Cosmic variance of $H_0$ in light of forthcoming high-redshift surveys

Abstract

Forthcoming surveys will extend the understanding of cosmological large scale structures up to unprecedented redshift. According to this perspective, we present a fully relativistic framework to evaluate the impact of stochastic inhomogeneities on the determination of the Hubble constant. To this aim, we work within linear perturbation theory and relate the fluctuations of the luminosity distance-redshift relation, in the Cosmic Concordance model, to the intrinsic uncertainty associated to the measurement of $H_0$ from high-redshift surveys ($0.15\le z\le 3.85$). We first present the detailed derivation of the luminosity distance-redshift relation 2-point correlation function and then provide analytical results for all the involved relativistic effects, such as peculiar velocity, lensing, time delay and (integrated) Sachs-Wolfe, and their angular spectra. Hence, we apply our analytical results to the study of high-redshift Hubble diagram, according to what has been recently claimed in literature. Following the specific of Euclid Deep Survey and LSST, we conclude that the cosmic variance associated with the measurement of the Hubble constant is at most of 0.1 %. Our work extends the analysis already done in literature for closer sources, where only peculiar velocity has been taken into account. We then conclude that deep surveys will provide an estimation of the $H_0$ which will be more precise than the one obtained from local sources, at least in regard of the intrinsic uncertainty related to a stochastic distribution of inhomogeneities.

arXiv comment26 pages, 9 figures. Typos fixed. Comments and references added. Version accepted for publication in Physical Review D

References in corpus (56)

• Baryonic Features in the Matter Transfer Function
• Stable clustering, the halo model and nonlinear cosmological power spectra
• Tensions between the Early and the Late Universe
• H0LiCOW XIII. A 2.4% measurement of $H_0$ from lensed quasars: $5.3\sigma$ tension between early and late-Universe probes
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• The trouble with $H_0$
• The Hubble Hunter's Guide
• Hydrogen Epoch of Reionization Array (HERA)
• Cosmology Intertwined II: The Hubble Constant Tension
• New physics in light of the $H_0$ tension: an alternative view
• CMB-S4 Science Case, Reference Design, and Project Plan
• Can interacting dark energy solve the $H_0$ tension?
• Calibration of the Tip of the Red Giant Branch (TRGB)
• On the Hubble constant tension in the SNe Ia Pantheon sample
• Reconciling Planck with the local value of $H_0$ in extended parameter space
• The Megamaser Cosmology Project. XIII. Combined Hubble constant constraints
• Reionization and the Cosmic Dawn with the Square Kilometre Array
• Fluctuations of the luminosity distance
• Why reducing the cosmic sound horizon alone can not fully resolve the Hubble tension
• Consistent Calibration of the Tip of the Red Giant Branch in the Large Magellanic Cloud on the Hubble Space Telescope Photometric System and a Re-determination of the Hubble Constant
• Light-cone averaging in cosmology: formalism and applications
• Scalar-tensor theories of gravity, neutrino physics, and the $H_0$ tension
• The value of H_0 in the inhomogeneous Universe
• Chameleon dark energy can resolve the Hubble tension
• Implication of the Hubble tension for the primordial Universe in light of recent cosmological data
• Average and dispersion of the luminosity-redshift relation in the concordance model
• The second-order luminosity-redshift relation in a generic inhomogeneous cosmology
• Determining the Hubble Constant without the Sound Horizon Scale: Measurements from CMB Lensing
• Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging
• Fractal universe and cosmic acceleration in a Lemaître-Tolman-Bondi scenario
• Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. II - Derivation
• Modeling relativistic contributions to the halo power spectrum dipole
• CMB-lensing beyond the Born approximation
• How does the cosmic large-scale structure bias the Hubble diagram?
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
• A new approach to the propagation of light-like signals in perturbed cosmological backgrounds
• CMB-lensing beyond the leading order: temperature and polarization anisotropies
• COFFE: a code for the full-sky relativistic galaxy correlation function
• The relativistic dipole and gravitational redshift on LSS
• Cosmological ensemble and directional averages of observables
• Galaxy Two-Point Correlation Function in General Relativity
• Impact of next-to-leading order contributions to CMB lensing
• Generalized covariant prescriptions for averaging cosmological observables
• The first Hubble diagram and cosmological constraints using superluminous supernova
• Non-linear general relativistic effects in the observed redshift
• Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average
• Hubble trouble or Hubble bubble?
• On the covariance of scalar averaging and backreaction in relativistic inhomogeneous cosmology
• Time of flight of ultra-relativistic particles in a realistic Universe: a viable tool for fundamental physics?
• Rotation of the CMB polarisation by foreground lensing
• Discriminating different models of luminosity-redshift distribution
• A structured analysis of Hubble tension
• Maximum Cosmological Information from Type-Ia Supernova Observations
• Coordinate independent approach to the calculation of the effects of local structure on the luminosity distance

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