arXiv subjects

Jaiyul Yoo

Publications and source records attributed to Jaiyul Yoo.

At least 19 recordsLinked to original sources

arXiv2026

Complete Second-Order Relativistic Derivation of the Observed Pulsar Timing Modulations

We present a fully nonlinear relativistic description of the observed pulsar timing modulations, defined through the ratio of the proper-time intervals between two successive emissions of radio pulses and their observations by a pulsar timing array. Working in the limit of a vanishing emission interval, we derive the observed pulsar timing modulation to second order in relativistic perturbation theory around a Minkowski background, without fixing a gauge and retaining the full scalar, vector, and tensor content of the metric perturbations. Although the derivation naturally introduces several gauge-dependent intermediate quantities, we explicitly demonstrate that they combine into a coordinate-independent expression. Moreover, we explicitly show that the second-order timing modulation from two neighboring radio pulses coincides with the observed redshift, defined as the fractional change in wavelength along a single geodesic. The agreement represents a nontrivial second-order realization of the exact nonlinear equivalence proven in Magi & Yoo 2026.

astro-ph.CO↗

arXiv2026

Exact Equivalence of the Observed Redshift and the Pulsar Timing Modulation in the Infinitesimal-Pulse Limit

The pulsar timing arrays (PTA) collect the times of arrival of radio signals from the millisecond pulsars, and gravitational waves can modulate their arrival times. Although the PTA observable involves successive radio pulses propagating along different light paths, its standard theoretical description at linear order in perturbations is equivalent to the Sachs-Wolfe formula for the observed redshift, which describes the fractional change in photon frequency along a single geodesic. While this equivalence is well known at linear order, its validity beyond first order has not been systematically addressed in the PTA literature. Here we show that, in the limit of vanishing proper-time separation between successive emission events, the timing modulation is exactly equal to the observed redshift, without expanding the spacetime geometry. For a finite emission interval, we derive the exact relation between the timing modulation and the observed redshift, and show that their difference is controlled by the ratio between the emission interval and the characteristic timescale over which the observed redshift varies.

astro-ph.CO↗

arXiv2025

Cosmic Dipoles from Large-Scale Structure Surveys

Large-scale structure surveys can be used to measure the dipole in the cosmic microwave background (CMB), in the luminosity distances inferred from type-Ia supernova observations, and in the spatial distribution of galaxies and quasars. The measurements of these cosmic dipoles appear to be mutually inconsistent, even though they are expected to indicate the common observer velocity. This observational tension may represent a significant challenge to the standard model of cosmology. Here we study in detail what contributes to the cosmic dipoles from CMB, supernova, and galaxy survey in the standard $Λ$CDM model, though our theoretical model can be applied beyond the standard model. While measurements of the cosmic dipoles yield the relative velocities between the source samples and the observer velocity, the motion of the observer is the dominant contribution in the conformal Newtonian gauge, and the intrinsic velocities of the samples fall steeply with increasing redshift of the sources. Hence the cosmic dipoles of CMB, type-Ia supernovae, and galaxies should be aligned but can have different amplitudes. We also clarify several misconceptions that are commonly found in the literature.

astro-ph.CO↗

arXiv2025

Lagrangian Perturbation Theory for Biased Tracers: Significance of the Number Conservation

The Lagrangian perturbation theory provides a simple yet powerful way of computing the nonlinear matter power spectrum, and it has been applied to biased tracers such as halos and galaxies. The number conservation of matter particles allows a simple relation between the fluctuations at the initial and the late times, which is essential in deriving the exact expression for the nonlinear matter power spectrum. Here we investigate the significance of the number conservation in the Lagrangian perturbation theory for biased tracers. We use $N$-body simulations to test the significance of number conservation by tracing dark matter halo samples in time. For the mass bin sample $Δ\log M_h~(h^{-1}M_{\odot})= 0.5$ at $z\simeq3$, the theoretical predictions for the halos overestimates the power spectrum at $z=0$ by a factor of three, while the simulation results match the theoretical predictions if the number conservation of halos is imposed in the simulations throughout the evolution. Starting with a halo sample at $z=0$ as another test, we trace back in time the particles that belong to the halos at~$z=0$ and use their center-of-mass positions as halo positions at $z>0$. The halo power spectra at $z>0$ from the simulations agree with the theoretical predictions of the Lagrangian perturbation theory. This numerical experiment proves that the number conservation is crucial in the Lagrangian perturbation theory predictions. We discuss the implications for various applications of the Lagrangian perturbation theory for biased tracers.

astro-ph.CO↗

arXiv2025

Infrared Sensitivity of Cosmological Probes In The Presence of Axion Field Fluctuations

We study the effects of long wavelength entropy fluctuations on cosmological probes such as galaxy clustering, luminosity distance, and CMB temperature anisotropies. Specifically, we consider fluctuations of a massless spectator scalar field set up in the early universe, which later acquires mass during the radiation-dominated era. We find that there are non-vanishing effects on observables, and the amplitude of these effects peaks for observables set up at the time of equal matter and radiation, and decreases as $η^{-2}$ where $η$ is the conformal time. Hence, the back-reaction effects are important for CMB anisotropies, but their impact on late-time observables is suppressed. In particular, the back-reaction effects are unable to explain the Hubble tension while they might alleviate the cosmic dipole tension. In contrast to a lot of the previous work on back-reaction, we work in position rather than momentum space.

astro-ph.CO↗

arXiv2025

Monopole Fluctuations in Galaxy Surveys

Galaxy clustering provides a powerful way to probe cosmology. This requires understanding of the background mean density of galaxy samples, which is estimated from the survey itself by averaging the observed galaxy number density over the angular position. The angle average includes not only the background mean density, but also the monopole fluctuation at each redshift. Here for the first time we compute the monopole fluctuations in galaxy surveys and investigate their impact on galaxy clustering. The monopole fluctuations vary as a function of redshift, and it is correlated with other fluctuations, affecting the two-point correlation function measurements. In an idealized all-sky survey, the rms fluctuation at $z=0.5$ can be as large as 7% of the two-point correlation function in amplitude at the BAO scale, and it becomes smaller than 1% at $z>2$. The monopole fluctuations are unavoidable, but they can be modeled. We discuss its relation to the integral constraint and the implications for the galaxy clustering analysis.

astro-ph.CO↗

arXiv2024

Infrared Sensitivity of Cosmological Probes in Horndeski Theory

Cosmological probes constructed in large-scale surveys are independent of the underlying theory of gravity, and their relativistic descriptions are indeed applicable to any theory of gravity. It was shown that the presence of fluctuations with wavelength much larger than the characteristic scales of the surveys has no impact on cosmological probes, if the matter content is adiabatic and the Einstein equations are used. In this paper we study the sensitivity of cosmological probes to infrared fluctuations in Horndeski theory. We find that the extra degree of freedom in the Horndeski scalar field can induce sensitivity to infrared fluctuations in the cosmological probes, even when the matter components are adiabatic on large scales. A generalized adiabatic condition including the extra dof, in contrast, guarantees that cosmological probes are devoid of infrared sensitivity, and this solution corresponds to the adiabatic modes à la Weinberg in Horndeski theory, which can be removed by a coordinate transformation in the infrared limit. We discuss the implications of our findings and the connections to the initial conditions.

astro-ph.CO↗

arXiv2023

Incompatibility of Standard Galaxy Bias Models in General Relativity

The standard model for galaxy bias is built in a Newtonian framework, and several attempts have been made in the past to put it in a relativistic framework. The focus of past works was, however, to use the same Newtonian formulation, but to provide its interpretation in a relativistic framework by either fixing a gauge condition or transforming to a local coordinate system. Here we demonstrate that these reverse-engineered approaches do not respect the diffeomorphism symmetry in general relativity, and we need to develop a covariant model of galaxy bias that is diffeomorphism compatible. We consider a simple toy model for galaxy bias and discuss the impact for measuring the primordial non-Gaussianity.

gr-qc↗

arXiv2023

Conditions for the Absence of Infrared Sensitivity in Cosmological Probes in Any Gravity Theories

Large-scale surveys allow us to construct cosmological probes such as galaxy clustering, weak gravitational lensing, the luminosity distance, and cosmic microwave background anisotropies. The gauge-invariant descriptions of these cosmological probes reveal the presence of numerous relativistic effects in the cosmological probes, and they are sensitive (or even divergent) to the long wave-length fluctuations in the initial conditions. In the standard $Λ$CDM model, this infrared sensitivity is absent due to subtle cancellations among the relativistic contributions, once the Einstein equation is used. Here we derive the most general conditions for the absence of infrared sensitivity in the cosmological probes without committing to general relativity. We discuss the implications of our results for gravity theories beyond general relativity.

astro-ph.CO↗

arXiv2023

Sample Variance in Cosmological Observations with a Narrow Field-of-View

Surveys with a narrow field-of-view can play an important role in probing cosmology, but inferences from these surveys suffer from large sample variance, arising from random fluctuations around the cosmic mean. The standard method for computing the sample variance is based on two key approximations: treating perturbations linearly and the survey geometry as a box. We demonstrate that it can lead to a significant underestimate of the sample variance in narrow surveys. We present a new method for accurately computing the sample variance and apply our method to the recent observations of the warm-hot intergalactic medium (WHIM) based on spectroscopic measurements of blazars. We find that the sample variances in these surveys are significantly larger than the quoted measurement errors; for example, the cosmic mean baryon density contained in the WHIM could be lower by $54\%$ at $1\text{-}σ$ fluctuation than estimated in one observation. Accurately quantifying the sample variance is essential in deriving correct interpretations of the measurements in surveys with a small field-of-view.

astro-ph.CO↗

arXiv2023

Infrared (in)sensitivity of relativistic effects in cosmological observable statistics

The relativistic effects in cosmological observables contain critical information about the initial conditions and gravity on large scales. Compared to the matter density fluctuation, some of these relativistic contributions scale with negative powers of comoving wave number, implying a growing sensitivity to infrared modes. However, this can be inconsistent with the equivalence principle and can also lead to infrared divergences in the observable $N$-point statistics. Recent perturbative calculations have shown that this infrared sensitivity is indeed spurious due to subtle cancellations in the cosmological observables that have been missed in the bulk of the literature. Here we demonstrate that the cosmological observable statistics are infrared-insensitive in a general and fully non-linear way, assuming diffeomorphism invariance and adiabatic fluctuations on large scales.

gr-qc↗

arXiv2022

Large gauge transformations, local coordinates and cosmological observables

In recent years new types of coordinate transformations have appeared in cosmology on top of the standard gauge transformations, such as the dilatations and special conformal transformations, or the ones leading to (conformal) Fermi coordinates. Some of these can remove effects that are invariant under the standard gauge transformations and also affect asymptotic boundary conditions, thus introducing a non-trivial ambiguity in our cosmological modeling. In this short note we point out that this ambiguity is irrelevant for the quantities we use to compare our model with observations -- the cosmological observable relations -- as they are invariant under all of these transformations. Importantly, this invariance holds only if one takes into account all the relativistic contributions to an observable, which is not the case in the literature in general. We finally also show that the practically-relevant property of conformal Fermi coordinates (a FLRW metric up to second order in distance) can be achieved through a globally-defined standard gauge transformation.

astro-ph.CO↗

arXiv2022

Living in a Non-Flat Universe: Theoretical Formalism

Recent analysis of the Planck measurements opened a possibility that we live in a non-flat universe. Given the renewed interest in non-zero spatial curvature, here we re-visit the light propagation in a non-flat universe and provide the gauge-invariant expressions for the cosmological probes: the luminosity distance, galaxy clustering, weak gravitational lensing, and cosmic microwave background anisotropies. With the positional dependence of the spatial metric, the light propagation in a non-flat universe is much more complicated than in a flat universe. Accounting for all the relativistic effects and including the vector and tensor contributions, we derive the expressions for the cosmological probes and explicitly verify their gauge invariance. We compare our results to previous work in a non-flat universe, if present, but this work represents the first comprehensive investigation of the cosmological probes in a non-flat universe. Our theoretical formalism in a non-flat universe will play a crucial role in constraining the spatial curvature in the upcoming large-scale surveys.

astro-ph.CO↗

arXiv2022

Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects

Assuming a LCDM universe in a single-field inflationary scenario, we compute the three-point correlation function of the observed matter density fluctuation in the squeezed triangular configuration, accounting for all the relativistic effects at the second order in perturbations. This squeezed three-point correlation function characterizes the local-type primordial non-Gaussianity, and it has been extensively debated in literature whether there exists a prominent feature in galaxy clustering on large scales in a single-field inflationary scenario either from the primordial origin or the intrinsic nonlinearity in general relativity. First, we show that theoretical descriptions of galaxy bias are incomplete in general relativity due to ambiguities in spatial gauge choice, while those of cosmological observables are independent of spatial gauge choice. Hence a proper relativistic description of galaxy bias is needed to reach a definitive conclusion in galaxy clustering. Second, we demonstrate that the gauge-invariant calculations of the cosmological observables remain unaffected by extra coordinate transformations like CFC or large diffeomorphism like dilatation. Finally, we show that the relativistic effects associated with light propagation in observations cancel each other, and hence there exists NO non-Gaussian contribution from the so-called projection effects.

astro-ph.CO↗

arXiv2022

Second-order gauge-invariant formalism for the cosmological observables: Complete verification of their gauge-invariance

Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light propagation and observations without choosing a gauge condition. For the first time, we have performed a complete verification of the validity of our second-order expressions by comparing their gauge-transformation properties from two independent methods: one directly obtained from their expressions in terms of metric perturbations and the other expected from their nonlinear relations. The expressions for the cosmological observables such as galaxy clustering and the luminosity distance are invariant under diffeomorphism and gauge-invariant at the observed position. We compare our results to the previous work and discuss the differences in the perturbative expressions. Our second-order gauge-invariant formalism constitutes a major step forward in the era of precision cosmology and its applications in the future will play a crucial role for going beyond the power spectrum and probing the early universe.

astro-ph.CO↗

arXiv2022

The spatial gauge-dependence of single-field inflationary bispectra

In single-field inflationary models the bispectra are usually given in the $ζ$-gauge, because its temporal part leads to the super-horizon conservation of fluctuations. However, this property is independent of the choice of {\it spatial} gauge, so in this letter we explore this freedom. We compute the variation of the bispectra under the most general spatial gauge transformation that is globally defined and privileges no point, direction or scale. In the squeezed configuration we then obtain a generalization of the classic $ζ$-gauge consistency relations, which we also derive through the `large diffeomorphism' approach for all four bispectra. At leading order in the long wave-number the transformation only affects the case where the long mode is a scalar. The first effect is a shift of the tilt factor, so that one can significantly reduce the amplitude of that contribution. Secondly, there is now an extra term depending on the triangle shape, the same as in solid inflation, which is due to the fact that the 3-metric has a scalar anisotropy in generic spatial gauge. At next-to-leading order there is no variation, so the conformal consistency relations of the $ζ$-gauge are preserved.

hep-th↗

arXiv2021

General Relativistic Effects in Weak Lensing Angular Power Spectra

Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. The wide sky coverage of Euclid makes angular scales down to $l_\mathrm{min}=10$ accessible. At such large angular scales, general relativistic effects manifest themselves, and the lensing magnification cannot be correctly described by the standard lensing convergence only. The impact of line-of-sight velocities on the magnification angular power spectrum, referred to as the Doppler magnification, is already well recognized in literature. In particular, it was suggested that the Doppler magnification could be extracted by measurements of both cosmic shear and magnification. In this work, we point out two previously neglected aspects with respect to this method. Firstly, the impact of the Doppler magnification is reduced through non-vanishing cross terms with the standard lensing convergence. This is particularly relevant when the sources are averaged over a bin of width $Δz\approx 0.1$, such as in Euclid's tomographic weak lensing survey. Secondly, general relativistic potential terms slightly enhance the signal. We present numerical calculations of all relativistic effects in the weak lensing angular power spectra on large scales.

astro-ph.CO↗

arXiv2021

Monopole Fluctuation of the CMB and its Gauge Invariance

The standard theoretical description $Θ(\hat n)$ of the observed CMB temperature anisotropies is gauge-dependent. It is, however, well known that the gauge mode is limited to the monopole and the higher angular multipoles $Θ_l$ ($l\geq1$) are gauge-invariant. Several attempts have been made in the past to properly define the monopole fluctuation, but the resulting values of the monopole power $C_0$ are infinite due to the infrared divergences. The infrared divergences arise from the contribution of the uniform gravitational potential to the monopole fluctuation, in violation of the equivalence principle. Here we present the gauge-invariant theoretical description of the observed CMB temperature anisotropies and compute the monopole power $C_0=1.66\times10^{-9}$ in a $Λ$CDM model. While the gauge-dependence in the standard calculations originates from the ambiguity in defining the hypersurface for the background CMB temperature $\bar T$ today, it is in fact well defined and one of the fundamental cosmological parameters. We argue that once the cosmological parameters are chosen, the monopole fluctuation can be unambiguously inferred from the angle-average of the observed CMB temperature, making it a model-dependent ''observable''. Adopting simple approximations for the anisotropy formation, we derive a gauge-invariant analytical expression for the observed CMB temperature anisotropies to study the CMB monopole fluctuation and the cancellation of the uniform gravitational potential contributions on large scales.

astro-ph.CO↗