<i>Hubble</i>parameter reconstruction from a principal component analysis: minimizing the bias

Ishida, Emille E. O.

doi:10.1051/0004-6361/201015281

Cited by 45 publications

(35 citation statements)

References 33 publications

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“…In other words, data should be able to provide reliable constraints on the behavior of cosmological parameters, running with redshift, independently of any cosmological model or underlying gravity theory. For example, it has been shown that a principal component analysis, adopting SNeIa data, can help to reconstruct the Hubble parameter [17]. This kind of procedure allows to determine H 0 and, in principle, any other cosmographic parameter with reasonable uncertainty and without any ad-hoc parameterizations.…”

Section: Luminosity Distance and Cosmographymentioning

confidence: 99%

Connecting early and late epochs by f(z)CDM cosmography

Benetti

Capozziello

2019

J. Cosmol. Astropart. Phys.

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Section: Luminosity Distance and Cosmographymentioning

confidence: 99%

Connecting early and late epochs by f(z)CDM cosmography

Benetti

Capozziello

2019

J. Cosmol. Astropart. Phys.

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“…Even sparser bases that require fewer coefficients for the reconstruction exist, e.g. the principal component basis as introduced in Ishida & de Souza (2011) or Maturi & Mignone (2009). Yet, these approaches are less suitable for our purpose than an analytic basis.…”

Section: Further Numerical Basesmentioning

confidence: 99%

Generalized model-independent characterization of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe

Wagner

Meyer

2019

Monthly Notices of the Royal Astronomical Society

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We determine the cosmic expansion rate from supernovae of type Ia to set up a databased distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrisation of a Friedmann cosmological model. The scale, determined by the Hubble constant H 0 , is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio D is determined from the Pantheon sample. Inserting D and its uncertainty into the lensing equations for given H 0 , esp. the time-delay equation between a pair of multiple images, allows to determine lens properties, esp. differences in the lensing potential (∆φ), without specifying a cosmological model. We expand the luminosity distances into an analytic orthonormal basis, determine the maximum-likelihood weights for the basis functions by a globally optimal χ 2 -parameter estimation, and derive confidence bounds by Monte-Carlo simulations. For typical strong lensing configurations between z = 0.5 and z = 1.0, ∆φ can be determined with a relative imprecision of 1.7%, assuming imprecisions of the time delay and the redshift of the lens on the order of 1%. With only a small, tolerable loss in precision, the model-independent lens characterisation developed in this paper series can be generalised by dropping the specific Friedmann model to determine D in favour of a data-based distance ratio. Moreover, for any astrophysical application, the approach presented here, provides distance measures for z ≤ 2.3 that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.nation with a cosmological model that assigns the redshift to a cosmic distance. So far, the cosmological standard model, as most precisely measured by Planck Collaboration et al. (2018), is inserted into these distance measures.As one example, in the gravitational lensing formalism, angular diameter distances between the observer and the lens D l , the observer and the source Ds, and the distance between the lens and the source D ls appear in the lensing equations to scale the (multiple) images, the source, and the deflection potential with respect to each other. The so-called lensing distance ratio D(z l , zs) = D l Ds D ls ,appears, for instance, in the time delay τij between two multiple images i and j of the same background galaxy located

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“…tions and the data is used to determine which subset of this basis is better constrained. Then, the function is reconstructed by using this subset [13,17,[20][21][22][23]. Another possibility is to use smoothing methods [24,25].…”

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confidence: 99%

A general reconstruction of the recent expansion history of the universe

Vitenti

Penna-Lima

2015

J. Cosmol. Astropart. Phys.

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Abstract. Distance measurements are currently the most powerful tool to study the expansion history of the universe without specifying its matter content nor any theory of gravitation. Assuming only an isotropic, homogeneous and flat universe, in this work we introduce a model-independent method to reconstruct directly the deceleration function via a piecewise function. Including a penalty factor, we are able to vary continuously the complexity of the deceleration function from a linear case to an arbitrary (n + 1)-knots spline interpolation. We carry out a Monte Carlo (MC) analysis to determine the best penalty factor, evaluating the bias-variance trade-off, given the uncertainties of the SDSS-II and SNLS supernova combined sample (JLA), compilations of baryon acoustic oscillation (BAO) and H(z) data. The biasvariance analysis is done for three fiducial models with different features in the deceleration curve. We perform the MC analysis generating mock catalogs and computing their best-fit. For each fiducial model, we test different reconstructions using, in each case, more than 10 4 catalogs in a total of about 5 × 10 5 . This investigation proved to be essential in determining the best reconstruction to study these data. We show that, evaluating a single fiducial model, the conclusions about the bias-variance ratio are misleading. We determine the reconstruction method in which the bias represents at most 10% of the total uncertainty. In all statistical analyses, we fit the coefficients of the deceleration function along with four nuisance parameters of the supernova astrophysical model. For the full sample, we also fit H 0 and the sound horizon r s (z d ) at the drag redshift. The bias-variance trade-off analysis shows that, apart from the deceleration function, all other estimators are unbiased. Finally, we apply the Ensemble Sampler Markov Chain Monte Carlo (ESMCMC) method to explore the posterior of the deceleration function up to redshift 1.3 (using only JLA) and 2.3 (JLA+BAO+H(z)). We obtain that the standard cosmological model agrees within 3σ level with the reconstructed results in the whole studied redshift intervals. Since our method is calibrated to minimize the bias, the error bars of the reconstructed functions are a good approximation for the total uncertainty.

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Hubbleparameter reconstruction from a principal component analysis: minimizing the bias

Cited by 45 publications

References 33 publications

Connecting early and late epochs by f(z)CDM cosmography

Connecting early and late epochs by f(z)CDM cosmography

Generalized model-independent characterization of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe

A general reconstruction of the recent expansion history of the universe

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