arXiv subjects

Jaiyul Yoo

Publications and source records attributed to Jaiyul Yoo.

At least 37 records · Page 2Linked to original sources

arXiv2021

Cutting out the cosmological middle man: General Relativity in the light-cone coordinates

Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the FLRW coordinates constitutes an efficient tool for the former task, but the latter is dramatically simpler in light-cone-adapted coordinates that trivialize the light rays towards the observer world-line. Here we point out that time evolution and observable reconstruction can be combined into a single computation that relates directly initial conditions to observables. This is possible if one works uniquely in such light-cone coordinates, thus completely bypassing the FLRW "middle-man" coordinates. We first present in detail these light-cone coordinates, extending and generalizing the presently available material in the literature, and construct a particularly convenient subset for cosmological perturbation theory. We then express the Einstein and energy-momentum conservation equations in these coordinates at the fully non-linear level. This is achieved through a careful 2+1+1 decomposition which leads to relatively compact expressions and provides good control over the geometrical interpretation of the involved quantities. Finally, we consider cosmological perturbation theory to linear order, paying attention to the remaining gauge symmetries and consistently obtaining gauge-invariant equations. Moreover, we show that it is possible to implement statistical homogeneity on stochastic fluctuations, despite the fact that the coordinate system privileges the observer world-line.

gr-qc↗

arXiv2020

Galaxy Power Spectrum in General Relativity

We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to $k^{-4}P_m(k)$ or $k^{-2}P_m(k)$ on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at $k\lesssim k_{eq}$, they need to be taken into account in the analysis of large-scale data.

astro-ph.CO↗

arXiv2020

Tetrad formalism for exact cosmological observables

The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be taken into account for reliable results at non-linear orders. This can be accomplished by introducing an orthonormal basis, or "tetrad", at the observer point, representing the frame with respect to which observations are performed. In this work we consider the tetrad formulation of General Relativity, thus associating tetrads to sources as well, and develop a new formalism for describing cosmological observables associated with localized sources. It is based on a manifold which we call the "observer space-time", whose coordinates are the proper time, redshift and angles an observer uses to parametrize measurements, and on which the rest of the observables are defined. This manifold does not have to be diffeomorphic to the true space-time and allows us to resolve caustics in the latter, in contrast to similar coordinate-based formalisms. As a concrete example, we work out the definitions and equations for the angular diameter distance, weak lensing and number count observables. As for the observables associated to the CMB, they lie inside the phase space distribution of the photon fluid, so we also revisit the construction of general-relativistic matrix kinetic theory from the tetrad formalism viewpoint. Here too the latter appears as the natural approach for relating the macroscopic dynamics to the microscopic quantum field theory, and therefore for constructing the matrix Boltzmann equations, without any approximation on the gravitational side. (... more in the manuscript)

astro-ph.CO↗

arXiv2020

General and consistent statistics for cosmological observations

This paper focuses on two aspects of the statistics of cosmological observables that are important for the next stages of precision cosmology. First, we note that the theory of reduced angular $N$-point spectra has only been developed in detail up to the trispectrum case and in a fashion that makes it difficult to go beyond. To fill this gap, here we present a constructive approach that provides a systematic description of reduced angular $N$-point spectra and their covariance matrices, for arbitrary $N$. Second, we focus on the common practice in the literature on cosmological observables, which consists in simply discarding a part of the expression, namely, the terms containing fields evaluated at the observer position. We point out that this is not justified beyond linear order in perturbation theory, as these terms contribute to all the multipoles of the corresponding spectra and with a magnitude that is of the same order as the rest of the non-linear corrections. We consider the possibility that the reason for neglecting these terms is a conceptual discomfort when using ensemble averages, which originates in an apparent tension between the ergodic hypothesis and the privileged position of the observer on the light-cone. We clarify this subtle issue by performing a careful derivation of the relation between the theoretical statistical predictions and the observational estimators for all $N$. We conclude that there is no inconsistency whatsoever in ensemble-averaging fields at and near the observer position, thus clearing the way for consistent and robust high-precision calculations.

astro-ph.CO↗

arXiv2020

Maximum Cosmological Information from Type-Ia Supernova Observations

Type-Ia supernova observations yield estimates of the luminosity distance, which includes not only the background luminosity distance, but also the fluctuation due to inhomogeneities in the Universe. In particular, the spatial correlation of the host galaxies is a dominant source of the fluctuation in the luminosity distance measurements. Utilizing the recent theoretical framework that accurately quantifies the information contents accounting for the three-dimensional correlation of the observables on the past-light cone, we compute the maximum cosmological information obtainable from idealized supernova surveys as a function of maximum redshift $z_m$. Here we consider two cosmological parameters $Ω_m$ and $w_0$ and show that these parameters can be constrained at maximum 1% levels in an idealized survey with $z_m=1$. We discuss how these fundamental limits set by cosmic variance can be overcome.

astro-ph.CO↗

arXiv2019

$\bar T$: A New Cosmological Parameter?

The background photon temperature $\bar T$ is one of the fundamental cosmological parameters. Despite its significance, $\bar T$ has never been allowed to vary in the data analysis, owing to the precise measurement of the comic microwave background (CMB) temperature by COBE FIRAS. However, even in future CMB experiments, $\bar T$ will remain unknown due to the unknown monopole contribution $Θ_0$ at our position to the observed (angle-averaged) temperature $\langle T\rangle^{\rm obs}$. By fixing $\bar T\equiv\langle T\rangle^{\rm obs}$, the standard analysis underestimates the error bars on cosmological parameters, and the best-fit parameters obtained in the analysis are biased in proportion to the unknown amplitude of $Θ_0$. Using the Fisher formalism, we find that these systematic errors are smaller than the error bars from the $Planck$ satellite. However, with $\bar T\equiv\langle T\rangle^{\rm obs}$, these systematic errors will always be present and irreducible, and future cosmological surveys might misinterpret the measurements.

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arXiv2019

Cosmological Information Contents on the Light-Cone

We develop a theoretical framework to describe the cosmological observables on the past light cone such as the luminosity distance, weak lensing, galaxy clustering, and the cosmic microwave background anisotropies. We consider that all the cosmological observables include not only the background quantity, but also the perturbation quantity, and they are subject to cosmic variance, which sets the fundamental limits on the cosmological information that can be derived from such observables, even in an idealized survey with an infinite number of observations. To quantify the maximum cosmological information content, we apply the Fisher information matrix formalism and spherical harmonic analysis to cosmological observations, in which the angular and the radial positions of the observables on the light cone carry different information. We discuss the maximum cosmological information that can be derived from five different observables: (1) type Ia supernovae, (2) cosmic microwave background anisotropies, (3) weak gravitational lensing, (4) local baryon density, and (5) galaxy clustering. We compare our results with the cosmic variance obtained in the standard approaches, which treat the light cone volume as a cubic box of simultaneity. We discuss implications of our formalism and ways to overcome the fundamental limit.

astro-ph.CO↗

arXiv2018

Galaxy Two-Point Correlation Function in General Relativity

We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off $(k_{\text{IR}} \leq H_0)$ in computing the gravitational potential contribution. Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge. We find that the terms at the observer position such as the coordinate lapses and the observer velocity (missing in the standard formalism) dominate over the other relativistic contributions in the conformal Newtonian gauge such as the source velocity, the gravitational potential, the integrated Sachs-Wolf effect, the Shapiro time-delay and the lensing convergence. Compared to the standard Newtonian theoretical predictions that consider only the density fluctuation and redshift-space distortions, the relativistic effects in galaxy clustering result in a few percent-level systematic errors beyond the scale of the baryonic acoustic oscillation. Our theoretical and numerical study provides a comprehensive understanding of the relativistic effects in the galaxy two-point correlation function, as it proves the validity of the theoretical prediction and accounts for effects that are often neglected in its numerical evaluation.

astro-ph.CO↗

arXiv2018

Non-linear general relativistic effects in the observed redshift

We present the second-order expression for the observed redshift, accounting for all the relativistic effects from the light propagation and from the frame change at the observer and the source positions. We derive the generic gauge-transformation law that any observable quantities should satisfy, and we verify our second-order expression for the observed redshift by explicitly checking its gauge transformation property. This is the first time an explicit verification is made for the second-order calculations of observable quantities. We present our results in popular gauge choices for easy use and discuss the origin of disagreements in previous calculations.

gr-qc↗

arXiv2018

Jacobi Mapping Approach for a Precise Cosmological Weak Lensing Formalism

Cosmological weak lensing has been a highly successful and rapidly developing research field since the first detection of cosmic shear in 2000. However, it has recently been pointed out in Yoo et al. that the standard weak lensing formalism yields gauge-dependent results and, hence, does not meet the level of accuracy demanded by the next generation of weak lensing surveys. Here, we show that the Jacobi mapping formalism provides a solid alternative to the standard formalism, as it accurately describes all the relativistic effects contributing to the weak lensing observables. We calculate gauge-invariant expressions for the distortion in the luminosity distance, the cosmic shear components and the lensing rotation to linear order including scalar, vector and tensor perturbations. In particular, the Jacobi mapping formalism proves that the rotation is fully vanishing to linear order. Furthermore, the cosmic shear components contain an additional term in tensor modes which is absent in the results obtained with the standard formalism. Our work provides further support and confirmation of the gauge-invariant lensing formalism needed in the era of precision cosmology.

astro-ph.CO↗

arXiv2018

Gauge-Invariant Formalism of Cosmological Weak Lensing

We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by the geodesic equation, the relation of the photon wavevector to the physical quantities requires the specification of the frames, where they are defined. By constructing the local tetrad bases at the observer and the source positions, we clarify the relation of the weak lensing observables such as the convergence, the shear, and the rotation to the physical size and shape defined in the source rest-frame and the observed angle and redshift measured in the observer rest-frame. Compared to the standard lensing formalism, additional relativistic effects contribute to all the lensing observables. We explicitly verify the gauge-invariance of the lensing observables and compare our results to previous work. In particular, we demonstrate that even in the presence of the vector and tensor perturbations, the physical rotation of the lensing observables vanishes at the linear order, while the tetrad basis rotates along the light propagation compared to a FRW coordinate. Though the latter is often used as a probe of primordial gravitational waves, the rotation of the tetrad basis is indeed not a physical observable. We further clarify its relation to the E-B decomposition in weak lensing. Our formalism provides a transparent and comprehensive perspective of cosmological weak lensing.

astro-ph.CO↗

arXiv2017

Exact non-linear equations for cosmological perturbations

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations -- scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

gr-qc↗

arXiv2017

Correlation function of the luminosity distances

We present the correlation function of the luminosity distances in a flat $Λ$CDM universe. Decomposing the luminosity distance fluctuation into the velocity, the gravitational potential, and the lensing contributions, we study their individual contributions to the correlation function. The lensing contribution is important at large redshift ($z\gtrsim 0.5$) but only for small angular separation ($θ\lesssim 3^\circ$), while the velocity contribution dominates over the other contributions at low redshift or at larger separation. However, the gravitational potential contribution is always subdominant at all scale, if the correct gauge-invariant expression is used. The correlation function of the luminosity distances depends significantly on the matter content, especially for the lensing contribution, thus providing a novel tool of estimating cosmological parameters.

astro-ph.CO↗

arXiv2017

Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average

Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their theoretical description is verified by checking its gauge-invariance. We argue that cosmological observables are invariant scalars under diffeomorphisms and as a consequence their theoretical description is gauge-invariant, only at linear order in perturbations. Beyond linear order, they are usually not gauge-invariant, and we provide the general law for the gauge-transformation that the perturbation part of an observable does obey. We apply this finding to derive the second-order expression for the observational light-cone average in cosmology and demonstrate that our expression is indeed invariant under diffeomorphisms.

astro-ph.CO↗

arXiv2017

Light-Cone Observables and Gauge-Invariance in the Geodesic Light-Cone Formalism

The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.

gr-qc↗

arXiv2017

Gauge-Invariance and Infrared Divergences in the Luminosity Distance

Measurements of the luminosity distance have played a key role in discovering the late-time cosmic acceleration. However, when accounting for inhomogeneities in the Universe, its interpretation has been plagued with infrared divergences in its theoretical predictions, which are in some cases used to explain the cosmic acceleration without dark energy. The divergences in most calculations are artificially removed by imposing an infrared cut-off scale. For the first time, we show that a gauge-invariant calculation of the luminosity distance is devoid of such divergences and consistent with the equivalence principle, eliminating the need to impose a cut-off scale. We present proper numerical calculations of the luminosity distance using the gauge-invariant expression and demonstrate that the numerical results with an ad hoc cut-off scale in previous calculations have negligible systematic errors as long as the cut-off scale is larger than the horizon scale. We discuss the origin of infrared divergences and their cancellation in the luminosity distance.

astro-ph.CO↗

arXiv2016

Unified Treatment of the Luminosity Distance in Cosmology

Comparing the luminosity distance measurements to its theoretical predictions is one of the cornerstones in establishing the modern cosmology. However, as shown in Biern & Yoo, its theoretical predictions in literature are often plagued with infrared divergences and gauge-dependences. This trend calls into question the sanity of the methods used to derive the luminosity distance. Here we critically investigate four different methods --- the geometric approach, the Sachs approach, the Jacobi mapping approach, and the geodesic light cone (GLC) approach to modeling the luminosity distance, and we present a unified treatment of such methods, facilitating the comparison among the methods and checking their sanity. All of these four methods, if exercised properly, can be used to reproduce the correct description of the luminosity distance.

astro-ph.CO↗

arXiv2016

Exact Analytic Solution for Non-Linear Density Fluctuation in a LCDM Universe

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a $Λ$CDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

gr-qc↗