28 pages, 7 figures. This is an author-created, un-copyedited version of an article published in JCAP. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at the DOI below. v3: Updated to match version published in JCAP
We develop a formalism for calculating soft limits of $n$-point inflationary correlation functions using separate universe techniques. Our method naturally allows for multiple fields and leads to an elegant diagrammatic approach. As an application we focus on the trispectrum produced by inflation with multiple light fields, giving explicit formulae for all possible single- and double-soft limits. We also investigate consistency relations and present an infinite tower of inequalities between soft correlation functions which generalise the Suyama-Yamaguchi inequality.
In the separate universe approach, an inhomogeneous universe is rephrased as a set of glued numerous homogeneous local patches. This is the essence of the gradient expansion and the $δN$ formalism, which have been widely used in solving a long wavelength evolution of the universe. In this paper, we show that the separate universe approach can be generically used, as long as a theory under consideration is local and preserves the spatial diffeomorphism invariance. Focusing on these two conditions, we also clarify the condition for the existence of the so-called Weinberg's adiabatic mode. Remark…
The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the phase space to homogeneous and isotropic degrees of freedom, it greatly simplifies the analysis of large-scale fluctuations. It is also a prerequisite for the stochastic-inflation formalism. In this work, we formulate the separate-universe approach in the Hamiltonian formalism, which allows us to analyse the full phase-space structure of the perturbations. Suc…
We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann-Robertson-Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data,…
(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 pert…
Voids have emerged as a novel probe of cosmology and large-scale structure. These regions of extreme underdensity are sensitive to physics beyond the standard model of cosmology, and can potentially be used as a testing ground to constrain new physics. We present the first determination of the linear void bias measured in separate universe simulations. Our methods are validated by comparing the separate universe response bias with the clustering bias of voids. We find excellent agreement between the two methods for voids identified in the halo field and the down-sampled dark matter field. For …
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate Friedmann-Robertson-Walker cosmology in their angle average. In order to be able to identify the local volume expansion and curvature in a long-wavelength perturbation with those of the separate universe, we show that the lapse perturbation must be much smaller in amplitude than the curvature potential on a time slicing that comoves with the Einstein tensor. Interpreti…
The large-scale statistics of observables such as the galaxy density are chiefly determined by their dependence on the local coarse-grained matter density. This dependence can be measured directly and efficiently in N-body simulations by using the fact that a uniform density perturbation with respect to some fiducial background cosmology is equivalent to modifying the background and including curvature, i.e., by simulating a "separate universe". We derive this mapping to fully non-linear order, and provide a step-by-step description of how to perform and analyse the separate universe simulatio…
We investigate impacts of long-wavelength gravitational waves (GWs) on nonlinear structure formation by utilizing the tidal separate universe simulations. Based on the equivalence of a long-wavelength GW to a uniform tidal field in a local frame, we provide a way to incorporate a long-wavelength GW into the tidal separate universe simulation as an effective anisotropic expansion. This methodology enables us to study effects of GWs on large-scale structure efficiently. We measure the anisotropic imprint in the local power spectrum from the tidal separate universe simulations with GWs, which cor…
Cosmic voids are biased tracers of the large-scale structure of the universe. Separate universe simulations (SUS) enable accurate measurements of this biasing relation by implementing the peak-background split (PBS). In this work, we apply the SUS technique to measure the void bias parameters. We confirm that the PBS argument works well for underdense tracers. The response of the void size distribution depends on the void radius. For voids larger (smaller) than the size at the peak of the distribution, the void abundance responds negatively (positively) to a long wavelength mode. The linear bi…
By absorbing fluctuations into a local background, separate universe simulations provide a powerful technique to characterize the response of small-scale observables to the long-wavelength density fluctuations, for example those of the power spectrum and halo mass function which lead to the squeezed-limit $n$-point function and halo bias, respectively. Using quintessence dark energy as the paradigmatic example, we extend these simulation techniques to cases where non-gravitational forces in other sectors establish a Jeans scale across which the growth of density fluctuations becomes scale depe…
The long-wavelength coherent overdensity and tidal force, which are not direct observables for a finite-volume survey, affect time evolution of cosmic structure formation and therefore clustering observables through the mode coupling. In this paper we develop an "anisotropic" separate universe (SU) simulation technique to simulate large-scale structure formation taking into account the effect of large-scale tidal force into the anisotropic expansion of local background. We modify the TreePM N-body simulation code to implement the anisotropic SU simulations, and then study the "response" functi…
We present a calibration of halo assembly bias using the Separate Universe technique. Specifically, we measure the response of halo abundances at fixed mass and concentration to the presence of an infinite-wavelength initial perturbation. We develop an analytical framework for describing the concentration dependence of this peak-background split halo bias -- a measure of assembly bias -- relying on the near-Lognormal distribution of halo concentration at fixed halo mass. The combination of this analytical framework and the Separate Universe technique allows us to achieve very high precision in…
Linear halo bias is the response of dark matter halo number density to a long wavelength fluctuation in the dark matter density. Using abundance matching between separate universe simulations which absorb the latter into a change in the background, we test the consistency relation between the change in a one point function, the halo mass function, and a two point function, the halo-matter cross correlation in the long wavelength limit. We find excellent agreement between the two at the $1-2\%$ level for average halo biases between $1 \lesssim \bar b_1 \lesssim 4$ and no statistically significa…
We provide a unified description of the hemispherical asymmetry in the cosmic microwave background generated by the mechanism proposed by Erickcek, Kamionkowski, and Carroll, using a delta N formalism that consistently accounts for the asymmetry-generating mode throughout. We derive a general form for the power spectrum which explicitly exhibits the broken translational invariance. This can be directly compared to cosmic microwave background observables, including the observed quadrupole and fNL values, automatically incorporating the Grishchuk--Zel'dovich effect. Our calculation unifies and e…
As statements regarding the soft limit of cosmological correlation functions, consistency relations are known to exist in any flat FRW universe. In this letter we explore the possibility of finding such relations in a spatially closed universe, where the soft limit $\textbf{q}\rightarrow 0$ does not exist in any rigorous sense. Despite the absence of spatial infinity of the spatial slices, we find the adiabatic modes and their associated consistency relations in a toy universe with background topology $R\times S^2$. Flat FRW universe adiabatic modes are recovered via taking the large radius li…
We present anisotropic "separate universe" simulations which modify the N-body code Gadget-4 in order to represent a large-scale tidal field through an anisotropic expansion factor. These simulations are used to measure the linear, quasi-linear and nonlinear response of the matter power spectrum to a spatially uniform trace-free tidal field up to wavenumber $k = 7 h \text{Mpc}^{-1}$. Together with the response to a large-scale overdensity measured in previous work, this completely describes the nonlinear matter bispectrum in the squeezed limit. We find that the response amplitude does not appr…
The primordial Universe might be highly inhomogeneous. We perform the 3+1D Numerical Relativity simulation for the evolution of scalar field in an initial inhomogeneous expanding Universe, and investigate how it populates the landscape with both de Sitter (dS) and AdS vacua. The simulation results show that eventually either the field in different region separates into different vacua, so that the expanding dS or AdS bubbles (the bubble wall is expanding but the spacetime inside AdS bubbles is contracting) come into being with clear bounderies, or overall region is dS expanding with a few smal…
In a universe with quintessence isocurvature, or perturbations in dark energy that are independent from the usual curvature perturbations, structure formation is changed qualitatively. The existence of two independent fields, curvature and isocurvature, causes the growth rate of matter perturbations to depend on their initial conditions. The quintessence perturbations cause their growth to depend on scale. We perform the first separate universe simulations for this cosmology. We demonstrate that the power spectrum response and the halo bias depend on scale and initial conditions and that the p…
The spatial curvature ($Ω_K$) of the Universe is one of the most fundamental quantities that could give a link to the early universe physics. In this paper we develop an approximate method to compute the nonlinear matter power spectrum, $P(k)$, for "non-flat" $Λ$CDM models using the separate universe (SU) ansatz which states that the effect of the curvature on structure formation is equivalent to that of long-wavelength density fluctuation ($δ_{\rm b}$) in a local volume in the "flat" $Λ$CDM model, via the specific mapping between the background cosmological parameters and redshifts in the non…
Anisotropic separate universe : Long-wavelength perturbations and conserved quantities
Ewha Womans University（梨花女子大学）；National Institute of Technology, Fukui College（福井工业技术学院）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Yokohama National University（横滨国立大学）
Locality in effective field theory for inflationary soft modes
Kyoto University（京都大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构粒子核研究研究所）；The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学）
We measure power spectrum response functions in the presence of baryonic physical processes using separate universe simulations with the IllustrisTNG galaxy formation model. The response functions describe how the small-scale power spectrum reacts to long-wavelength perturbations and they can be efficiently measured with the separate universe technique by absorbing the effects of the long modes into a modified cosmology. Specifically, we focus on the total first-order matter power spectrum response to an isotropic density fluctuation $R_1(k,z)$, which is fully determined by the logarithmic der…
Cosmic background neutrinos have a large velocity dispersion, which causes the evolution of long-wavelength density perturbations to depend on scale. This scale-dependent growth leads to the well-known suppression in the linear theory matter power spectrum that is used to probe neutrino mass. In this paper, we study the impact of long-wavelength density perturbations on small-scale structure formation. By performing separate universe simulations where the long-wavelength mode is absorbed into the local expansion, we measure the responses of the cold dark matter (CDM) power spectrum and halo ma…
Inflation in the early Universe is a grand phase transition which have produced the seeds of all the structures we now observe. We focus on the non-equilibrium aspect of this phase transition especially the inevitable infrared (IR) divergence associated to the the quantum and classical fields during the inflation. There is a long history of research for removing this IR divergence for healthy perturbation calculations. On the other hand, the same IR divergence is quite relevant and have developed the primordial density fluctuations in the early Universe. We develop a unified formalism in which…
We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias $b_1$ and $b_2$ on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy $α$ to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work which exploits the near-Lognormal shape of the distribution of $α$ and results in very high precision calibrations. We present convenient fitting functions for the dependence of $b_1$ and…
In view of cosmological parameters being measured to ever higher precision, theoretical predictions must also be computed to an equally high level of precision. In this work we investigate the impact on such predictions of relaxing some of the simplifying assumptions often used in these computations. In particular, we investigate the importance of slow-roll corrections in the computation of multi-field inflation observables, such as the amplitude of the scalar spectrum $P_ζ$, its spectral tilt $n_s$, the tensor-to-scalar ratio $r$ and the non-Gaussianity parameter $f_{NL}$. To this end we use …
We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model and has distinct dependence on cosmological parameters. We demonstrate that the position-dependent PDF is characterized by variations in the local mean density, and we compute the linear response of the PDF to the local density using separate universe N-body simulations. The linear response of the PDF to the local density field can be thought of as the linea…
Correlation functions of two long-wavelength modes with several short-wavelength modes are shown to be related to lower order correlation functions, using the background wave method, and independently, by exploiting symmetries of the wavefunction of the Universe. These soft identities follow from the non-linear extension of the adiabatic modes of Weinberg, and their generalization by Hinterbichler et. al. The extension is shown to be unique. A few checks of the identities are presented.
To generate initial conditions for cosmological $N$-body simulations, one needs to prepare a uniform distribution of simulation particles, so-called the pre-initial condition (pre-IC). The standard method to construct the pre-IC is to place the particles on the lattice grids evenly spaced in the three-dimensional spatial coordinates. However, even after the initial displacement of each particle according to cosmological perturbations, the particle distribution remains to display an artificial anisotropy. Such an artifact causes systematic effects in simulations at later time until the evolved …
Metals form an essential part of the Universe at all scales. Without metals we would not exist, and the Cosmos would look completely different. Metals are primarily born through nuclear processes in stars. They leave their cradles through winds or explosions, and then start their journey through space. This can lead them in and out of astronomical objects on all scales, ranging from comets, planets, stars, entire galaxies, groups and clusters of galaxies to the largest structures of the Universe. Their wanderings are fundamental in determining how these objects, and the entire universe, evolve…
Using a reliably measured intrinsic (i.e. corrected for absorption effects) present-day luminosity function of high-mass X-ray binaries (HMXBs) in the 0.25-2 keV energy band per unit star-formation rate, we estimate the preheating of the early Universe by soft X-rays from such systems. We find that X-ray irradiation, mainly executed by ultraluminous and supersoft ultraluminous X-ray sources with luminosity L> 10^39 erg/s, could significantly heat (T>T_cmb, where T_cmb is the temperature of the cosmic microwave background) the intergalactic medium by z~10 if the specific X-ray emissivity of the…
In the expanding universe, two interacting fields are no longer in thermal contact when the interaction rate becomes smaller than the Hubble expansion rate. After decoupling, two subsystems are usually treated separately in accordance with equilibrium thermodynamics and the thermodynamic entropy gives a fiducial quantity conserved in each subsystem. In this paper, we discuss a correction to this paradigm from quantum entanglement of two coupled fields. The thermodynamic entropy is generalized to the entanglement entropy. We formulate a perturbation theory to derive the entanglement entropy and…
SkyPy is an open-source Python package for simulating the astrophysical sky. It comprises a library of physical and empirical models across a range of observables and a command-line script to run end-to-end simulations. The library provides functions that sample realisations of sources and their associated properties from probability distributions. Simulation pipelines are constructed from these models using a YAML-based configuration syntax, while task scheduling and data dependencies are handled internally and the modular design allows users to interface with external software. SkyPy is deve…
