在寒冷的暗物质宇宙中出现的第一批物体对结构形成模型提出了艰巨的挑战。在超小规模范围内，清洁发展机制的结构几乎同时在各种规模上形成。分层聚类不再提供理论分析的指导原则，进行可信的模拟所需的计算时间变得非常高。为了深入了解这个问题，我们对爱因斯坦-德西特宇宙学进行了高分辨率（N=720^3 - 1584^3）模拟，其中初始功率谱为P（k）propto k^n，-2.5 < n <-1。自相似标度比以前的低分辨率模拟更有说服力地建立了n=-1和n=-2的自相似标度，并且首次建立了n=-2.25的自相似标度。然而，在我们的n=-2.5模拟中，有限的盒子大小效应会导致自相似标度的偏离。我们比较我们的结果与预测的功率谱（单回路）微扰理论，并表明，由麦当劳建议的重整化群方法提高微扰理论的能力，预测的功率谱在准线性政权。在非线性区域，我们的功率谱与Peacock & Dodds和Smith等人广泛使用的拟合公式有很大不同，并提出了一个新的拟合公式。我们的研究结果的稳定聚类假设与晕模型的辩论的影响进行了讨论。我们的功率谱与高k极限下的稳定聚类假设的预测不一致，并为晕模型提供了证据。然而，本文所提倡的拟合公式是纯经验的，而不是从晕轮模型的特定公式推导出来的。
英文摘要：
The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.
The evolution of cosmic perturbations in a two-component ultralight axionic universe is investigated. We present the first spectral computation of perturbations in multi-component universes. A particular case composed of light extreme axions and free massive particles offers a possibility for the formation of very high-redshift massive galaxies, which are typically required to host massive early quasars. Our computation retains the information of perturbed velocities for individual axion components, opening a new avenue for setting up initial conditions for future axion dark matter simulations…
The cosmic background (CB) radiation, encompassing the sum of emission from all sources outside our own Milky Way galaxy across the entire electromagnetic spectrum, is a fundamental phenomenon in observational cosmology. Many experiments have been conceived to measure it (or its constituents) since the extragalactic Universe was first discovered; in addition to estimating the bulk (cosmic monopole) spectrum, directional variations have also been detected over a wide range of wavelengths. Here we gather the most recent of these measurements and discuss the current status of our understanding of…
The hot gas in clusters of galaxies creates a distinctive spectral distortion in the cosmic microwave background (CMB) via the Sunyaev-Zel'dovich (SZ) effect. The spectral signature of the SZ can be used to measure the CMB temperature at cluster redshift ($T_{\rm CMB}(z)$) and to constrain the monopole of the y-type spectral distortion of the CMB spectrum. In this work, we start showing the measurements of $T_{\rm CMB}(z)$ for a sample extracted from the Second Catalog of galaxy clusters produced by Planck (PSZ2) and containing 75 clusters selected from CHEX-MATE. Then we show the forecasts fo…
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…
Inflation drives quantum fluctuations beyond the Hubble horizon, freezing them out before the small-scale modes re-enter during the radiation dominated epoch, and subsequently decay, while large-scale modes re-enter later during the matter dominated epoch and grow. This distinction shapes the matter power spectrum and provides observational evidence in support of the standard model. In this paper, we demonstrate that another mechanism, based on the fluctuation growth in the R_h=ct universe, itself an FLRW cosmology with the added constraint of zero active mass (i.e., rho+3p=0), also accounts v…
We derive the power spectrum of primordial quantum fluctuations in an inflationary universe for curvature parameter ${\mathcal K}=1$. This is achieved through a Born--Oppenheimer type of approximation scheme from the Wheeler--DeWitt equation of canonical quantum gravity using gauge-invariant variables. Compared to the flat model, the closed model exhibits a deficit of power at large scales.
The spatial distribution of neutral hydrogen (HI) in the Universe contains a wealth of cosmological information. The 21 cm emission line can be used to map the HI up to very high redshift and therefore reveal us something about the evolution of the large scale structures in the Universe. However little is known about the abundance and clustering properties of the HI over cosmic time. Motivated by this, we build an analytic framework where the relevant parameters that govern how the HI is distributed among dark matter halos can be fixed using observations. At the same time we provide tools to s…
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…
The Cosmic Microwave Background (CMB) radiation lensing is a promising tool to study the physics of early universe. In this work we probe the imprints of deviations from isotropy and scale invariance of primordial curvature perturbation power spectrum on CMB lensing potential and convergence. Specifically, we consider a scale-dependent hemispherical asymmetry in primordial power spectrum. We show that the CMB lensing potential and convergence and also the cross-correlation of the CMB lensing and late time galaxy convergence can probe the amplitude and the scale dependence of the dipole modulat…
While galaxy cluster catalogs were compiled many decades ago, other structural elements of cosmic web are detected at definite level only in the newest works. For example, extragalactic filaments were described by velocity field and SDSS galaxy distribution during the last years. Large-scale structure of the Universe could be also mapped in the future using ATHENA observations in X-rays and SKA in radio band. Until detailed observations are not available for the most volume of Universe, some integral statistical parameters can be used for its description. Such methods as galaxy correlation fun…
We work out the Standard Model (SM) mass spectrum during inflation with quantum corrections, and explore its observable consequences in the squeezed limit of non-Gaussianity. Both non-Higgs and Higgs inflation models are studied in detail. We also illustrate how some inflationary loop diagrams can be computed neatly by Wick-rotating the inflation background to Euclidean signature and by dimensional regularization.
We revisit the Boltzmann equation governing the spectrum of energetic particles originating from the decay of massive progenitors during the process of thermalization. We assume that these decays occur when the background temperature $T$ is much less than the mass $M$ of the progenitor. We pay special attention to the IR cutoff provided by the thermal bath, and include the suppression resulting from the interference of multiple scattering reactions (LPM effect). We solve the resulting integral equation numerically, and construct an accurate analytical fit of the solutions.
We derive in detail the equations of motion for the tensorial modes of primordial metric perturbations in the Coupled-Scalar-Tachyon Bounce Universe. We solve for the gravitational wave equations in the pre-bounce contraction and the post-bounce expansion epochs. To match the solutions of the tensor perturbations, we idealise the bounce process yet retaining the essential physical properties of the bounce universe. We put forward two matching conditions: one ensures the continuity of the gravitational wave functions and the other respects the symmetric nature of the bounce dynamics. The matchi…
Acoustic peaks in the Cosmic Microwave Background (CMB) temperature spectrum as observed by the Planck satellite appear to be smoother than our expectation from the standard model lensing effect. This anomalous effect can be also mimicked by a spatially closed Universe with a very low value of Hubble constant that consequently aggravates the already existing discordance between cosmological observations. We reconstruct a signature from the early Universe, a particular form of oscillation in the primordial spectrum of quantum fluctuations with a characteristic frequency, that solves all these a…
The scalar perturbation induced gravitational waves are a probe of the primordial density perturbation spectrum on small scales. In this paper, we show that they can also probe the thermal history of the universe. We assume the universe underwent a stage with a constant equation of state parameter $w$, followed by the radiation-dominated stage of the conventional big bang universe. We find that the infrared slope of the power spectrum of the induced stochastic gravitational wave background for decelerating cosmologies is related to the equation of state of the universe. Furthermore, the induce…
We introduce a new cosmic emulator for the matter power spectrum covering eight cosmological parameters. Targeted at optical surveys, the emulator provides accurate predictions out to a wavenumber k~5/Mpc and redshift z<=2. Besides covering the standard set of LCDM parameters, massive neutrinos and a dynamical dark energy of state are included. The emulator is built on a sample set of 36 cosmological models, carefully chosen to provide accurate predictions over the wide and large parameter space. For each model, we have performed a high-resolution simulation, augmented with sixteen medium-reso…
The parameters of the original log-normal mass spectrum of primordial black holes (PBH) are approximately adjusted on the basis of existing observational data on supermassive black holes in the galactic centers and the mass distribution of the near-solar mass black holes in the Galaxy. Together with the assumption that PBHs make all or a noticeable mass fraction of the cosmological dark matter, it allows to fix the parameters of the original mass spectrum. The predicted, in this way, the number density of MACHOs is found to be about an order of magnitude below the observed value. A possible re…
We investigate constraints on the spectral index of primordial gravitational waves (GWs), paying particular attention to a blue-tilted spectrum. Such constraints can be used to test a certain class of models of the early Universe. We investigate observational bounds from LIGO+Virgo, pulsar timing and big bang nucleosynthesis, taking into account the suppression of the amplitude at high frequencies due to reheating after inflation and also late-time entropy production. Constraints on the spectral index are presented by changing values of parameters such as reheating temperatures and the amount …
Emergent cosmological models, together with the Big Bang and bouncing scenarios, are among the possible descriptions of the early Universe. This work aims at clarifying some general features of the primordial tensor power spectrum in this specific framework. In particular, some naive beliefs are corrected. Using a toy model, we investigate the conditions required to produce a scale invariant spectrum and show to which extent this spectrum can exhibit local features sensitive to the details of the scale factor evolution near the transition time.
The spectrum of primordial gravitational waves (GWs), especially its tilt $n_T$, carries significant information about the primordial universe. Combining recent aLIGO and Planck2015+BK14 data, we find that the current limit is $n_T=0.016^{+0.614}_{-0.989}$ at 95% C.L. We also estimate the impacts of Einstein Telescope and LISA on constraining $n_T$. Moreover, based on the effective field theory of cosmological perturbations, we make an attempt to confront some models of early universe scenarios, which produce blue-tilted GWs spectrum ($n_T>0$), with the corresponding datasets.
Exact numerical primordial primordial power spectra are computed and plotted for the for the best-fit Planck 2018 curved universe parameters. It is found that the spectra have generic cut-offs and oscillations within the observable window for the level of curvature allowed by current CMB measurements and provide a better fit to current data. Derivations for the Mukhanov-Sasaki equation for curved universes are presented and analysed, and theoretical implications for the quantum and classical initial conditions for inflation are discussed within the curved regime.
A model for the acoustic production of gravitational waves at a first order phase transition is presented. The source of gravitational radiation is the sound waves generated by the explosive growth of bubbles of the stable phase. The model assumes that the sound waves are linear and that their power spectrum is determined by the characteristic form of the sound shell around the expanding bubble. The predicted power spectrum has two length scales, the average bubble separation and the sound shell width when the bubbles collide. The peak of the power spectrum is at wavenumbers set by the sound s…
The cosmological constant is not necessarily small in the early universe. If a scalar field obtains a vacuum expectation value after a phase transition (PT), a possibly large cosmological constant could present before PT. The early cosmological constant (ECC) and the PT process may be detectable from dark radiation (DR) today, such as in the cosmic axion background. We show that for a broad class of DR models, the DR density and spectrum are significantly modified by the presence of an ECC. From the density and the spectrum of the DR today, we can deduce the temperature and the strength of the…
We study the effect of hotter or colder particles on the evolution of the chiral magnetic field in the early universe. We are interested in the temperature dependent term in the chiral vortical effect. There are no changes in the magnetic energy spectrum at large lengthscales but in the Kolmogorov regime we do find a difference. Our numerical results show that the Gaussian peak in the magnetic spectrum becomes negatively skewed. The negatively skewed peak can be fitted with a beta distribution. Analytically one can relate the non-Gaussianity of the distribution to the temperature dependent vor…
We calculate the primordial power spectrum of tensor perturbations, within the emergent universe scenario, incorporating a version of the Continuous Spontaneous Localization (CSL) model as a mechanism capable of: breaking the initial symmetries of the system, generating the perturbations, and also achieving the quantum-to-classical transition of such perturbations. We analyze how the CSL model modifies the characteristics of the B-mode CMB polarization power spectrum, and we explore their differences with current predictions from the standard concordance cosmological model. We have found that,…
Massive fields in the primordial universe function as standard clocks and imprint clock signals in the density perturbations that directly record the scale factor of the primordial universe as a function of time, a(t). A measurement of such signals would identify the specific scenario of the primordial universe in a model-independent fashion. In this Letter, we introduce a new mechanism through which quantum fluctuations of massive fields function as standard clocks. The clock signals appear as scale-dependent oscillatory signals in the power spectrum of alternative scenarios to inflation.
Modern cosmological surveys are delivering datasets characterized by unprecedented quality and statistical completeness; this trend is expected to continue into the future as new ground- and space-based surveys come online. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. At low redshifts, the surveys probe the nonlinear regime of structure formation where cosmological simulations are the primary means of obtaining the required information. The computational cost of sufficiently resolved large-volume simulations makes …
After inflation the Universe presumably undergoes a phase of reheating which in effect starts the thermal big bang cosmology. However, so far we have very little direct experimental or observational evidence of this important phase of the Universe. In this letter, we argue that measuring the spectrum of freely propagating relativistic particles, i.e. dark radiation, produced during reheating may provide us with powerful information on the reheating phase. To demonstrate this possibility we consider a situation where the dark radiation is produced in the decays of heavy, non-relativistic partic…
Recently, we had numerically shown that, for a non-minimal coupling that is a simple power of the scale factor, scale invariant magnetic fields arise in a class of bouncing universes. In this work, we {\it analytically} evaluate the spectrum of magnetic and electric fields generated in a sub-class of such models. We illustrate that, for cosmological scales which have wavenumbers much smaller than the wavenumber associated with the bounce, the shape of the spectrum is preserved across the bounce. Using the analytic solutions obtained, we also illustrate that the problem of backreaction is sever…
Revisiting the spectrum of a scalar field in an anisotropic universe
School of Liberal Arts and Sciences, Korea National University of Transportation（韩国国立交通大学生命科学与艺术学院）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
The low frequency part of the gravitational wave spectrum generated by local physics, such as a phase transition or parametric resonance, is largely fixed by causality, offering a clean window into the early Universe. In this work, this low frequency end of the spectrum is analyzed with an emphasis on a physical understanding, such as the suppressed production of gravitational waves due to the excitation of an over-damped harmonic oscillator and their enhancement due to being frozen out while outside the horizon. Due to the difference between sub-horizon and super-horizon physics, it is inevit…
To derive a power spectrum for energy density inhomogeneities in a closed universe, we study a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and non-relativistic matter epochs. (For our purposes it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invaria…
