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Register a new userEstimating CDM Particle Trajectories in the Mildly Non-Linear Regime of Structure Formation. Implications for the Density Field in Real and Redshift Space
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We obtain approximations for the CDM particle trajectories starting from Lagrangian Perturbation Theory. These estimates for the CDM trajectories result in approximations for the density in real and redshift space, as well as for the momentum density that are better than what standard Eulerian and Lagrangian perturbation theory give. For the real space density, we find that our proposed approximation gives a good cross-correlation (>95%) with the non-linear density down to scales almost twice smaller than the non-linear scale, and six times smaller than the corresponding scale obtained using linear theory. This allows for a speed-up of an order of magnitude or more in the scanning of the cosmological parameter space with N-body simulations for the scales relevant for the baryon acoustic oscillations. Possible future applications of our method include baryon acoustic peak reconstruction, building mock galaxy catalogs, momentum field reconstruction.
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We present a simple physically motivated picture for the mildly non-linear regime of structure formation, which captures the effects of the bulk flows. We apply this picture to develop a method to significantly reduce the sample variance in cosmological N-body simulations at the scales relevant to the Baryon Acoustic Oscillations (BAO). The results presented in this paper will allow for a speed-up of an order of magnitude (or more) in the scanning of the cosmological parameter space using N-body simulations for studies which require a good handle of the mildly non-linear regime, such as those targeting the BAO. Using this physical picture we develop a simple formula, which allows for the rapid calculation of the mildly non-linear matter power spectrum to percent level accuracy, and for robust estimation of the BAO scale.
We introduce a novel approach, the Cosmological Trajectories Method (CTM), to model nonlinear structure formation in the Universe by expanding gravitationally-induced particle trajectories around the Zeldovich approximation. A new Beyond Zeldovich approximation is presented, which expands the CTM to leading second-order in the gravitational interaction and allows for post-Born gravitational scattering. In the Beyond Zeldovich approximation we derive the exact expression for the matter clustering power spectrum. This is calculated to leading order and is available in the CTM MODULE. We compare the Beyond Zeldovich approximation power spectrum and correlation function to other methods including 1-loop Standard Perturbation Theory (SPT), 1-loop Lagrangian Perturbation Theory (LPT) and Convolution Lagrangian Perturbation Theory (CLPT). We find that the Beyond Zeldovich approximation power spectrum performs well, matching simulations to within $pm{10}%$, on mildly non-linear scales, and at redshifts above $z=1$ it outperforms the Zeldovich approximation. We also find that the Beyond Zeldovich approximation models the BAO peak in the correlation function at $z=0$ more accurately, to within $pm{5}%$ of simulations, than the Zeldovich approximation, SPT 1-loop and CLPT.
We propose two effective parameters that fully characterise galactic-scale structure formation at high redshifts ($zgtrsim5$) for a variety of dark matter (DM) models that have a primordial cutoff in the matter power spectrum. Our description is within the recently proposed ETHOS framework and includes standard thermal Warm DM (WDM) and models with dark acoustic oscillations (DAOs). To define and explore this parameter space, we use high-redshift zoom-in simulations that cover a wide range of non-linear scales from those where DM should behave as CDM ($ksim10,h,{rm Mpc}^{-1}$), down to those characterised by the onset of galaxy formation ($ksim500,h,{rm Mpc}^{-1}$). We show that the two physically motivated parameters $h_{rm peak}$ and $k_{rm peak}$, the amplitude and scale of the first DAO peak, respectively, are sufficient to parametrize the linear matter power spectrum and classify the DM models as belonging to effective non-linear structure formation regions. These are defined by their relative departure from Cold DM ($k_{rm peak}rightarrowinfty$) and WDM ($h_{rm peak}=0$) according to the non-linear matter power spectrum and halo mass function. We identify a region where the DAOs still leave a distinct signature from WDM down to $z=5$, while a large part of the DAO parameter space is shown to be degenerate with WDM. Our framework can then be used to seamlessly connect a broad class of particle DM models to their structure formation properties at high redshift without the need of additional $N$-body simulations.
I derive a nonlinear local relation between the redshift-space density field and the real-space velocity field. The relation accounts for radial character of redshift distortions, and it is not restricted to the limit of the distant observer. Direct comparisons between the observed redshift-space density fields and the real-space velocity fields possess all of the advantages of the conventional redshift-space analyses, while at the same time they are free of their disadvantages. In particular, neither the model-dependent reconstruction of the density field in real space is necessary, nor is the reconstruction of the nonlinear velocity field in redshift space, questionable because of its vorticity at second order. The nonlinear redshift-space velocity field is irrotational only in the distant observer limit, and that limit is not a good approximation for shallow catalogs of peculiar velocities currently available. Unlike the conventional redshift-space comparisons, the comparison proposed here does not have to be restricted to the linear regime. Accounting for nonlinear effects removes one of the sources of bias in the estimate of beta. Moreover, the nonlinear effects break the Omega-bias degeneracy plaguing all analyses based on linear theory.
Aims. Using the VIMOS Public Extragalactic Redshift Survey (VIPERS) we aim to jointly estimate the key parameters that describe the galaxy density field and its spatial correlations in redshift space. Methods. We use the Bayesian formalism to jointly reconstruct the redshift-space galaxy density field, power spectrum, galaxy bias and galaxy luminosity function given the observations and survey selection function. The high-dimensional posterior distribution is explored using the Wiener filter within a Gibbs sampler. We validate the analysis using simulated catalogues and apply it to VIPERS data taking into consideration the inhomogeneous selection function. Results. We present joint constraints on the anisotropic power spectrum as well as the bias and number density of red and blue galaxy classes in luminosity and redshift bins as well as the measurement covariances of these quantities. We find that the inferred galaxy bias and number density parameters are strongly correlated although these are only weakly correlated with the galaxy power spectrum. The power spectrum and redshift-space distortion parameters are in agreement with previous VIPERS results with the value of the growth rate $fsigma_8 = 0.38$ with 18% uncertainty at redshift 0.7.
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