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Register a new userTesting one-loop galaxy bias: joint analysis of power spectrum and bispectrum
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Alexander Eggemeier
Publication date
2021
fields
Physics
and research's language is
English
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We present a joint likelihood analysis of the real-space power spectrum and bispectrum measured from a variety of halo and galaxy mock catalogs. A novel aspect of this work is the inclusion of nonlinear triangle configurations for the bispectrum, made possible by a complete next-to-leading order (one-loop) description of galaxy bias, as is already common practice for the power spectrum. Based on the goodness-of-fit and the unbiasedness of the parameter posteriors, we accomplish a stringent validation of this model compared to the leading order (tree-level) bispectrum. Using measurement uncertainties that correspond to an effective survey volume of $6,(mathrm{Gpc}/h)^3$, we determine that the one-loop corrections roughly double the applicable range of scales, from $sim 0.17,h/mathrm{Mpc}$ (tree-level) to $sim 0.3,h/mathrm{Mpc}$. This converts into a $1.5 - 2$x improvement on constraints of the linear bias parameter at fixed cosmology, and a $1.5 - 2.4$x shrinkage of uncertainties on the amplitude of fluctuations $A_s$, which clearly demonstrates the benefit of extracting information from nonlinear scales despite having to marginalize over a larger number of bias parameters. Besides, our precise measurements of galaxy bias parameters up to fourth order allow for thorough comparisons to coevolution relations, showing excellent agreement for all contributions generated by the nonlocal action of gravity. Using these relations in the likelihood analysis does not compromise the model validity and is crucial for obtaining the quoted improvements on $A_s$. We also analyzed the impact of higher-derivative and scale-dependent stochastic terms, finding that for a subset of our tracers the former can boost the performance of the tree-level model with constraints on $A_s$ that are only slightly degraded compared to the one-loop model.
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We investigate the impact of different assumptions in the modeling of one-loop galaxy bias on the recovery of cosmological parameters, as a follow up of the analysis done in the first paper of the series at fixed cosmology. We use three different synthetic galaxy samples whose clustering properties match the ones of the CMASS and LOWZ catalogues of BOSS and the SDSS Main Galaxy Sample. We investigate the relevance of allowing for either short range non-locality or scale-dependent stochasticity by fitting the real-space galaxy auto power spectrum or the combination of galaxy-galaxy and galaxy-matter power spectrum. From a comparison among the goodness-of-fit ($chi^2$), unbiasedness of cosmological parameters (FoB), and figure-of-merit (FoM), we find that a four-parameter model (linear, quadratic, cubic non-local bias, and constant shot-noise) with fixed quadratic tidal bias provides a robust modelling choice for the auto power spectrum of the three samples, up to $k_{rm max}=0.3,h,mathrm{Mpc}^{-1}$ and for an effective volume of $6,h^{-3},mathrm{Gpc}^3$. Instead, a joint analysis of the two observables fails at larger scales, and a model extension with either higher derivatives or scale-dependent shot-noise is necessary to reach a similar $k_{rm max}$, with the latter providing the most stable results. These findings are obtained with three, either hybrid or perturbative, prescriptions for the matter power spectrum, texttt{RESPRESSO}, gRPT and EFT. In all cases, the inclusion of scale-dependent shot-noise increases the range of validity of the model in terms of FoB and $chi^2$. Interestingly, these model extensions with additional free parameters do not necessarily lead to an increase in the maximally achievable FoM for the cosmological parameters $left(h,,Omega_ch^2,,A_sright)$, which are generally consistent to those of the simpler model at smaller $k_{rm max}$.
We perform a joint analysis of the power spectrum and the bispectrum of the CMB temperature and polarization anisotropies to improve the constraints on isocurvature modes. We construct joint likelihoods, both for the existing Planck data, and to make forecasts for the future LiteBIRD and CMB-S4 experiments. We assume a general two-field inflation model with five free parameters, leading to one isocurvature mode (which can be CDM density, neutrino density or neutrino velocity) arbitrarily correlated with the adiabatic mode. We theoretically assess in which cases (of detecting and/or fixing parameters) improvements can be expected, to guide our subsequent numerical analyses. We find that for Planck, which detected neither isocurvature modes nor primordial non-Gaussianity, the joint analysis does not improve the constraints in the general case. However, if we fix additional parameters in the model, the improvements can be highly significant depending on the chosen parameter values. For LiteBIRD+CMB-S4 we study in which regions of parameter space compatible with the Planck results the joint analysis will improve the constraints or the significance of a detection. We find that, while for CDM isocurvature this region is very small, for the neutrino isocurvature modes it is much larger. In particular for neutrino velocity it can be about half of the Planck-allowed region, where the joint analysis reduces the isocurvature error bars by up to 70%. In addition the joint analysis can also improve the error bars of some of the standard cosmological parameters, by up to 30% for $theta_{MC}$ for example, by breaking the degeneracies with the correlation parameter between adiabatic and isocurvature modes.
One of the cornerstones of general relativity is the equivalence principle. However, the validity of the equivalence principle has only been established on solar system scales for standard matter fields; this result cannot be assumed to hold for the non-standard matter fields that dominate the gravitational dynamics on cosmological scales. Here we show how the equivalence principle may be tested on cosmological scales for non-standard matter fields using the odd multipoles of the galaxy cross-power spectrum and bispectrum. This test makes use of the imprint on the galaxy cross-power spectrum and bispectrum by the parity-violating general relativistic deformations of the past-light cone, and assumes that galaxies can be treated as test particles that are made of baryons and cold dark matter. This assumption leads to a non-zero galaxy-baryon relative velocity if the equivalence principle does not hold between baryons and dark matter. We show that the relative velocity can be constrained to be less than 28% of the galaxy velocity using the cross-power spectrum of the HI intensity mapping/H$alpha$ galaxy survey and the bispectrum of the H$alpha$ galaxy survey.
We use hydrodynamical separate universe simulations with the IllustrisTNG model to predict the local primordial non-Gaussianity (PNG) bias parameters $b_{phi}$ and $b_{phidelta}$, which enter at leading order in the galaxy power spectrum and bispectrum. This is the first time that $b_{phidelta}$ is measured from either gravity-only or galaxy formation simulations. For dark matter halos, the popular assumption of universality overpredicts the $b_{phidelta}(b_1)$ relation in the range $1 lesssim b_1 lesssim 3$ by up to $Delta b_{phidelta} sim 3$ ($b_1$ is the linear density bias). The adequacy of the universality relation is worse for the simulated galaxies, with the relations $b_{phi}(b_1)$ and $b_{phidelta}(b_1)$ being generically redshift-dependent and very sensitive to how galaxies are selected (we test total, stellar and black hole mass, black hole mass accretion rate and color). The uncertainties on $b_{phi}$ and $b_{phidelta}$ have a direct, often overlooked impact on the constraints of the local PNG parameter $f_{rm NL}$, which we study and discuss. For a survey with $V = 100{rm Gpc}^3/h^3$ at $z=1$, uncertainties $Delta b_{phi} lesssim 1$ and $Delta b_{phidelta} lesssim 5$ around values close to the fiducial can yield relatively unbiased constraints on $f_{rm NL}$ using power spectrum and bispectrum data. We also show why priors on galaxy bias are useful even in analyses that fit for products $f_{rm NL} b_{phi}$ and $f_{rm NL} b_{phidelta}$. The strategies we discuss to deal with galaxy bias uncertainties can be straightforwardly implemented in existing $f_{rm NL}$ constraint analyses (we provide fits for some of the bias relations). Our results motivate more works with galaxy formation simulations to refine our understanding of $b_{phi}$ and $b_{phidelta}$ towards improved constraints on $f_{rm NL}$.
The apparent anisotropies of the galaxy clustering in observable redshift space provide a unique opportunity to simultaneously probe cosmic expansion and gravity on cosmological scales via the Alcock--Paczynski effect and redshift-space distortions. While the improved theoretical models have been proposed and developed to describe the apparent anisotropic clustering at weakly non-linear scales, the applicability of these models is still limited in the presence of the non--perturbative smearing effect caused by the randomness of the relative velocities. Although the cosmological constraint from the anisotropic clustering will be certainly improved with a more elaborate theoretical model, we here consider an alternative way by using the statistical power of both the power spectrum and bispectrum at large scales. Based on the Fisher matrix analysis, we estimate the benefit of combining the power spectra and bispectra, finding that the constraints on the cosmic expansion and growth of structure will be improved by a factor of two. This compensates for the loss of constraining power using the power spectrum alone due to the randomness of the relative velocities.
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