Parameter estimation biases due to contributions from the Rees-Sciama effect to the integrated Sachs-Wolfe spectrum

Schäfer, Björn Malte; Kalovidouris, Angelos Fotios; Heisenberg, Lavinia

doi:10.1111/j.1365-2966.2011.19125.x

Cited by 8 publications

(10 citation statements)

References 62 publications

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“…This behaviour can approximately be described by the inverse root of the polynomial order

σ_{μ} \propto 1 / \sqrt{q}

. A similar characteristic was found in the application of this method to the weak lensing shear spectra (Schaefer & Heisenberg ). Clearly, the cosmological parameter Ω m profits most from the tomographic method, which was already indicated by its sensitivity improvement discussed in Section .…”

Section: Statisticssupporting

confidence: 72%

“…Conditional errors in parameters constrained only by the cross‐spectra decrease by up to ≈30 per cent in the case of the matter density parameter Ω m . While for the cross‐spectra only the conditional errors already show saturation at quite a low number of included polynomials q ≈ 5, it would still be worth improving this method in order to reach even higher orders, since marginalized errors for the full signal have not yet saturated at a cumulative order of q = 8. Using the wrong model in the construction of the polynomials can introduce an estimation bias in cosmological parameters. This effect was thoroughly studied in a similar approach for weak lensing measurements (Schaefer & Heisenberg ). In most cases the bias was found to be small compared with the statistical errors.…”

Section: Discussionmentioning

confidence: 99%

“…In this work we aim to formulate a tomographic approach with the help of an orthogonal set of weighting polynomials, which is similar to a former application to weak lensing spectra (Schaefer & Heisenberg ). The orthogonality of the polynomials will generically lead to a diagonal signal covariance matrix and will therefore provide cumulative statistical independent measurements with increasing polynomial order.…”

Section: Introductionmentioning

confidence: 99%

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Integrated Sachs-Wolfe tomography with orthogonal polynomials

Jürgens

Schäfer

2012

Monthly Notices of the Royal Astronomical Society

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Topic of this article are tomographic measurements of the integrated Sachs-Wolfe effect with specifically designed, orthogonal polynomials which project out statistically independent modes of the galaxy distribution. The polynomials are contructed using the Gram-Schmidt orthogonalisation method. To quantify the power of the iSW-effect in contraining cosmological parameters we perfom a combined Fisher matrix analysis for the iSW-, galaxy- and cross-spectra for wCDM cosmologies using the survey characteristics of PLANCK and EUCLID. The signal to noise ratio has also been studied for other contemporary galaxy surveys, such as SDSS, NVSS and 2MASS. For the cross-spectra our tomographic method provides a 16% increase in the signal to noise ratio and an improvement of up to 30% in conditional errors on parameters. Including all spectra, the marginalised errors approach an inverse square-root dependence with increasing cumulative polynomial order which underlines the statistical independence of the weighted signal spectra.Comment: 9 pages, 12 figures, submitted to MNRA

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“…This behaviour can approximately be described by the inverse root of the polynomial order

σ_{μ} \propto 1 / \sqrt{q}

Section: Statisticssupporting

confidence: 72%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integrated Sachs-Wolfe tomography with orthogonal polynomials

Jürgens

Schäfer

2012

Monthly Notices of the Royal Astronomical Society

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“…For a review, see Cooray (); in more recent work, Smith, Hernandez‐Monteagudo & Seljak () provide a comparison with N ‐body simulations and perturbation theory, and Cai et al () give a comparison of linear and non‐linear effects on the reconstructed ISW maps from ray tracing of CMB photons through N ‐body simulations. Finally, Schäfer, Kalovidouris & Heisenberg () quantify the parameter estimation bias due to this non‐linear effect and show that it is small compared to the statistical uncertainty imparted by cosmic variance.…”

Section: The State Of the Iswmentioning

confidence: 99%

The significance of the integrated Sachs-Wolfe effect revisited

Giannantonio

Crittenden

Nichol

et al. 2012

Monthly Notices of the Royal Astronomical Society

101

133

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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

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“…In general, it is assumed that the ISW is called the ReesSciama effect on non-linear scales and that it will produce a negatively correlated signal owing to non-linear growing modes of the matter distribution (Schaefer et al 2011;Cai et al 2010). However, some non-linear modes could also be decaying for example because of major mergers or tidal stripping, or because of alternative cosmologies as in Afshordi et al (2011).…”

Section: Field-to-field Comparisonmentioning

confidence: 99%

Measuring the integrated Sachs-Wolfe effect

Dupé

Rassat

Starck

et al. 2011

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Context. One of the main challenges of modern cosmology is to understand the nature of the mysterious dark energy that causes the cosmic acceleration. The integrated Sachs-Wolfe (ISW) effect is sensitive to dark energy, and if detected in a universe where modified gravity and curvature are excluded, presents an independent signature of dark energy. The ISW effect occurs on large scales where cosmic variance is high and where owing to the Galactic confusion we lack large amounts of data in the CMB as well as large-scale structure maps. Moreover, existing methods in the literature often make strong assumptions about the statistics of the underlying fields or estimators. Together these effects can severely limit signal extraction. Aims. We aim to define an optimal statistical method for detecting the ISW effect that can handle large areas of missing data and minimise the number of underlying assumptions made about the data and estimators. Methods. We first review current detections (and non-detections) of the ISW effect, comparing statistical subtleties between existing methods, and identifying several limitations. We propose a novel method to detect and measure the ISW signal. This method assumes only that the primordial CMB field is Gaussian. It is based on a sparse inpainting method to reconstruct missing data and uses a bootstrap technique to avoid assumptions about the statistics of the estimator. It is a complete method, which uses three complementary statistical methods. Results. We apply our method to Euclid-like simulations and show we can expect a ∼7σ model-independent detection of the ISW signal with WMAP7-like data, even when considering missing data. Other tests return ∼5σ detection levels for a Euclid-like survey. We find that detection levels are independent from whether the galaxy field is normally or lognormally distributed. We apply our method to the 2 Micron All Sky Survey (2MASS) and WMAP7 CMB data and find detections in the 1.0−1.2σ range, as expected from our simulations. As a by-product, we have also reconstructed the full-sky temperature ISW field from the 2MASS data.Conclusions. We present a novel technique based on sparse inpainting and bootstrapping, which accurately detects and reconstructs the ISW effect.

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Parameter estimation biases due to contributions from the Rees-Sciama effect to the integrated Sachs-Wolfe spectrum

Cited by 8 publications

References 62 publications

Integrated Sachs-Wolfe tomography with orthogonal polynomials

Integrated Sachs-Wolfe tomography with orthogonal polynomials

The significance of the integrated Sachs-Wolfe effect revisited

Measuring the integrated Sachs-Wolfe effect

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