Bayesian evidence of non-standard inflation: isocurvature perturbations and running spectral index

Bayesian model comparison penalizes models with more free parameters that are allowed to vary over a wide range, and thus offers the most robust method to decide whether some given data require new parameters. In this paper, we ask a simple question: do current cosmological data require extensions of the simplest single-field inflation models? Specifically, we calculate the Bayesian evidence of a totally anti-correlated isocurvature perturbation and a running spectral index of the scalar curvature perturbation. These parameters are motivated by recent claims that the observed temperature anisotropy of the cosmic microwave background on large angular scales is too low to be compatible with the simplest inflation models. Both a subdominant, anti-correlated cold dark matter isocurvature component and a negative running index succeed in lowering the large-scale temperature power spectrum. We show that the introduction of isocurvature perturbations is disfavored, whereas that of the running spectral index is only moderately favored, even when the BICEP2 data are included in the analysis without any foreground subtraction.Comment: 5 pages, 2 figures. Minor modifications, to match version published in January 201

Using correlations between CMB lensing and large-scale structure to measure primordial non-Gaussianity

We apply a new method to measure primordial non-Gaussianity, using the cross-correlation between galaxy surveys and the CMB lensing signal to measure galaxy bias on very large scales, where local-type primordial non-Gaussianity predicts a $k^2$ divergence. We use the CMB lensing map recently published by the Planck collaboration, and measure its external correlations with a suite of six galaxy catalogues spanning a broad redshift range. We then consistently combine correlation functions to extend the recent analysis by Giannantonio et al. (2013), where the density-density and the density-CMB temperature correlations were used. Due to the intrinsic noise of the Planck lensing map, which affects the largest scales most severely, we find that the constraints on the galaxy bias are similar to the constraints from density-CMB temperature correlations. Including lensing constraints only improves the previous statistical measurement errors marginally, and we obtain $f_{\mathrm{NL}} = 12 \pm 21$ (1$\sigma$) from the combined data set. However, the lensing measurements serve as an excellent test of systematic errors: we now have three methods to measure the large-scale, scale-dependent bias from a galaxy survey: auto-correlation, and cross-correlation with both CMB temperature and lensing. As the publicly available Planck lensing maps have had their largest-scale modes at multipoles $l<10$ removed, which are the most sensitive to the scale-dependent bias, we consider mock CMB lensing data covering all multipoles. We find that, while the effect of $f_{\mathrm{NL}}$ indeed increases significantly on the largest scales, so do the contributions of both cosmic variance and the intrinsic lensing noise, so that the improvement is small.Comment: 5 pages, 3 figures. Additional references added. Submitted to MNRA

Constraints on primordial isocurvature perturbations and spatial curvature by Bayesian model selection

We present posterior likelihoods and Bayesian model selection analysis for generalized cosmological models where the primordial perturbations include correlated adiabatic and cold dark matter isocurvature components. We perform nested sampling with flat and, for the first time, curved spatial geometries of the Universe, using data from the cosmic microwave background (CMB) anisotropies, the Union supernovae (SN) sample and a combined measurement of the integrated Sachs-Wolfe (ISW) effect. The CMB alone favors a 3% (positively correlated) isocurvature contribution in both the flat and curved cases. The non-adiabatic contribution to the observed CMB temperature variance is 0 < alpha_T < 7% at 98% CL in the curved case. In the flat case, combining the CMB with SN data artificially biases the result towards the pure adiabatic LCDM concordance model, whereas in the curved case the favored level of non-adiabaticity stays at 3% level with all combinations of data. However, the ratio of Bayes factors, or Delta ln(evidence), is more than 5 points in favor of the flat adiabatic LCDM model, which suggests that the inclusion of the 5 extra parameters of the curved isocurvature model is not supported by the current data. The results are very sensitive to the second and third acoustic peak regions in the CMB temperature angular power: therefore a careful calibration of these data will be required before drawing decisive conclusions on the nature of primordial perturbations. Finally, we point out that the odds for the flat non-adiabatic model are 1:3 compared to the curved adiabatic model. This may suggest that it is not much less motivated to extend the concordance model with 4 isocurvature degrees of freedom than it is to study the spatially curved adiabatic model.Comment: 15 pages, 5 figures. V2: References and future predictions added; accepted by PR

Constraining dark sector perturbations II: ISW and CMB lensing tomography

Any Dark Energy (DE) or Modified Gravity (MG) model that deviates from a cosmological constant requires a consistent treatment of its perturbations, which can be described in terms of an effective entropy perturbation and an anisotropic stress. We have considered a recently proposed generic parameterisation of DE/MG perturbations and compared it to data from the Planck satellite and six galaxy catalogues, including temperature-galaxy (Tg), CMB lensing-galaxy and galaxy-galaxy (gg) correlations. Combining these observables of structure formation with tests of the background expansion allows us to investigate the properties of DE/MG both at the background and the perturbative level. Our constraints on DE/MG are mostly in agreement with the cosmological constant paradigm, while we also find that the constraint on the equation of state w (assumed to be constant) depends on the model assumed for the perturbation evolution. We obtain $w=-0.92^{+0.20}_{-0.16}$ (95% CL; CMB+gg+Tg) in the entropy perturbation scenario; in the anisotropic stress case the result is $w=-0.86^{+0.17}_{-0.16}$. Including the lensing correlations shifts the results towards higher values of w. If we include a prior on the expansion history from recent Baryon Acoustic Oscillations (BAO) measurements, we find that the constraints tighten closely around $w=-1$, making it impossible to measure any DE/MG perturbation evolution parameters. If, however, upcoming observations from surveys like DES, Euclid or LSST show indications for a deviation from a cosmological constant, our formalism will be a useful tool towards model selection in the dark sector.Comment: 25 pages, 8 figures; minor update for consistency with version accepted by JCAP (13/01/2015

The significance of the integrated Sachs-Wolfe effect revisited

We revisit the state of the integrated Sachs-Wolfe (ISW) effect measurements in light of newly available data and address criticisms about the measurements which have recently been raised. We update the data set previously assembled by Giannantonio et al. to include new data releases for both the cosmic microwave background (CMB) and the large-scale structure (LSS) of the Universe. We find that our updated results are consistent with previous measurements. By fitting a single template amplitude, we now obtain a combined significance of the ISW detection at the 4.4 sigma level, which fluctuates by 0.4 sigma when alternative data cuts and analysis assumptions are considered. We also make new tests for systematic contaminations of the data, focusing in particular on the issues raised by Sawangwit et al. Amongst them, we address the rotation test, which aims at checking for possible systematics by correlating pairs of randomly rotated maps. We find results consistent with the expected data covariance, no evidence for enhanced correlation on any preferred axis of rotation, and therefore no indication of any additional systematic contamination. We publicly release the results, the covariance matrix, and the sky maps used to obtain them.Comment: 19 pages, 10 figures. MNRAS in pres

Chaplygin gas in light of recent Integrated Sachs--Wolfe effect data

We investigate the possibility of constraining Chaplygin dark energy models with current Integrated Sachs Wolfe effect data. In the case of a flat universe we found that generalized Chaplygin gas models must have an energy density such that $\Omega_c >0.55$ and an equation of state $w <-0.6$ at 95% c.l.. We also investigate the recently proposed Silent Chaplygin models, constraining $\Omega_c >0.55$ and $w <-0.65$ at 95% c.l.. Better measurements of the CMB-LSS correlation will be possible with the next generation of deep redshift surveys. This will provide independent and complementary constraints on unified dark energy models such as the Chaplygin gas.Comment: 5 pages, 4 figure

Combining clustering and abundances of galaxy clusters to test cosmology and primordial non-Gaussianity

We present the clustering of galaxy clusters as a useful addition to the common set of cosmological observables. The clustering of clusters probes the large-scale structure of the Universe, extending galaxy clustering analysis to the high-peak, high-bias regime. Clustering of galaxy clusters complements the traditional cluster number counts and observable-mass relation analyses, significantly improving their constraining power by breaking existing calibration degeneracies. We use the maxBCG galaxy clusters catalogue to constrain cosmological parameters and cross-calibrate the mass-observable relation, using cluster abundances in richness bins and weak-lensing mass estimates. We then add the redshift-space power spectrum of the sample, including an effective modelling of the weakly non-linear contribution and allowing for an arbitrary photometric redshift smoothing. The inclusion of the power spectrum data allows for an improved self-calibration of the scaling relation. We find that the inclusion of the power spectrum typically brings a $\sim 50$ per cent improvement in the errors on the fluctuation amplitude $\sigma_8$ and the matter density $\Omega_{\mathrm{m}}$. Finally, we apply this method to constrain models of the early universe through the amount of primordial non-Gaussianity of the local type, using both the variation in the halo mass function and the variation in the cluster bias. We find a constraint on the amount of skewness $f_{\mathrm{NL}} = 12 \pm 157$ ($1\sigma$) from the cluster data alone.Comment: 12 pages, 10 figures, 2 tables. Minor changes to match published version on MNRA