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Register a new userPrimordial Non-Gaussianity from Biased Tracers: Likelihood Analysis of Real-Space Power Spectrum and Bispectrum
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Added by
Azadeh Moradinezhad Dizgah
Publication date
2020
fields
Physics
and research's language is
English
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Upcoming galaxy redshift surveys promise to significantly improve current limits on primordial non-Gaussianity (PNG) through measurements of 2- and 3-point correlation functions in Fourier space. However, realizing the full potential of this dataset is contingent upon having both accurate theoretical models and optimized analysis methods. Focusing on the local model of PNG, parameterized by $f_{rm NL}$, we perform a Monte-Carlo Markov Chain analysis to confront perturbation theory predictions of the halo power spectrum and bispectrum in real space against a suite of N-body simulations. We model the halo bispectrum at tree-level, including all contributions linear and quadratic in $f_{rm NL}$, and the halo power spectrum at 1-loop, including tree-level terms up to quadratic order in $f_{rm NL}$ and all loops induced by local PNG linear in $f_{rm NL}$. Keeping the cosmological parameters fixed, we examine the effect of informative priors on the linear non-Gaussian bias parameter on the statistical inference of $f_{rm NL}$. A conservative analysisof the combined power spectrum and bispectrum, in which only loose priors are imposed and all parameters are marginalized over, can improve the constraint on $f_{rm NL}$ by more than a factor of 5 relative to the power spectrum-only measurement. Imposing a strong prior on $b_phi$, or assuming bias relations for both $b_phi$ and $b_{phidelta}$ (motivated by a universal mass function assumption), improves the constraints further by a factor of few. In this case, however, we find a significant systematic shift in the inferred value of $f_{rm NL}$ if the same range of wavenumber is used. Likewise, a Poisson noise assumption can lead to significant systematics, and it is thus essential to leave all the stochastic amplitudes free.
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Large-scale Fourier modes of the cosmic density field are of great value for learning about cosmology because of their well-understood relationship to fluctuations in the early universe. However, cosmic variance generally limits the statistical precision that can be achieved when constraining model parameters using these modes as measured in galaxy surveys, and moreover, these modes are sometimes inaccessible due to observational systematics or foregrounds. For some applications, both limitations can be circumvented by reconstructing large-scale modes using the correlations they induce between smaller-scale modes of an observed tracer (such as galaxy positions). In this paper, we further develop a formalism for this reconstruction, using a quadratic estimator similar to the one used for lensing of the cosmic microwave background. We incorporate nonlinearities from gravity, nonlinear biasing, and local-type primordial non-Gaussianity, and verify that the estimator gives the expected results when applied to N-body simulations. We then carry out forecasts for several upcoming surveys, demonstrating that, when reconstructed modes are included alongside directly-observed tracer density modes, constraints on local primordial non-Gaussianity are generically tightened by tens of percents compared to standard single-tracer analyses. In certain cases, these improvements arise from cosmic variance cancellation, with reconstructed modes taking the place of modes of a separate tracer, thus enabling an effective multitracer approach with single-tracer observations.
After reionisation, the 21cm emission line of neutral hydrogen within galaxies provides a tracer of dark matter. Next-generation intensity mapping surveys, with the SKA and other radio telescopes, will cover large sky areas and a wide range of redshifts, facilitating their use as probes of primordial non-Gaussianity. {Previous works have shown that the bispectrum can achieve tight constraints on primordial non-Gaussianity with future surveys that are purposely designed for intensity mapping in interferometer mode}. Here we investigate the constraints attainable from surveys operating in single-dish mode, rev{using the combined power spectrum and bispectrum signal}. In the case of the power spectrum, single-dish surveys typically outperform interferometer surveys. We find that the reverse holds for the bispectrum: single-dish surveys are not competitive with surveys designed for interferometer mode.
The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors ${bf k_1,k_2,k_3}$ with respect to the line of sight. Here we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane parallel approximation only the first four even $ell$ multipoles have non-zero values, and we present explicit analytical expressions for all the non-zero multipoles {it i.e.} upto $ell=6,m=4$. The ratio of the different multipole moments to the real space bispectrum depends only on $beta_1$ the linear redshift distortion parameter and the shape of the triangle. Considering triangles of all possible shapes, we have studied how this ratio depends on the shape of the triangle for $beta_1=1$. We have also studied the $beta_1$ dependence for some of the extreme triangle shapes. If measured in future, these multipole moments hold the potential of constraining $beta_1$. The results presented here are also important if one wishes to constrain $f_{text{NL}}$ using redshift surveys.
We present the one-loop perturbation theory for the power spectrum of the marked density field of matter and biased tracers in real- and redshift-space. The statistic has been shown to yield impressive constraints on cosmological parameters; to exploit this, we require an accurate and computationally inexpensive theoretical model. Comparison with $N$-body simulations demonstrates that linear theory fails on all scales, but inclusion of one-loop Effective Field Theory terms gives a substantial improvement, with $sim 5%$ accuracy at $z = 1$. The expansion is less convergent in redshift-space (achieving $sim 10%$ accuracy), but there are significant improvements for biased tracers due to the freedom in the bias coefficients. The large-scale theory contains non-negligible contributions from all perturbative orders; we suggest a reorganization of the theory that contains all terms relevant on large-scales, discussing both its explicit form at one-loop and structure at infinite-loop. This motivates a low-$k$ correction term, leading to a model that is sub-percent accurate on large scales, albeit with the inclusion of two (three) free coefficients in real- (redshift-)space. We further consider the effects of massive neutrinos, showing that beyond-EdS corrections to the perturbative kernels are negligible in practice. It remains to see whether the purported gains in cosmological parameters remain valid for biased tracers and can be captured by the theoretical model.
Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power spectrum and bispectrum for high-precision measurements of primordial non-Gaussianity. In turn, these measurements will allow us to distinguish between various models of inflation. However, precision observations require theoretical precision at least at the same level. We extend the theoretical understanding of the galaxy bispectrum by incorporating a consistent general relativistic model of galaxy bias at second order, in the presence of local primordial non-Gaussianity. The influence of primordial non-Gaussianity on the bispectrum extends beyond the galaxy bias and the dark matter density, due to redshift-space effects. The standard redshift-space distortions at first and second order produce a well-known primordial non-Gaussian imprint on the bispectrum. Relativistic corrections to redshift-space distortions generate new contributions to this primordial non-Gaussian signal, arising from: (1)~a coupling of first-order scale-dependent bias with first-order relativistic observational effects, and (2)~linearly evolved non-Gaussianity in the second-order velocity and metric potentials which appear in relativistic observational effects. Our analysis allows for a consistent separation of the relativistic `contamination from the primordial signal, in order to avoid biasing the measurements by using an incorrect theoretical model. We show that the bias from using a Newtonian analysis of the squeezed bispectrum could be $Delta fnlsim 5$ for a Stage IV H$alpha$ survey.
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