to dynamical effects. In other cases, the spin should reflect the natal spin of the primary BH which are currently theoretically unconstrained. We argue that the three currently published LIGO systems (GW150914, GW151226, LVT151012) suggest that this spin is small. The resultant effective spin distribution of gravitational wave sources should thus be bi-model if this classic GW progenitor channel is indeed dominant. While this is consistent with the LIGO detections thus far, it is in contrast to the three best-measured high-mass x-ray binary (HMXB) systems. A comparison of the spin distribution of HMXBs and GW sources should ultimately reveal whether or not these systems arise from similar astrophysical channels.

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arXiv2016

GW150914: Spin based constraints on the merger time of the progenitor system

We explore the implications of the observed low spin of GW150914 within the context of stellar astrophysics and progenitor models. We conclude that many of the recently proposed scenarios are in marked tension with this observation. We derive a simple model for the observed spin in the case that the progenitor system was a field binary composed of a black hole (BH) and a Wolf-Rayet star and explore the implications of the observed spin for this model. The spin observation allows us to place a lower limit for the delay time between the formation of the BH+BH binary and the actual merger, $t_{\textrm{merge}}$. We use typical values for these systems to derive $t_{\textrm{merge}}\gtrsim10^{8}\,\textrm{yr}$, which proves to be an important diagnostic for different progenitor models. We anticipate the next series of events, and the associated spin parameters, will ultimately yield critical constraints on formation scenarios and on stellar parameters describing the late-stage evolution of massive stars.

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arXiv2016

The Effective Field Theory of Large Scale Structure at Two Loops: the apparent scale dependence of the speed of sound

We study the Effective Field Theory of Large Scale Structure for cosmic density and momentum fields. We show that the finite part of the two-loop calculation and its counterterms introduce an apparent scale dependence for the leading order parameter $c_\text{s}^2$ of the EFT starting at k=0.1 h/Mpc. These terms limit the range over which one can trust the one-loop EFT calculation at the 1 % level to k<0.1 h/Mpc at redshift z=0. We construct a well motivated one parameter ansatz to fix the relative size of the one- and two-loop counterterms using their high-k sensitivity. Although this one parameter model is a very restrictive choice for the counterterms, it explains the apparent scale dependence of $c_\text{s}^2$ seen in simulations. It is also able to capture the scale dependence of the density power spectrum up to k$\approx$ 0.3 h/Mpc at the 1 % level at redshift $z=0$. Considering a simple scheme for the resummation of large scale motions, we find that the two loop calculation reduces the need for this IR-resummation at k<0.2 h/Mpc. Finally, we extend our calculation to momentum statistics and show that the same one parameter model can also describe density-momentum and momentum-momentum statistics.

astro-ph.CO↗

arXiv2016

LSS constraints with controlled theoretical uncertainties

Forecasts and analyses of cosmological observations often rely on the assumption of a perfect theoretical model over a defined range of scales. We explore how model uncertainties and nuisance parameters in perturbative models of the matter and galaxy spectra affect constraints on neutrino mass and primordial non-Gaussianities. We provide a consistent treatment of theoretical errors and argue that their inclusion is a necessary step to obtain realistic cosmological constraints. We find that galaxy surveys up to high redshifts will allow a detection of the minimal neutrino mass and local non-Gaussianity of order unity, but improving the constraints on equilateral non-Gaussianity beyond the CMB limits will be challenging. We argue that similar considerations apply to analyses where theoretical models are based on simulations.

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arXiv2016

Equivalence Principle and the Baryon Acoustic Peak

We study the dominant effect of a long wavelength density perturbation $δ(λ_L)$ on short distance physics. In the non-relativistic limit, the result is a uniform acceleration, fixed by the equivalence principle, and typically has no effect on statistical averages due to translational invariance. This same reasoning has been formalized to obtain a "consistency condition" on the cosmological correlation functions. In the presence of a feature, such as the acoustic peak at $l_{\rm BAO}$, this naive expectation breaks down for $λ_L<l_{\rm BAO}$. We calculate a universal piece of the three-point correlation function in this regime. The same effect is shown to underlie the spread of the acoustic peak, and is calculable to all orders in the long modes. This can be used to improve the result of perturbative calculations - a technique known as "infra-red resummation" - and is explicitly applied to the one-loop calculation of power spectrum. Finally, the success of BAO reconstruction schemes is argued to be another empirical evidence for the validity of the results.

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arXiv2015

Implications of the scalar tilt for the tensor-to-scalar ratio

We investigate the possible implications of the measured value of the scalar tilt $n_s$ for the tensor-to-scalar ratio $r$ in slow-roll, single-field inflationary models. The measured value of the tilt satisfies $n_s -1\sim 1/N_*$, where $N_* \sim 60$ is the number of $e$-folds for observationally relevant scales. If this is not a coincidence and the scaling holds for different values of $N$, it strongly suggests that either $r$ is as big as $10^{-1}$ (a possibility in tension with the recent data), or smaller than $10^{-2}$ and exponentially dependent on $n_s$. A large region of the ($n_s$,$r$) plane is not compatible with this scaling.

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arXiv2015

Detecting Primordial $B$-Modes after Planck

We update the forecasts for the measurement of the tensor-to-scalar ratio $r$ for various ground-based experiments (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloons (EBEX 10k and Spider) and satellites (CMBPol, COrE and LiteBIRD), taking into account the recent Planck data on polarized dust and using a component separation method. The forecasts do not change significantly with respect to previous estimates when at least three frequencies are available, provided foregrounds can be accurately described by few parameters. We argue that a theoretically motivated goal for future experiments is $r\sim2\times10^{-3}$, and that this is achievable if the noise is reduced to $\sim1\,μ$K-arcmin and lensing is reduced to $10\%$ in power. We study the constraints experiments will be able to put on the frequency and $\ell$-dependence of the tensor signal as a check of its primordial origin. Futuristic ground-based and balloon experiments can have good constraints on these parameters, even for $r\sim2\times10^{-3}$. For the same value of $r$, satellites will marginally be able to detect the presence of the recombination bump, the most distinctive feature of the primordial signal.

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arXiv2015

Lagrangian Formulation of the Eulerian-EFT

We study the counter terms in the Eulerian version of the EFT of Large Scale Structure. We reformulate the equations to solve for the displacement of fluid elements as a bookkeeping variable and study the structure of the counter terms in this formulation. We show that in many cases the time dependence of the amplitude of the counter terms is irrelevant, as solutions obtained for various time dependences differ by terms that can be reabsorbed by higher order counter terms. We show that including all effects due to the non-locality in time and the time dependence of the counter terms there are six new parameters relevant for the two loop power spectrum calculation. We give explicit expressions for all these terms and study the contributions to them from large and small modes. We show that the shape of all these terms is very similar.

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