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Late-time approaches to the Hubble tension deforming H(z), worsen the growth tension

G. Alestas,L. Perivolaropoulos

Published 2021 in Unknown venue

ABSTRACT

Many late time approaches for the solution of the Hubble tension use a late time smooth deformation of the Hubble expansion rate H (z) of the Planck18/ΛCDM best fit H (z) to match the locally measured value of H0 while effectively keeping the comoving distance to the last scattering surface r (zrec) and ωm ≡ Ω0mh fixed to maintain consistency with Planck CMB measurements. A well known problem of these approaches is that they worsen the fit to low z distance probes (BAO and SnIa). Here we show that another problem of these approaches is that they worsen the level of the Ω0m − σ8 growth tension. We use the CPL parametrization of H (z) corresponding to evolving dark energy equation of state parameter w(z) = w0 + w1 z 1+z with local measurements H0 prior and fixed values of Ω0mh and r (zrec) and identify the pairs (w0, w1) that satisfy these conditions. We show that for these models theΩ0m −σ8 tension between dynamical probe data (redshift space distortions) and CMB constraints is worse than the corresponding tension that appears in the case of the standard Planck18/ΛCDM model. We justify this feature using a full numerical solution of the growth equation and fit to the data, as well as by using approximate analytic properties of the growth factor of perturbations δρ ρ (z) solution. A similar problem has been pointed out for early time approaches to the Hubble crisis. The problem does not affect recent proposed solutions of the Hubble crisis involving a SnIa intrinsic luminosity transition at zt ' 0.01 that can fully resolve both the Hubble and the growth tensions while being consistent with the Cepheid distance calibrators at z < 0.01.

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