Optimal dataset combining in f_nl constraints from large scale structure in an idealised case

We consider the problem of optimal weighting of tracers of structure for the purpose of constraining the non-Gaussianity parameter f_NL. We work within the Fisher matrix formalism expanded around fiducial model with f_NL=0 and make several simplifying assumptions. By slicing a general sample into infinitely many samples with different biases, we derive the analytic expression for the relevant Fisher matrix element. We next consider weighting schemes that construct two effective samples from a single sample of tracers with a continuously varying bias. We show that a particularly simple ansatz for weighting functions can recover all information about f_NL in the initial sample that is recoverable using a given bias observable and that simple division into two equal samples is considerably suboptimal when sampling of modes is good, but only marginally suboptimal in the limit where Poisson errors dominate.Comment: 6 pages, 5 figures; v2: comment on weighting for PS determination, fixed a couple of typos; v3: revised, matches version accepted by JCA

Measuring primordial non-gaussianity without cosmic variance

Non-gaussianity in the initial conditions of the universe is one of the most powerful mechanisms to discriminate among the competing theories of the early universe. Measurements using bispectrum of cosmic microwave background anisotropies are limited by the cosmic variance, i.e. available number of modes. Recent work has emphasized the possibility to probe non-gaussianity of local type using the scale dependence of large scale bias from highly biased tracers of large scale structure. However, this power spectrum method is also limited by cosmic variance, finite number of structures on the largest scales, and by the partial degeneracy with other cosmological parameters that can mimic the same effect. Here we propose an alternative method that solves both of these problems. It is based on the idea that on large scales halos are biased, but not stochastic, tracers of dark matter: by correlating a highly biased tracer of large scale structure against an unbiased tracer one eliminates the cosmic variance error, which can lead to a high signal to noise even from the structures comparable to the size of the survey. The square of error improvement on non-gaussianity parameter f_nl relative to the power spectrum method scales as Pn/2, where P and n is the power spectrum and the number density of the biased tracer, respectively. For an ideal survey out to z=2 the error reduction can be as large as a factor of seven, which should guarantee a detection of non-gaussianity from an all sky survey of this type. The improvements could be even larger if high density tracers that are sensitive to non-gaussianity can be identified and measured over a large volume.Comment: 7 page

Non-Gaussianity and large-scale structure in a two-field inflationary model

Single field inflationary models predict nearly Gaussian initial conditions and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constraints on the local non-Gaussianity parameter $\tilde f_{\rm NL}$ and the ratio $\xi$ of the amplitude of primordial perturbations due to the inflaton and curvaton using WMAP and SDSS data

Inverted initial conditions: Exploring the growth of cosmic structure and voids

We introduce and explore "paired" cosmological simulations. A pair consists of an A and B simulation with initial conditions related by the inversion δAðx; tinitialÞ ¼ −δBðx; tinitialÞ (underdensities substituted for overdensities and vice versa). We argue that the technique is valuable for improving our understanding of cosmic structure formation. The A and B fields are by definition equally likely draws from ΛCDM initial conditions, and in the linear regime evolve identically up to the overall sign. As nonlinear evolution takes hold, a region that collapses to form a halo in simulation A will tend to expand to create a void in simulation B. Applications include (i) contrasting the growth of A-halos and B-voids to test excursion-set theories of structure formation, (ii) cross-correlating the density field of the A and B universes as a novel test for perturbation theory, and (iii) canceling error terms by averaging power spectra between the two boxes. Generalizations of the method to more elaborate field transformations are suggested

How to measure redshift-space distortions without sample variance

We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter beta=f/b=(dlnD/dlna)/b (where D is the growth rate and a the expansion factor), to a much better precision than one could achieve with a single tracer, to an arbitrary precision in the low noise limit. In combination with the power spectrum of the tracers this allows a much more precise measurement of the bias-free velocity divergence power spectrum, f^2 P_m - in fact, in the low noise limit f^2 P_m can be measured as well as would be possible if velocity divergence was observed directly, with rms improvement factor ~[5.2(beta^2+2 beta+2)/beta^2]^0.5 (e.g., ~10 times better than a single tracer for beta=0.4). This would allow a high precision determination of f D as a function of redshift with an error as low as 0.1%. We find up to two orders of magnitude improvement in Figure of Merit for the Dark Energy equation of state relative to Stage II, a factor of several better than other proposed Stage IV Dark Energy surveys. The ratio b_2/b_1 will be determined with an even greater precision than beta, producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with signal to noise of unity on scales of interest, and are not optimized for this technique. Our results suggest that this strategy may need to be revisited as there are large gains to be achieved from surveys with higher number densities of galaxies.Comment: 22 pages, 13 figure

Snowmass2021 Cosmic Frontier: Report of the CF04 Topical Group on Dark Energy and Cosmic Acceleration in the Modern Universe

Cosmological observations in the new millennium have dramatically increased our understanding of the Universe, but several fundamental questions remain unanswered. This topical group report describes the best opportunities to address these questions over the coming decades by extending observations to the $z<6$ universe. The greatest opportunity to revolutionize our understanding of cosmic acceleration both in the modern universe and the inflationary epoch would be provided by a new Stage V Spectroscopic Facility (Spec-S5) which would combine a large telescope aperture, wide field of view, and high multiplexing. Such a facility could simultaneously provide a dense sample of galaxies at lower redshifts to provide robust measurements of the growth of structure at small scales, as well as a sample at redshifts $2<z<5$ to measure cosmic structure at the largest scales, spanning a sufficient volume to probe primordial non-Gaussianity from inflation, to search for features in the inflationary power spectrum on a broad range of scales, to test dark energy models in poorly-explored regimes, and to determine the total neutrino mass and effective number of light relics. A number of compelling opportunities at smaller scales should also be pursued alongside Spec-S5. The science collaborations analyzing DESI and LSST data will need funding for a variety of activities, including cross-survey simulations and combined analyses. The results from these experiments can be greatly improved by smaller programs to obtain complementary data, including follow-up studies of supernovae and spectroscopy to improve photometric redshift measurements. The best future use of the Vera C. Rubin Observatory should be evaluated later this decade after the first LSST analyses have been done. Finally, investments in pathfinder projects could enable powerful new probes of cosmology to come online in future decades.Comment: Topical Group Report for CF04 (Dark Energy and Cosmic Acceleration in the Modern Universe) for Snowmass 202