CDM Parameters Research Articles

EZ-CDM: Fast, simple, robust, and accurate estimation of circular diffusion model parameters.

The investigation of cognitive processes that form the basis of decision-making in paradigms involving continuous outcomes has gained the interest of modeling researchers who aim to develop a dynamic decision theory that accounts for both speed and accuracy. One of the most important of these continuous models is the circular diffusion model (CDM, Smith. Psychological Review, 123(4), 425. 2016), which posits a noisy accumulation process mathematically described as a stochastic two-dimensional Wiener process inside a disk. Despite the considerable benefits of this model, its mathematical intricacy has limited its utilization among scholars. Here, we propose a straightforward and user-friendly method for estimating the CDM parameters and fitting the model to continuous-scale data using simple formulas that can be readily computed and do not require theoretical knowledge of model fitting or extensive programming. Notwithstanding its simplicity, we demonstrate that the aforementioned method performs with a level of accuracy that is comparable to that of the maximum likelihood estimation method. Furthermore, a robust version of the method is presented, which maintains its simplicity while exhibiting a high degree of resistance to contaminant responses. Additionally, we show that the approach is capable of reliably measuring the key parameters of the CDM, even when these values are subject to across-trial variability. Finally, we demonstrate the practical application of the method on experimental data. Specifically, an illustrative example is presented wherein the method is employed along with estimating the probability of guessing. It is hoped that the straightforward methodology presented here will, on the one hand, help narrow the divide between theoretical constructs and empirical observations on continuous response tasks and, on the other hand, inspire cognitive psychology researchers to shift their laboratory investigations towards continuous response paradigms.

Cosmology with the Planck T−E correlation coefficient

Tensions in cosmological parameters measurement motivate a revisit of the effects of instrumental systematics. In this article, we focus on the Pearson's correlation coefficient of the cosmic microwave background temperature and polarization E modes $\mathcal{R}_\ell^{\rm TE}$ which has the property of not being biased by multiplicative instrumental systematics. We build a $\mathcal{R}_\ell^{\rm TE}$-based likelihood for the Planck data, and present the first constraints on $\Lambda$CDM parameters from the correlation coefficient. Our results are compatible with parameters derived from a power spectra based likelihood. In particular the value of the Hubble parameter $H_0$ characterizing the expansion of the Universe today, 67.5 $\pm$ 1.3 km/s/Mpc, is consistent with the ones inferred from standard CMB analysis. We also discuss the consistency of the Planck correlation coefficient with the one computed from the most recent ACTPol power spectra.

Measurements of the E -mode polarization and temperature- E -mode correlation of the CMB from SPT-3G 2018 data

We present measurements of the $E$-mode ($EE$) polarization power spectrum and temperature-$E$-mode ($TE$) cross-power spectrum of the cosmic microwave background using data collected by SPT-3G, the latest instrument installed on the South Pole Telescope. This analysis uses observations of a 1500 deg$^2$ region at 95, 150, and 220 GHz taken over a four month period in 2018. We report binned values of the $EE$ and $TE$ power spectra over the angular multipole range $300 \le \ell < 3000$, using the multifrequency data to construct six semi-independent estimates of each power spectrum and their minimum-variance combination. These measurements improve upon the previous results of SPTpol across the multipole ranges $300 \le \ell \le 1400$ for $EE$ and $300 \le \ell \le 1700$ for $TE$, resulting in constraints on cosmological parameters comparable to those from other current leading ground-based experiments. We find that the SPT-3G dataset is well-fit by a $\Lambda$CDM cosmological model with parameter constraints consistent with those from Planck and SPTpol data. From SPT-3G data alone, we find $H_0 = 68.8 \pm 1.5 \mathrm{km\,s^{-1}\,Mpc^{-1}}$ and $\sigma_8 = 0.789 \pm 0.016$, with a gravitational lensing amplitude consistent with the $\Lambda$CDM prediction ($A_L = 0.98 \pm 0.12$). We combine the SPT-3G and the Planck datasets and obtain joint constraints on the $\Lambda$CDM model. The volume of the 68% confidence region in six-dimensional $\Lambda$CDM parameter space is reduced by a factor of 1.5 compared to Planck-only constraints, with only slight shifts in central values. We note that the results presented here are obtained from data collected during just half of a typical observing season with only part of the focal plane operable, and that the active detector count has since nearly doubled for observations made with SPT-3G after 2018.

Subhorizon linear Nash–Greene perturbations with constraints on H(z) and the deceleration parameter q(z)

The Hubble parameter H ( z ) , as a function of redshift, is modified by the presence of a new term originated from the extrinsic curvature in a four embedded space–time. Assuming an asymptotic expansion factor a ∼ 0 or, equivalently z → ∞ , it is obtained a nearly resemblance of the present model ( β -model) with the w CDM model with H ( z ) ∼ H w C D M ( z ) at background level. We test the models using a pack of recent datasets as the “Gold 2018” growth-rate data, the best-fit Planck2018/ Λ CDM parameters on the Cosmic Microwave Background (CMB), the Baryon Acoustic Oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the Hubble parameter data with redshift ranging from 0 . 01 < z < 2 . 3 . Performing the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) to ascertain the statistical viability of the model from Jeffreys’ scale, we apply a joint likelihood analysis to the data with the Markov Chain Monte Carlo (MCMC) method. We find that the present model is in very good agreement with observations with a close statistical equivalence with the Λ CDM and w CDM cosmologies at 1- σ level. We also show that a mild alleviation of the σ 8 discrepancy between the growth amplitude factor and the matter content ( σ 8 - Ω m ) of the observations from CMB and Large Scale Structure (LSS) probes. A comparison of the aforementioned full pack of data in MCMC chains is made with the resulting MCMC from Pantheon SNIa+ H ( z ) in order to analyse the sensitivity of the models and how they respond to a cosmography analysis on the evolution of H ( z ) and the deceleration parameter q ( z ) . As a result, we find that only the β -model can be unaffected to the variations of the previous datasets due to its several minima in the likelihood (degeneracies) of the related parameters with an overall percentage relative difference up to 8%. • Subhorizon linear perturbations in the embedding context. • Statistical equivalence of the present model with the Λ CDM and w CDM cosmologies at 1- σ level. • Cosmography analysis on the evolution of H ( z ) and the deceleration parameter q ( z ) • Mild alleviation of the σ 8 discrepancy.

Constraints on sigma _8 and degeneracies from linear Nash-Greene perturbations in subhorizon scale

Using a joint statistical analysis, we test a four-dimensional FLRW model embedded in a five-dimensional bulk based on the Nash-Greene embedding theorem. Performing a Markov Chain Monte Carlo (MCMC) modelling, we combine observational data sets as those of the recent growth data, the best-fit Planck2018/varLambda CDM parameters on the Cosmic Microwave Background (CMB), the Baryon Acoustic Oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the Hubble parameter data. From linear Nash-Greene fluctuations of the metric, we show the related perturbed equations in longitudinal Newtonian gauge to obtain the evolution of growth matter. A mild alleviation may be obtained from the degeneracies on the model parameter analyzing the sigma tension between the growth amplitude factor and the matter content in the plane (sigma _8-varOmega _m) on the observations from CMB and Large Scale Structure (LSS) probes. The Akaike Information Criterion (AIC) is also applied and we find a relative statistical consistence of the present model with both varLambda CDM and wCDM models lower than 1% of percentage difference at early times on the evolution of the Hubble function H(z). We also apply the Om(z) diagnosis to distinguish the present model from varLambda CDM and wCDM models.

Model comparison of Lambda CDM vs R_h=ct using cosmic chronometers

In 2012, Bilicki and Seikel (Mon Not R Astron Soc 425:1664, 2012) showed that H(z) data reconstructed using Gaussian Process Regression from cosmic chronometers and baryon acoustic oscillations, conclusively rules out the R_h=ct model. These results were disputed by Melia and collaborators in two different works (Melia and Maier in Mon Not R Astron Soc 432:2669, 2013; Melia and Yennapureddy in JCAP 2018:034, 2018), who showed using both an unbinned analysis and Gaussian Process reconstructed H(z) data from chronometers, that R_h=ct is favored over Lambda CDM model. To resolve this imbroglio, we carry out model comparison of Lambda CDM versus R_h=ct by independently reproducing the above claims using the latest chronometer data. We perform model selection between these two models using Bayesian model comparison. We find that no one model between Lambda CDM and R_h=ct is decisively favored when uniform priors on Lambda CDM parameters are used. However, if we use priors centered around the Planck best-fit values, then Lambda CDM is very strongly preferred over R_h=ct.

New physics in light of the H0 tension: An alternative view

The strong discrepancy between local and inverse distance ladder estimates of the Hubble constant $H_0$ could be pointing towards new physics beyond $\Lambda$CDM. Several attempts to address this tension through new physics rely on extended models, featuring extra free parameters beyond the 6 $\Lambda$CDM parameters. However, marginalizing over extra parameters has the effect of broadening the uncertainties on the inferred parameters, and it is often the case that within these models the $H_0$ tension is addressed due to larger uncertainties rather than a genuine shift in the central value of $H_0$. What happens if a physical theory is able to fix the extra parameters to a specific set of non-standard values? The degrees of freedom of the model are reduced with respect to the standard case where the extra parameters are free to vary. Focusing on the dark energy equation of state $w$ and the effective number of relativistic species $N_{\rm eff}$, I find that physical theories able to fix $w \approx -1.3$ or $N_{\rm eff} \approx 3.95$ would lead to an estimate of $H_0$ from CMB, BAO, and SNeIa data in perfect agreement with the local distance ladder estimate, without broadening its uncertainty. These two non-standard models are, from a model-selection perspective, strongly disfavoured with respect to $\Lambda$CDM. However, models that predict $N_{\rm eff} \approx 3.45$ would be able to bring the tension down to $1.5\sigma$ while only being weakly disfavored with respect to $\Lambda$CDM, whereas models that predict $w \approx -1.1$ would be able to bring the tension down to $2\sigma$ (at the cost of the preference for $\Lambda$CDM being definite). Finally, I estimate dimensionless multipliers relating variations in $H_0$ to variations in $w$ and $N_{\rm eff}$, which can be used to repeat the analysis of this paper in light of future more precise local distance ladder estimates of $H_0$.

On the tension between growth rate and CMB data

We analyze the claimed tension between redshift space distorsions measurements of f(z)sigma _8(z) and the predictions of standard varLambda CDM (Planck 2015 and 2018) cosmology. We consider a dataset consisting of 17 data points extending up to redshift z=1.52 and corrected for the Alcock-Paczynski effect. Thus, calculating the evolution of the growth factor in a wCDM cosmology, we find that the tension for the best fit parameters w, varOmega _m and sigma _8 with respect to the Planck 2018 varLambda CDM parameters is below 2sigma in all the marginalized confidence regions.

Analytic Calculation of Covariance between Cosmological Parameters from Correlated Data Sets, with an Application to SPTpol.

Consistency checks of cosmological data sets are an important tool because they may suggest systematic errors or the type of modifications to ΛCDM necessary to resolve current tensions. In this work, we derive an analytic method for calculating the level of correlations between model parameters from two correlated cosmological data sets, which complements more computationally expensive simulations. This method is an extension of the Fisher analysis that assumes a Gaussian likelihood and a known data covariance matrix. We apply this method to the South Pole Telescope Polarimeter (SPTpol) temperature and polarization cosmic microwave background (CMB) spectra (TE and EE). We find weak correlations between ΛCDM parameters with a 9% correlation between the TE-only and EE-only constraints on H 0 and a 25% and 32% correlation for log(A s ) and n s respectively. The TE-EE parameter differences are consistent with zero, with a probability to exceed of 0.53. Using simulations we show that this test is independent of the consistency of the SPTpol TE and EE band powers with the best-fit ΛCDM model spectra. Despite the negative correlations between the TE and EE power spectra, the correlations between TE-only and EE-only ΛCDM parameters are positive. Ignoring correlations in the TT-TE and TE-EE comparisons biases the χ 2 low, artificially making parameters look more consistent. Therefore, we conclude that these correlations need to be accounted for when performing internal consistency checks of the TT versus TE versus EE power spectra for future CMB analyses.

Improving constraints on fundamental physics parameters with the clustering of Sunyaev-Zeldovich selected galaxy clusters

Upcoming millimeter experiments that probe the cosmic microwave background (CMB) will observe tens of thousands of galaxy clusters through the thermal Sunyaev-Zeldovich (tSZ) effect. tSZ selected clusters are powerful probes of cosmological models, as they trace the late-time growth of structure. Late-time structure growth is highly sensitive to extensions to the standard cosmological model ($\Lambda$CDM), such as the sum of the neutrino masses, the dark energy equation of state, and modifications to general relativity. The nominal statistic used for cluster observations is their abundances as a function of redshift. We investigate what additional cosmological information is gained after including the clustering signal of clusters, the cluster power spectrum. We forecast the cluster power spectra for the upcoming Simons Observatory and a CMB Stage-4-like experiment and find that the cluster power spectrum reduces marginalized constraints on the dark energy equation of state by $3$--$12\%$ and the growth index by $5$--$8\%$, for example. We present the constraints using a generalized figure of merit and find improvements ranging from $12$--$18\%$ for extensions, $12$--$19\%$ for the astrophysical nuisance parameters, and $14$--$25\%$ for $\Lambda$CDM parameters. We also find that if the bias of clusters as a tracer of the matter density can be measured to within $3\%$ or better, these improvements can be increased by up to a factor of $6$. We discuss the possibility of utilizing the clustering signal to address specific systematic uncertainties present in cluster abundance measurements.

Hints of modified gravity in cosmos and in the lab?

General Relativity (GR) is consistent with a wide range of experiments/observations from millimeter scales up to galactic scales and beyond. However, there are reasons to believe that GR may need to be modified because it includes singularities (it is an incomplete theory) and also it requires fine-tuning to explain the accelerating expansion of the universe through the cosmological constant. Therefore, it is important to check various experiments and observations beyond the above range of scales for possible hints of deviations from the predictions of GR. If such hints are found it is important to understand which classes of modified gravity theories are consistent with them. The goal of this review is to summarize recent progress on these issues. On sub-millimeter scales, we show an analysis of the data of the Washington experiment [D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R. Heckel, C. D. Hoyle and H. E. Swanson, Phys. Rev. Lett. 98 (2007) 021101, arXiv:hep-ph/0611184 [hep-ph]] searching for modifications of Newton’s Law on sub-millimeter scales and demonstrate that a spatially oscillating signal is hidden in this dataset. We demonstrate that even though this signal cannot be explained in the context of standard modified theories (viable scalar tensor and [Formula: see text] theories), it is a rather generic prediction of nonlocal gravity theories. On cosmological scales we review recent analyses of Redshift Space Distortion (RSD) data which measure the growth rate of cosmological perturbations at various redshifts and show that these data are in some tension with the [Formula: see text]CDM parameter values indicated by Planck/2015 CMB data at about [Formula: see text] level. This tension can be reduced by allowing for an evolution of the effective Newton constant that determines the growth rate of cosmological perturbations. We conclude that even though this tension between the data and the predictions of GR could be due to systematic/statistical uncertainties of the data, it could also constitute early hints pointing towards a new gravitational theory.

Covariant Canonical Gauge Gravitation and Cosmology

The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations necessarily embrace a quadratic Riemann term added to Einstein’s linear equation. The quadratic term endows space-time with inertia generating a dynamic response of the space-time geometry to deformations relative to (Anti) de Sitter geometry. A “deformation parameter” is identified, the inverse dimensionless coupling constant governing the relative strength of the quadratic invariant in the Hamiltonian, and directly observable via the deceleration parameter q0. The quadratic invariant makes the system inconsistent with Einstein’s constant cosmological term, Λ = const. In the Friedman model this inconsistency is resolved with the scaling ansatz of a “cosmological function”, Λ(a), where a is the scale parameter of the FLRW metric. The cosmological function can be normalized such that with the A CDM parameter set the present-day observables, the Hubble constant and the deceleration parameter, can be reproduced. With this parameter set we recover the dark energy scenario in the late epoch. The proof that inflation in the early phase is caused by the “geometrical fluid” representing the inertia of space-time is yet pending, though. Nevertheless, as according to the CCGG theory the present-day cosmological function, identified with the currently observed Λobs, is a balanced mix of two contributions. These are the (A)dS curvature plus the residual vacuum energy of space-time and matter. The curvature term is proportional to the deformation parameter given by the coupling strength of the quadratic Riemann term. This allows for a fresh look at the Cosmological Constant Problem that plagues the standard Einstein-Friedman cosmology.

Sounds Discordant: Classical Distance Ladder and ΛCDM-based Determinations of the Cosmological Sound Horizon

Abstract Type Ia supernovae, calibrated by classical distance ladder methods, can be used, in conjunction with galaxy survey two-point correlation functions, to empirically determine the size of the sound horizon r s. Assumption of the ΛCDM model, together with data to constrain its parameters, can also be used to determine the size of the sound horizon. Using a variety of cosmic microwave background (CMB) data sets to constrain ΛCDM parameters, we find the model-based sound horizon to be larger than the empirically determined one with a statistical significance of between 2σ and 3σ, depending on the data set. If reconciliation requires a change to the cosmological model, we argue that change is likely to be important in the two decades of scale factor evolution prior to recombination. Future CMB observations will therefore likely be able to test any such adjustments; e.g., a third-generation CMB survey like SPT-3G can achieve a threefold improvement in the constraints on r s in the ΛCDM model extended to allow additional light degrees of freedom.

Strong bounds on sum of neutrino masses in a 12 parameter extended scenario with non-phantom dynamical dark energy (w(z)ge -1)

We obtained constraints on a 12 parameter extended cosmological scenario including non-phantom dynamical dark energy (NPDDE) with CPL parametrization. We also include the six Lambda CDM parameters, number of relativistic neutrino species (N_{text {eff}}) and sum over active neutrino masses (sum m_{nu }), tensor-to-scalar ratio (r_{0.05}), and running of the spectral index (n_{run}). We use CMB Data from Planck 2015; BAO Measurements from SDSS BOSS DR12, MGS, and 6dFS; SNe Ia Luminosity Distance measurements from the Pantheon Sample; CMB B-mode polarization data from BICEP2/Keck collaboration (BK14); Planck lensing data; and a prior on Hubble constant (73.24pm 1.74 km/s/Mpc) from local measurements (HST). We have found strong bounds on the sum of the active neutrino masses. For instance, a strong bound of sum m_{nu } < 0.123 eV (95% CL) comes from Planck+BK14+BAO. Although we are in such an extended parameter space, this bound is stronger than a bound of sum m_{nu }< 0.158 eV (95% CL) obtained in Lambda text {CDM}+sum m_{nu } with Planck+BAO. Varying A_{text {lens}} instead of r_{0.05} however leads to weaker bounds on sum m_{nu }. Inclusion of the HST leads to the standard value of N_{text {eff}} = 3.045 being discarded at more than 68% CL, which increases to 95% CL when we vary A_{text {lens}} instead of r_{0.05}, implying a small preference for dark radiation, driven by the H_0 tension.

Interacting Dark Energy in the Dark SU(2) R Model

We explore the cosmological implications of the interactions among the dark particles in the dark $SU(2)_R$ model. It turns out that the relevant interaction is between dark energy and dark matter, through a decay process. With respect to the standard $\Lambda$CDM model, it changes only the background equations. We note that the observational aspects of the model are dominated by degeneracies between the parameters that describe the process. Thus, only the usual $\Lambda$CDM parameters, such as the Hubble expansion rate and the dark energy density parameter (interpreted as the combination of the densities of the dark energy doublet) could be constrained by observations at this moment.

Evolution of the fσ8 tension with the Planck15/ΛCDM determination and implications for modified gravity theories

We construct an updated extended compilation of distinct (but possibly correlated) $f\sigma_8(z)$ Redshift Space Distortion (RSD) data published between 2006 and 2018. It consists of 63 datapoints and is significantly larger than previously used similar datasets. After fiducial model correction we obtain the best fit $\Omega_{0m}-\sigma_8$ $\Lambda$CDM parameters and show that they are at a $5\sigma$ tension with the corresponding Planck15/$\Lambda$CDM values. Introducing a nontrivial covariance matrix correlating randomly $20\%$ of the RSD datapoints has no significant effect on the above tension level. We show that the tension disappears (becomes less than $1\sigma$) when a subsample of the 20 most recently published data is used. A partial cause for this reduced tension is the fact that more recent data tend to probe higher redshifts (with higher errorbars) where there is degeneracy among different models due to matter domination. Allowing for a nontrivial evolution of the effective Newton's constant as $G_{\textrm{eff}}(z)/G_{\textrm{N}} = 1 + g_a \left(\frac{z}{1+z}\right)^2 - g_a \left(\frac{z}{1+z}\right)^4$ ($g_a$ is a parameter) and fixing a \plcdm background we find $g_a=-0.91\pm 0.17$ from the full $f\sigma_8$ dataset while the 20 earliest and 20 latest datapoints imply $g_a=-1.28^{+0.28}_{-0.26}$ and $g_a=-0.43^{+0.46}_{-0.41}$ respectively. Thus, the more recent $f\sigma_8$ data appear to favor GR in contrast to earlier data. Finally, we show that the parametrization $f\sigma_8(z)=\lambda \sigma_8 \Omega(z)^\gamma /(1+z)^\beta$ provides an excellent fit to the solution of the growth equation for both GR ($g_a=0$) and modified gravity ($g_a\neq 0$).

Bayesian correction of H(z) data uncertainties

We compile 41 $H(z)$ data from literature and use them to constrain O$\Lambda$CDM and flat $\Lambda$CDM parameters. We show that the available $H(z)$ suffers from uncertainties overestimation and propose a Bayesian method to reduce them. As a result of this method, using $H(z)$ only, we find, in the context of O$\Lambda$CDM, $H_0=69.5\pm2.5\mathrm{\,km\,s^{-1}Mpc^{-1}}$, $\Omega_m=0.242\pm0.036$ and $\Omega_\Lambda=0.68\pm0.14$. In the context of flat $\Lambda$CDM model, we have found $H_0=70.4\pm1.2\mathrm{\,km\,s^{-1}Mpc^{-1}}$ and $\Omega_m=0.256\pm0.014$. This corresponds to an uncertainty reduction of up to 30\% when compared to the uncorrected analysis in both cases.

Tension and constraints on modified gravity parametrizations of Geff(z) from growth rate and Planck data

We construct an updated and extended compilation of growth rate data consisting of 34 points and including corrections for model dependence. In order to maximize the independence of the datapoints we also construct a subsample of this compilation (`Gold' growth dataset) which consists of 18 datapoints. We test the consistency of this dataset with the best fit Planck15/$\Lambda$CDM parameters in the context of General Relativity (GR) using the evolution equation for the growth factor $\delta(a)$ with a $w$CDM background. We find tension at the $\sim 3 \sigma$ level between the best fit parameters $w$ (the dark energy equation of state), $\Omega_{0m}$ (the matter density parameter) and $\sigma_8$ (the matter power spectrum normalization on scales $8h^{-1}$Mpc) and the corresponding Planck15/$\Lambda$CDM parameters. We show that the tension disappears if we allow for evolution of the effective Newton's constant, parametrized as $G_{eff}(a)/G_N = 1 + g_a(1-a)^n-g_a(1-a)^{2n}$ with $n\ge2$ where $g_a$, $n$ are parameters of the model, $a$ is the scale factor and $z = 1/a-1$ is the redshift. This parametrization satisfies three criteria: a. $G_{eff} > 0$, b. Consistency with Big Bang Nucleosynthesis ($G_{eff}(a\ll 1)/G_N=1$), c. Consistency with solar system tests ($G_{eff}(a=1)/G_N=1$ and $G_{eff}'(a=1)/G_N=0$). We show that the best fit form of $G_{eff}(z)$ obtained from the growth data corresponds to weakening gravity at recent redshifts (decreasing function of $z$) and we demonstrate that this behavior is not consistent with any scalar-tensor Lagrangian with a real scalar field. Finally, we use MGCAMB to find the best fit $G_{eff}(z)$ obtained from the Planck CMB power spectrum on large angular scales and show that it is a mildly increasing function of $z$, in $3\sigma$ tension with the corresponding decreasing best fit $G_{eff}(z)$ obtained from the growth data.

Towards optimal cosmological parameter recovery from compressed bispectrum statistics

Over the next decade, improvements in cosmological parameter constraints will be driven by surveys of large-scale structure. Its inherent non-linearity suggests that significant information will be embedded in higher correlations beyond the two-point function. Extracting this information is extremely challenging: it requires accurate theoretical modelling and significant computational resources to estimate the covariance matrix describing correlations between different Fourier configurations. We investigate whether it is possible to reduce the covariance matrix without significant loss of information by using a proxy that aggregates the bispectrum over a subset of Fourier configurations. Specifically, we study the constraints on $\Lambda$CDM parameters from combining the power spectrum with (a) the modal bispectrum decomposition, (b) the line correlation function and (c) the integrated bispectrum. We forecast the error bars achievable on $\Lambda$CDM parameters using these proxies in a future galaxy survey and compare them to those obtained from measurements of the Fourier bispectrum, including simple estimates of their degradation in the presence of shot noise. Our results demonstrate that the modal bispectrum performs as well as the Fourier bispectrum, even with considerably fewer modes than Fourier configurations. The line correlation function has good performance but does not match the modal bispectrum. The integrated bispectrum is comparatively insensitive to changes in the background cosmology. We find that adding bispectrum data can improve constraints on bias parameters and the normalization $\sigma_8$ by up to 5 compared to power spectrum measurements alone. For other parameters, improvements of up to $\sim$ 20% are possible. Finally, we use a range of theoretical models to explore how the sophistication required for realistic predictions varies with each proxy. (abridged)

CMB lens sample covariance and consistency relations

Gravitational lensing information from the two and higher point statistics of the CMB temperature and polarization fields are intrinsically correlated because they are lensed by the same realization of structure between last scattering and observation. Using an analytic model for lens sample covariance, we show that there is one mode, separately measurable in the lensed CMB power spectra and lensing reconstruction, that carries most of this correlation. Once these measurements become lens sample variance dominated, this mode should provide a useful consistency check between the observables that is largely free of sampling and cosmological parameter errors. Violations of consistency could indicate systematic errors in the data and lens reconstruction or new physics at last scattering, any of which could bias cosmological inferences and delensing for gravitational waves. A second mode provides a weaker consistency check for a spatially flat universe. Our analysis isolates the additional information supplied by lensing in a model independent manner but is also useful for understanding and forecasting CMB cosmological parameter errors in the extended $\Lambda$CDM parameter space of dark energy, curvature and massive neutrinos. We introduce and test a simple but accurate forecasting technique for this purpose that neither double counts lensing information nor neglects lensing in the observables.