# H_{0} Tension, Phantom Dark Energy and Cosmological Parameter Degeneracies

Published in *Physical Review D*, 2020

# Abstract

Dark energy with equation of state parameter w<-1 can produce amplified cosmic acceleration at late times, thus increasing the value of H_{0} favoured by CMB data and releasing the tension with local measurements of H_{0}. In order to demonstrate this hypothesis, we show that the best fit value of H_{0} in the context of the CMB power spectrum is degenerate with a constant equation of state parameter w, in accordance with the approximate effective linear equation H_{0}+30.93·w-36.47=0 This equation is derived by assuming that both Ω_{0m}·h^{2} and the co-moving angular diameter distance to the last scattering surface remain constant and equal to their best fit Planck/ΛCDM values as H_{0}, Ω_{0m} and w vary. This secures that the predicted CMB spectrum remains practically unchanged and equal to its best fit ΛCDM form. For w=-1, this linear degeneracy equation leads to the best fit H_{0}=67.4 km sec^{-1} Mpc^{-1} as expected. For w=-1.22 the corresponding predicted CMB best fit Hubble constant is H_{0}=74 km sec^{-1} Mpc^{-1} which is identical with the value obtained by local distance ladder measurements, therefore leading to an apparent resolution of the Hubble tension. We verify the above H_{0} degeneracy equation by fitting a wCDM model with fixed values of w to the Planck data and show that the above linear degeneracy equation is accurate to within less than 0.63% in the range -1.5<w<1, while the quality of fit to the Planck data remains practically unchanged in the parameter region. Finally we show how these results can be extended in the case of an evolving equation of state parameter w(z) leading to degenerate regions in the parameter space of parameters appearing in the form of w(z) where the predicted CMB power spectrum remains practically invariant. We analyse in detail this degeneracy for the CPL parametrization and identify analytically the full w_{0}-w_{1} parameter region that leads to a best fit H_{0}=74 km sec^{-1} Mpc^{-1} in the context of the Planck CMB spectrum.

# Cite

If you use any of the above codes or the figures in a published work please cite the following paper: *H _{0} Tension, Phantom Dark Energy and Cosmological Parameter Degeneracies*

George Alestas, Lavrentios Kazantzidis and Leandros Perivolaropoulos

Phys.Rev.D 101 (2020) 12, 123516, arxiv:2004.08363.

Any further questions/comments are welcome.

# Authors Lists

George Alestas - g.alestas@uoi.gr

Lavrentios Kazantzidis - l.c.kazantzidis@gmail.com

Leandros Perivolaropoulos - leandros@uoi.gr