Combining spectroscopic and photometric surveys using angular cross-correlations – II. Parameter constraints from different physical effects

Observational probes of cosmic acceleration

Unveiling the physics behind the accelerating expansion of the Universe, which was discovered in 1998, is one of the most challenging tasks in modern sciences. In theory, the cosmic acceleration may result from the fact that approximately two thirds energy density of the Universe is provided by Dark Energy, a yet unknown energy component, or imply that general relativity, the most successful theory of gravity within the solar system established by Einstein, may need to be extended on cosmological scales. In principle, the scenarios of energy and modified gravity can yield identical cosmic expansion history, but predict different structure growth. Therefore, this dark degeneracy can be broken by studying the evolution history of the cosmic structure with large galaxy surveys. Galaxy surveys is one of the key probes for energy and gravity, which can be used to reconstruct the history of cosmic expansion and structure growth using baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) respectively. BAO is a specific three-dimensional clustering pattern of galaxies due to interactions between photons and baryons in the early Universe. Back in the early cosmic epochs, photons scattered with electrons and electrons interacted with protons, making photons and protons (baryonic matter) glued together. There are two opposite forces exerting on this tightly coupled plasma: the pressure of photons and gravity acting on baryons. Similar to what happens to a vibrating spring vertically fixed on the ground, the photon-baryon plasma underwent Oscillations, propagating waves in the same way as the sound does. Therefore, this physical process is called Baryonic Acoustic Oscillations. The effect of the BAO is to push galaxies apart until at a specific time, called the cosmic recombination, when the temperature of the Universe becomes so low that no more photon-baryon interaction can happen. Since then, the separation among galaxies is frozen at a characteristic scale, which is about 150 Mpc depending on the energy content of the Universe, making it a standard ruler to be used to infer the expansion history of the Universe, thus BAO is one of the key probes for the nature of energy. RSD is another special three-dimensional clustering pattern of galaxies, but it is due to local motions of the galaxies under gravity. Suppose galaxies only co-move with the cosmic background without moving locally, the clustering of galaxies should be isotropic, in other words, there are same number of galaxy pairs along or across lines of sight of the observer. However, this is not the case in the real world. Galaxies move towards nearby galaxies due to gravity, thus they have velocities. As we infer galaxies positions from their line-of-sight velocities in astronomy, the peculiar velocities can distort galaxies positions, which results in a distortion, called Redshift Space Distortions, in the 3D clustering of galaxies. RSD plays a key role in cosmology as it can directly be used to infer the nature of gravity (remember the peculiar motion is caused by gravity!). The Baryonic Oscillation Spectroscopic Survey (BOSS) program, part of the Sloan Digital Sky Survey (SDSS)-III project, is the largest completed galaxy survey in the world. BOSS has enabled us to investigate energy and gravity to a unprecedented precision, which has implied a 3.5 sigma evidence for the dynamics of energy. Ongoing and forthcoming galaxy surveys including the extended Baryonic Oscillation Spectroscopic Survey (eBOSS), Dark Energy Spectroscopic Instrument (DESI) and Prime Focus Spectrograph (PFS), will be able to probe the Universe at higher redshifts with much higher precision, which will be providing key observational support for the study of cosmic acceleration.

We present forecast errors on a wide range of cosmological parameters obtained from a photometric cluster catalogue of a future wide-field Euclid-like survey. We focus in particular on the total neutrino mass as constrained by a combination of the galaxy cluster number counts and correlation function. For the latter we consider only the shape information and the Baryon Acoustic Oscillations (BAO), while marginalising over the spectral amplitude and the redshift space distortions. In addition to the cosmological parameters of the standard ΛCDM+ν model we also consider a non-vanishing curvature, and two parameters describing a redshift evolution for the dark energy equation of state. For completeness, we also marginalise over a set of ``nuisance'' parameters, representing the uncertainties on the cluster mass determination. We find that combining cluster counts with power spectrum information greatly improves the constraining power of each probe taken individually, with errors on cosmological parameters being reduced by up to an order of magnitude. In particular, the best improvements are for the parameters definingthe dynamical evolution of dark energy, where cluster counts break degeneracies. Moreover, the resulting error on neutrino mass is at the level of σ(Mν) ∼ 0.9 eV, comparable with that derived from present Lyα forest measurements and Cosmic Microwave background (CMB) data in the framework of a non-flat Universe. Further adopting Planck priors and reducing the number of free parameters to a ΛCDM+ν cosmology allows to place constraints on the total neutrino mass of σ(Mν) ∼ 0.08 eV, close to the lower bound enforced by neutrino oscillation experiments. Finally, in the optimistic case where uncertainties in the calibration of the mass-observable relation were so small to be neglected, the combination of Planck priors with cluster counts and power spectrum would constrain the total neutrino mass down to σ(Mν) ∼ 0.034 eV, i.e. the minimum neutrino mass predicted by oscillation experiments would be detected in a ΛCDM framework. We thus show that galaxy clusters from future wide galaxy surveys will be an excellent tool for studying cosmology and fundamental physics.

We study the applicability of several galaxy environment measures (n^th-nearest-neighbor distance, counts in an aperture, and Voronoi volume) within deep redshift surveys. Mock galaxy catalogs are employed to mimic representative photometric and spectroscopic surveys at high redshift (z ~ 1). We investigate the effects of survey edges, redshift precision, redshift-space distortions, and target selection upon each environment measure. We find that even optimistic photometric redshift errors (\sigma_z = 0.02) smear out the line-of-sight galaxy distribution irretrievably on small scales; this significantly limits the application of photometric redshift surveys to environment studies. Edges and holes in a survey field dramatically affect the estimation of environment, with the impact of edge effects depending upon the adopted environment measure. These edge effects considerably limit the usefulness of smaller survey fields (e.g. the GOODS fields) for studies of galaxy environment. In even the poorest groups and clusters, redshift-space distortions limit the effectiveness of each environment statistic; measuring density in projection (e.g. using counts in a cylindrical aperture or a projected n^th-nearest-neighbor distance measure) significantly improves the accuracy of measures in such over-dense environments. For the DEEP2 Galaxy Redshift Survey, we conclude that among the environment estimators tested the projected n^th-nearest-neighbor distance measure provides the most accurate estimate of local galaxy density over a continuous and broad range of scales.

The various measurements of the linear matter density perturbation amplitude obtained from the observations of the cosmic microwave background (CMB) anisotropy, weak gravitational lensing, galaxy cluster mass function, matter power spectrum, and redshift space distortions are compared. The Planck data on the CMB temperature anisotropy spectrum at high multipoles, ℓ > 1000 (where the effect of gravitational lensing is most significant), are shown to give a measurement of the matter density perturbation amplitude that contradicts all other measurements of this quantity from both Planck CMB anisotropy data and other data at a significance level of about 3.7σ. Thus, at present these data should not be combined together for the calculations of constraints on cosmological parameters. Except for the Planck data on the CMB temperature anisotropy spectrum at high multipoles, all the remaining measurements of the density perturbation amplitude agree well between themselves and give the following constraints: σ8 = 0.792± 0.006 on the linear matter density perturbation amplitude, Ωm = 0.287± 0.007 on the matter density parameter, and H0 = 69.4 ± 0.6 km s−1 Mpc−1 on the Hubble constant. Various constraints on the sum of neutrino masses and the number of neutrino flavors can be obtained by additionally taking into account the data on baryon acoustic oscillations and (or) direct Hubble constant measurements in the local Universe.

We investigate the cosmological implications of the latest growth of structure measurement from the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS Data Release 11 with particular focus on the sum of the neutrino masses, $\sum m_{\nu}$. We examine the robustness of the cosmological constraints from the Baryon Acoustic Oscillation (BAO) scale, the Alcock-Paczynski effect and redshift-space distortions ($D_V/r_s$, $F_{\rm AP}$, $f\sigma_8$) of \citet{Beutler:2013b}, when introducing a neutrino mass in the power spectrum template. We then discuss how the neutrino mass relaxes discrepancies between the Cosmic Microwave Background (CMB) and other low-redshift measurements within $\Lambda$CDM. Combining our cosmological constraints with WMAP9 yields $\sum m_{\nu} = 0.36\pm0.14\,$eV ($68\%$ c.l.), which represents a $2.6\sigma$ preference for non-zero neutrino mass. The significance can be increased to $3.3\sigma$ when including weak lensing results and other BAO constraints, yielding $\sum m_{\nu} = 0.35\pm0.10\,$eV ($68\%$ c.l.). However, combining CMASS with Planck data reduces the preference for neutrino mass to $\sim 2\sigma$. When removing the CMB lensing effect in the Planck temperature power spectrum (by marginalising over $A_{\rm L}$), we see shifts of $\sim 1\sigma$ in $\sigma_8$ and $\Omega_m$, which have a significant effect on the neutrino mass constraints. In case of CMASS plus Planck without the $A_{\rm L}$-lensing signal, we find a preference for a neutrino mass of $\sum m_{\nu} = 0.34\pm 0.14\,$eV ($68\%$ c.l.), in excellent agreement with the WMAP9+CMASS value. The constraint can be tightened to $3.4\sigma$ yielding $\sum m_{\nu} = 0.36\pm 0.10\,$eV ($68\%$ c.l.) when weak lensing data and other BAO constraints are included.

Massive spectroscopic surveys will measure the redshift space distortion\n(RSD) induced by galaxy peculiar velocity to unprecedented accuracy. We develop\na new method to improve the RSD modeling and to carry out robust reconstruction\nof the 3D large scale peculiar velocity through galaxy redshift surveys, in\nlight of RSD. (1) We propose a mathematically unique and physically motivated\ndecomposition of peculiar velocity into three eigen-components of different\norigins, different scale dependences and different impacts on RSD. (2) This\ndecomposition has the potential to simplify and improve the RSD modeling. We\nderive a new formula for the redshift space power spectrum. Under the velocity\ndecomposition scheme, all high order Gaussian corrections and non-Gaussian\ncorrection of order $\\delta^3$ can be taken into account without introducing\nextra model uncertainties. We find that the leading order contribution $\\propto\n(1+f\\tilde{W}(k)u^2)^2$ differs from the Kaiser formula by a function\n$\\tilde{W}(k)\\leq 1$. We hence identify a significant systematic error causing\nunderestimation of the structure growth parameter $f$ by as much as $O(10%)$\neven at relatively large scale $k=0.1h/$Mpc. The velocity decomposition also\nreveals the three origins of the finger of God (FOG) effect. (3) The velocity\ndecomposition clarifies issues in peculiar velocity reconstruction through 3D\ngalaxy distribution. We discuss two possible ways to carry out the velocity\nreconstruction. Both use the otherwise troublesome RSD in velocity\nreconstruction as a valuable source of information. Both have the advantage to\nrender the reconstruction of a stochastic 3D field into the reconstruction of a\ndeterministic window function $W^s(k,u)$ of limited degrees of\nfreedom...[abridged]\n

Angular cosmological correlators are infamously difficult to compute due to the highly oscillatory nature of the projection integrals. Motivated by recent development on analytic approaches to cosmological perturbation theory, in this paper we present an efficient method for computing cosmological four-point correlations in angular space, generalizing previous works on lower-point functions. This builds on the FFTLog algorithm that approximates the matter power spectrum as a sum over power-law functions, which makes certain momentum integrals analytically solvable. The computational complexity is drastically reduced for correlators in a “separable” form—we define a suitable notion of separability for cosmological trispectra, and derive formulas for angular correlators of different separability classes. As an application of our formalism, we compute the angular galaxy trispectrum at tree level, with and without primordial non-Gaussianity. This includes effects of redshift space distortion and bias parameters up to cubic order. We also compute the non-Gaussian covariance of the angular matter power spectrum due to the connected four-point function, beyond the Limber approximation. We demonstrate that, in contrast to the standard lore, the Limber approximation can fail for the non-Gaussian covariance computation even for large multipoles.

Weak lensing (WL) distortions of distant galaxy images are sensitive to neutrino masses by probing the suppression effect on clustering strengths of total matter in large-scale structure. We use the latest measurements of WL correlations, the Canada-France-Hawaii Telescope Legacy Survey data, to explore constraints on neutrino masses. We find that, while the WL data alone cannot place a stringent limit on neutrino masses due to parameter degeneracies, the constraint can be significantly improved when combined with other cosmological probes, such as the WMAP 5-year data (WMAP5) and the distance measurements of type-Ia supernovae (SNe) and baryon acoustic oscillations (BAO). The upper bounds on the sum of neutrino masses are $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}=1.1$, 0.76, and 0.54 eV (95% CL) for $\mathrm{WL}+\mathrm{WMAP}5$, $\mathrm{WMAP}5+\mathrm{SNe}+\mathrm{BAO}$, and $\mathrm{WL}+\mathrm{WMAP}5+\mathrm{SNe}+\mathrm{BAO}$, respectively, assuming a flat $\ensuremath{\Lambda}\mathrm{CDM}$ model with finite-mass neutrinos. In deriving these constraints, our analysis includes the non-Gaussian covariances of the WL correlation functions to properly take into account significant correlations between different angles.

In this paper, we explore a fractal model of the universe proposed by Calcagni (J High Energy Phys 03:120, 2010) for a power-counting renormalizable field theory living in a fractal spacetime. Considering a timelike fractal profile, we derived field equations in fractal cosmology, in order to explore the structure formation and the expansion history in fractal universe. Numerical investigations based on matter power spectra diagrams report higher structure growth in fractal cosmology, being in contrast to local galaxy surveys. Additionally, according to the evolution of Hubble parameter diagrams, it can be understood that Hubble constant would decrease in fractal cosmology, which is also incompatible with low redshift estimations of H_0. So, concerning primary numerical studies, it seems that fractal cosmology is not capable to alleviate the tensions between local and global observational probes. Then, in pursuance of more accurate results, we constrain the fractal cosmology by observational data, including Planck cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations (BAO), and redshift-space distortions (RSD) data. The derived constraints on fractal dimension beta indicate that there is no considerable deviation from standard model of cosmology.

A new determination of the sound horizon scale in angular coordinates is presented. It makes use of ~ 0.6 x 10^6 Luminous Red Galaxies, selected from the Sloan Digital Sky Survey imaging data, with photometric redshifts. The analysis covers a redshift interval that goes from z=0.5 to z=0.6. We find evidence of the Baryon Acoustic Oscillations (BAO) signal at the ~ 2.3 sigma confidence level, with a value of theta_{BAO} (z=0.55) = (3.90 \pm 0.38) degrees, including systematic errors. To our understanding, this is the first direct measurement of the angular BAO scale in the galaxy distribution, and it is in agreement with previous BAO measurements. We also show how radial determinations of the BAO scale can break the degeneracy in the measurement of cosmological parameters when they are combined with BAO angular measurements. The result is also in good agreement with the WMAP7 best-fit cosmology. We obtain a value of w_0 = -1.03 \pm 0.16 for the equation of state parameter of the dark energy, Omega_M = 0.26 \pm 0.04 for the matter density, when the other parameters are fixed. We have also tested the sensitivity of current BAO measurements to a time varying dark energy equation of state, finding w_a = 0.06 \pm 0.22 if we fix all the other parameters to the WMAP7 best-fit cosmology.

We derive and test an approximation for the angular power spectrum of galaxy number counts in the flat sky limit. The standard density and redshift space distortion (RSD) terms in the resulting approximation are distinct to the Limber approximation, providing an accurate result for multipoles as low as ℓ ≃ 10, where the corresponding Limber approximation is completely inaccurate. At equal redshift the accuracy of the density and RSD (standard) terms is around 0.2% for z < 3 and 0.5% at z = 5, even to ℓ < 50. At unequal redshifts, if we consider the total power spectrum, the precision is better than 5% only for very small redshift differences, δ <δ0 (≃ 3.6×10−4(1+z)2.14) where the standard terms are well-approximated, or for large enough redshift differences δ >δ1 (≃ 0.33(r(z)H(z))/(z+1)) where the lensing terms dominate. The flat sky expressions for the pure lensing and the lensing-density cross-correlation terms are equivalent to the Limber approximation. For arbitrary redshift differences, the Limber approximation achieves an accuracy of 0.5% (above ℓ ≃ 40 for pure lensing and ℓ ≃ 80 for density-lensing). Besides being very accurate, the flat sky approximation is computationally much simpler and can therefore be very useful for data analysis and forecasts with MCMC methods. This will be particularly crucial for upcoming galaxy surveys that will measure the power spectrum of galaxy number counts.

It has been shown that time delay of strong gravitational lensing is not only an effective cosmological probe to constrain the Hubble constant, the matter density and the curvature of the universe but also useful for breaking the degeneracy of the dark energy equation of state and thus provide complementarity with other popular probes, such as type Ia supernovae, baryon acoustic oscillations, and cosmic microwave background radiation. Interestingly, compared to traditional strong lensing systems where quasars act as sources, strongly lensed gravitational waves (GWs) from compact binary coalescence and their electromagnetic (EM) counterparts systems have been recently proposed to be more powerful for studying cosmology since GWs and their EM counterparts are transients. Short durations of GWs and their EM counterparts are very advantageous to time delay measurement and lens profile modeling. Here, in the framework of Chevalier-Polarski-Linder (CPL) parametrization, we investigate improvement of constraining power on dark energy equation of state due to including time delay measurements of strong lensed GW systems. It is suggested that, on the basis of the third generation ground-based detector, e.g. Einstein Telescope, adding time delay of only 30 strong lensed GW systems to type Ia supernovae and cosmic microwave background radiation can improve the dark energy figure of merit by a factor 2. For the traditional standard siren method where the uncertainties of luminosity distances of GWs are $\sim10\%$, a few $\times~10^4$ events are expected to present similar constraints. In the precision cosmology era, this progress is of great significance for studying the nature of dark energy.

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratios in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially resolved spectroscopy for thousands of nearby galaxies (median ). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGNs and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5 m Sloan Foundation Telescope at the Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5 m du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in 2016 July.

One of the most prominent challenges to the standard Lambda cold dark matter ($\Lambda$CDM) cosmology is the tension between the structure growth parameter $S_8$ constrained by the cosmic microwave background (CMB) data and the smaller one suggested by the cosmic shear data. Recent studies show that, for $\Lambda$CDM cosmology, redshift-space distortion (RSD) data also prefers a smaller $S_8$ that is $\sim 2$-$3\sigma$ lower than the CMB value, but the result is sensitive to the cosmological model. In the present work we update the RSD constraint on $S_8$ with the most up-to-date RSD data set where the correlation between data points are properly taken into account. To reduce the model dependence, we add in our Monte Carlo Markov Chain calculation the most up-to-date data sets of Type Ia supernovae (SN) and baryon acoustic oscillations (BAO), whose correlation with RSD is also taken into account, to constrain the background geometry. For $\Lambda$CDM cosmology we find $S_8= 0.812 \pm 0.026$, which is $\sim 2\sigma$ larger than previous studies, and hence is consistent with the CMB constraint. By replacing $\Lambda$CDM with the Parameterization based on cosmic Age (PAge), an almost model-independent description of the late universe, we find that the RSD + SN + BAO constraint on $S_8$ is insensitive to the cosmological model.