A new method to determine large scale structure from the luminosity distance

2018

Int. J. Mod. Phys. D

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The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of H 0 estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about 0.07. About 40% of the Cepheids used for SN calibration are directly affected because are located along the directions of these inhomogeneities. We compute with different methods the effects of these inhomogeneities on the low-redshift luminosity and angular diameter distance using an exact solution of the Einstein's equations, linear perturbation theory and a low-redshift expansion. We confirm that at low redshift the dominant effect is the non relativist Doppler redshift correction, which is proportional to the volume averaged density contrast and to the comoving distance from the center. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the ΛCDM prediction based on cosmological parameters obtained from large scale observations.The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the 2M + + 1 density field maps used to obtain the peculiar velocity 2 for redshift correction were for z ≤ 0.06, which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to z = 0.07. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of H CM B 0 obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.

Section: Reconstructing the Density Field From The Luminosity Distancementioning

confidence: 99%

Hubble trouble or Hubble bubble?

2018

Int. J. Mod. Phys. D

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“…A detailed derivation of these equations is given in [45]. Notice that ρ 0 and initial conditions k(z = 0), η(z = 0) are fixed according to a 0 , H 0 and q 0 .…”

Section: Inhomogeneity Model and Inverted Density Profilementioning

confidence: 99%

“…In this paper we improve and apply the inversion method derived in [24] and [45] to obtain the local density map from standard candles luminosity distance observations. The inversion method requires as input a smooth function for the luminosity distance D L (z) which we obtain with a model independent fit of a combination of Cepheids-hosting galaxies from R16 and low redshift (z < 0.4) SNe from the UNION 2.1 catalogue of [46].…”

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confidence: 99%

“…All SNe in a given field give rise to a radial profile averaging over the corresponding window. Assuming that shear effects can be neglected , which is expected to be a valid approximation at small redshift [47], we reconstruct the radial density profile for each field based on the inversion method described in [45], with some modifications necessary to take into account the corrections to the growth factor due to the cosmological constant.…”

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confidence: 99%

See 1 more Smart Citation

Probing homogeneity with standard candles

Chiang

J. Cosmol. Astropart. Phys.

Nugier

et al. 2019

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We show that standard candles can provide some valuable information about the density contrast, which could be particularly important at redshifts where other observations are not available. We use an inversion method to reconstruct the local radial density profile from luminosity distance observations assuming background cosmological parameters obtained from large scale observations. Using type Ia Supernovae, Cepheids and the cosmological parameters from the Planck mission we reconstruct the radial density profiles along two different directions of the sky. We compare these profiles to other density maps obtained from luminosity density, in particular Keenan et al. 2013 and the 2M++ galaxy catalogue. The method independently confirms the existence of inhomogeneities, could be particularly useful to correctly normalize density maps from galaxy surveys with respect to the average density of the Universe, and could clarify the apparent discrepancy between local and large scale estimations of the Hubble constant. When better observational supernovae data will be available, the accuracy of the reconstructed density profiles will improve and will allow to further investigate the existence of structures whose size is beyond the reach of galaxy surveys.

“…This is particularly important when trying to determine the metric of the Universe. Different numerical [23,[27][28][29][30][31][32] and analytical [33] inversion methods have been developed in absence of the cosmological constant.…”

Section: Introductionmentioning

confidence: 99%

Reconstructing the metric of the local Universe from number counts observations

Vallejo

J. Cosmol. Astropart. Phys.

2017

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Number counts observations available with new surveys such as the Euclid mission will be an important source of information about the metric of the Universe. We compute the low red-shift expansion for the energy density and the density contrast using an exact spherically symmetric solution in presence of a cosmological constant. At low red-shift the expansion is more precise than linear perturbation theory prediction. We then use the local expansion to reconstruct the metric from the monopole of the density contrast. We test the inversion method using numerical calculations and find a good agreement within the regime of validity of the red-shift expansion. The method could be applied to observational data to reconstruct the metric of the local Universe with a level of precision higher than the one achievable using perturbation theory.