Constraints on Neutrino Mass and Light Degrees of Freedom in Extended Cosmological Parameter Spaces

From a combination of probes including the cosmic microwave background (WMAP7+SPT), Hubble constant (HST), baryon acoustic oscillations (SDSS+2dFGRS), and supernova distances (Union2), we have explored the extent to which the constraints on the effective number of neutrinos and sum of neutrino masses are affected by our ignorance of other cosmological parameters, including the curvature of the universe, running of the spectral index, primordial helium abundance, evolving late-time dark energy, and early dark energy. In a combined analysis of the effective number of neutrinos and sum of neutrino masses, we find mild (2.2 sigma) preference for additional light degrees of freedom. However, the effective number of neutrinos is consistent with the canonical expectation of 3 massive neutrinos and no extra relativistic species to within 1 sigma when allowing for evolving dark energy and relaxing the strong inflation prior on the curvature and running. The agreement improves with the possibility of an early dark energy component, itself constrained to be less than 5% of the critical density (95% CL) in our expanded parameter space. In extensions of the standard cosmological model, the derived amplitude of linear matter fluctuations sigma_8 is found to closely agree with low-redshift cluster abundance measurements. The sum of neutrino masses is robust to assumptions of the effective number of neutrinos, late-time dark energy, curvature, and running at the level of 1.2 eV (95% CL). The upper bound degrades to 2.0 eV (95% CL) when further including the early dark energy density and primordial helium abundance as additional free parameters. Even in extended cosmological parameter spaces, Planck alone could determine the possible existence of extra relativistic species at 4 sigma confidence and constrain the sum of neutrino masses to 0.2 eV (68% CL).Comment: 14 pages, 4 figures. Minor refinements, reflects version accepted for publication in PRD (slow to get the paper published because of sickness

Weak lensing and dark energy: the impact of dark energy on nonlinear dark matter clustering

We examine the influence of percent-level dark energy corrections to the nonlinear matter power spectrum on constraints of the dark energy equation of state from future weak lensing probes. We explicitly show that a poor approximation (off by > 10%) to the nonlinear corrections causes a > 1 sigma bias on the determination of the dark energy equation of state. Future weak lensing surveys must therefore incorporate dark energy modifications to the nonlinear matter power spectrum accurate to the percent-level, to avoid introducing significant bias in their measurements. For the WMAP5 cosmology, the more accurate power spectrum is more sensitive to dark energy properties, resulting in a factor of two improvement in dark energy equation of state constraints. We explore the complementary constraints on dark energy from future weak lensing and supernova surveys. A space-based, JDEM-like survey measures the equation of state in five independent redshift bins to ~10%, while this improves to ~5% for a wide-field ground-based survey like LSST. These constraints are contingent upon our ability to control weak lensing systematic uncertainties to the sub-percent level.Comment: 12 pages, 12 figures. Typo in Eqn 8 correcte

Model independent inference of the expansion history and implications for the growth of structure

We model the expansion history of the Universe as a Gaussian Process and find constraints on the dark energy density and its low-redshift evolution using distances inferred from the Luminous Red Galaxy (LRG) and Lyman-alpha (Ly$\alpha$) datasets of the Baryon Oscillation Spectroscopic Survey, supernova data from the Joint Light-curve Analysis (JLA) sample, Cosmic Microwave Background (CMB) data from the Planck satellite, and local measurement of the Hubble parameter from the Hubble Space Telescope ($\mathsf H0$). Our analysis shows that the CMB, LRG, Ly$\alpha$, and JLA data are consistent with each other and with a $\Lambda$CDM cosmology, but the ${\mathsf H0}$ data is inconsistent at moderate significance. Including the presence of dark radiation does not alleviate the ${\mathsf H0}$ tension in our analysis. While some of these results have been noted previously, the strength here lies in that we do not assume a particular cosmological model. We calculate the growth of the gravitational potential in General Relativity corresponding to these general expansion histories and show that they are well-approximated by $\Omega_{\rm m}^{0.55}$ given the current precision. We assess the prospects for upcoming surveys to measure deviations from $\Lambda$CDM using this model-independent approach.Comment: 13 pages, 7 figures, code available at: https://github.com/dkirkby/gphis

Sheer shear: weak lensing with one mode

3D data compression techniques can be used to determine the natural basis of radial eigenmodes that encode the maximum amount of information in a tomographic large-scale structure survey. We explore the potential of the Karhunen-Lo\`eve decomposition in reducing the dimensionality of the data vector for cosmic shear measurements, and apply it to the final data from the \cfh survey. We find that practically all of the cosmological information can be encoded in one single radial eigenmode, from which we are able to reproduce compatible constraints with those found in the fiducial tomographic analysis (done with 7 redshift bins) with a factor of ~30 fewer datapoints. This simplifies the problem of computing the two-point function covariance matrix from mock catalogues by the same factor, or by a factor of ~800 for an analytical covariance. The resulting set of radial eigenfunctions is close to ell-independent, and therefore they can be used as redshift-dependent galaxy weights. This simplifies the application of the Karhunen-Lo\`eve decomposition to real-space and Fourier-space data, and allows one to explore the effective radial window function of the principal eigenmodes as well as the associated shear maps in order to identify potential systematics. We also apply the method to extended parameter spaces and verify that additional information may be gained by including a second mode to break parameter degeneracies. The data and analysis code are publicly available at https://github.com/emiliobellini/kl_sample.Comment: 15 pages, 16 figures. Accepted version on OJ

Implications of a transition in the dark energy equation of state for the H0H_0 and σ8\sigma_8 tensions

We explore the implications of a rapid appearance of dark energy between the redshifts ($z$) of one and two on the expansion rate and growth of perturbations. Using both Gaussian process regression and a parameteric model, we show that this is the preferred solution to the current set of low-redshift ($z<3$) distance measurements if $H_0=73~\rm km\,s^{-1}\,Mpc^{-1}$ to within 1\% and the high-redshift expansion history is unchanged from the $\Lambda$CDM inference by the Planck satellite. Dark energy was effectively non-existent around $z=2$, but its density is close to the $\Lambda$CDM model value today, with an equation of state greater than $-1$ at $z<0.5$. If sources of clustering other than matter are negligible, we show that this expansion history leads to slower growth of perturbations at $z<1$, compared to $\Lambda$CDM, that is measurable by upcoming surveys and can alleviate the $\sigma_8$ tension between the Planck CMB temperature and low-redshift probes of the large-scale structure.Comment: 24 pages, 16 figure

Are Light Sterile Neutrinos Preferred or Disfavored by Cosmology?

We find that the viability of a cosmological model that incorporates 2 sterile neutrinos with masses around 1 eV each, as favored by global neutrino oscillation analyses including short baseline results, is significantly dependent on the choice of datasets included in the analysis and the ability to control the systematic uncertainties associated with these datasets. Our analysis includes a variety of cosmological probes including the cosmic microwave background (WMAP7+SPT), Hubble constant (HST), galaxy power spectrum (SDSS-DR7), and supernova distances (SDSS and Union2 compilations). In the joint observational analysis, our sterile neutrino model is equally favored as a LCDM model when using the MLCS light curve fitter for the supernova measurements, and strongly disfavored by the data at \Delta\chi^2 ~ 18 when using the SALT2 fitter. When excluding the supernova measurements, the sterile neutrino model is disfavored by the other datasets at \Delta\chi^2 ~ 12, and at best becomes mildly disfavored at \Delta\chi^2 ~ 3 when allowing for curvature, evolving dark energy, additional relativistic species, running of the spectral index, and freedom in the primordial helium abundance. No single additional parameter accounts for most of this effect. Therefore, if laboratory experiments continue to favor a scenario with roughly eV mass sterile neutrinos, and if this becomes decisively disfavored by cosmology, then a more exotic cosmological model than explored here may become necessary.Comment: 10 pages, 3 figures. Minor refinements, reflects version accepted for publication in PR

Beyond Two Dark Energy Parameters

Our ignorance of the dark energy is generally described by a two-parameter equation of state. In these approaches a particular {\it ad hoc} functional form is assumed, and only two independent parameters are incorporated. We propose a model-independent, multi-parameter approach to fitting the dark energy, and show that next-generation surveys will constrain the equation of state in three or more independent redshift bins to better than 10%. Future knowledge of the dark energy will surpass two numbers (e.g., [$w_0$,$w_1$] or [$w_0$,$w_a$]), and we propose a more flexible approach to the analysis of present and future data.Comment: 4 pages, 1 figure; Discussion expanded to include next-generation BAO surveys and possible systematics in SN surveys; reflects version accepted for publication in Phys. Rev. Let

Cross-correlating Sunyaev-Zel'dovich and weak lensing maps

We present novel statistical tools to cross-correlate frequency cleaned thermal Sunyaev–Zel'dovich (tSZ) maps and tomographic weak lensing (wl) convergence maps. Moving beyond the lowest order cross-correlation, we introduce a hierarchy of mixed higher order statistics, the cumulants and cumulant correlators, to analyse non-Gaussianity in real space, as well as corresponding polyspectra in the harmonic domain. Using these moments, we derive analytical expressions for the joint two-point probability distribution function for smoothed tSZ (y) and convergence (κ) maps. The presence of tomographic information allows us to study the evolution of higher order mixed tSZ–wl statistics with redshift. We express the joint PDFs pκy(κ, y) in terms of individual one-point PDFs [pκ(κ), py(y)] and the relevant bias functions [bκ(κ), by(y)]. Analytical results for two different regimes are presented that correspond to the small and large angular smoothing scales. Results are also obtained for corresponding hotspots in the tSZ and convergence maps. In addition to results based on hierarchical techniques and perturbative methods, we present results of calculations based on the lognormal approximation. The analytical expressions derived here are generic and applicable to cross-correlation studies of arbitrary tracers of large-scale structure including, e.g., that of tSZ and soft X-ray background. We provide detailed comparison of our analytical results against state of the art Millennium Gas Simulations with and without non-gravitational effects such as pre-heating and cooling. Comparison of these results with gravity only simulations, shows reasonable agreement and can be used to isolate effect of non-gravitational physics from observational data

Testing Gravity on Cosmic Scales: A Case Study of Jordan-Brans-Dicke Theory

We provide an end-to-end exploration of a distinct modified gravitational theory in Jordan-Brans-Dicke (JBD) gravity, from an analytical and numerical description of the background expansion and linear perturbations, to the nonlinear regime captured with a hybrid suite of $N$-body simulations, to the parameter constraints from existing cosmological probes. The nonlinear corrections to the matter power spectrum due to baryons, massive neutrinos, and modified gravity are simultaneously modeled and propagated in the cosmological analysis for the first time. In the combined analysis of the Planck CMB temperature, polarization, and lensing reconstruction, Pantheon supernova distances, BOSS measurements of BAO distances, the Alcock-Paczynski effect, and the growth rate, along with the joint ($3\times2$pt) dataset of cosmic shear, galaxy-galaxy lensing, and overlapping redshift-space galaxy clustering from KiDS and 2dFLenS, we constrain the JBD coupling constant, $\omega_{\rm BD}>1540$ (95% CL), the effective gravitational constant, $G_{\rm matter}/G=0.997\pm0.029$, the sum of neutrino masses, $\sum m_{\nu}<0.12$ eV (95% CL), and the baryonic feedback amplitude, $B<2.8$ (95% CL), all in agreement with the standard model expectation. We show that the uncertainty in the gravitational theory alleviates the tension between KiDS$\times$2dFLenS and Planck to below $1\sigma$ and the tension in the Hubble constant between Planck and the direct measurement of Riess et al. (2019) down to ~$3\sigma$; however, we find no substantial model selection preference for JBD gravity relative to $\Lambda$CDM. We further show that the neutrino mass bound degrades by up to a factor of $3$ as the $\omega_{\rm BD}$ parameterization becomes more restrictive, and that a positive shift in $G_{\rm matter}/G$ suppresses the CMB damping tail in a way that might complicate future inferences of small-scale physics. (Abridged)Comment: 48 pages, 24 figures, PRD submitte