<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>w</mml:mi><mml:mo>−</mml:mo><mml:mi>M</mml:mi></mml:math> phantom transition at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>z</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo><</mml:mo><mml:mn>0.1</mml:mn></mml:math> as a resolution of the Hubble tension
George Alestas, Lavrentios Kazantzidis, Leandros Perivolaropoulos
Abstract
A rapid phantom transition of the dark energy equation of state parameter $w$ at a transition redshift ${z}_{t}<0.1$ of the form $w(z)=\ensuremath{-}1+\mathrm{\ensuremath{\Delta}}w\text{ }\mathrm{\ensuremath{\Theta}}({z}_{t}\ensuremath{-}z)$ with $\mathrm{\ensuremath{\Delta}}w<0$ can lead to a higher value of the Hubble constant while closely mimicking a $\mathrm{Planck}18/\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ form of the comoving distance $r(z)={\ensuremath{\int}}_{0}^{z}\frac{d{z}^{\ensuremath{'}}}{H({z}^{\ensuremath{'}})}$ for $z>{z}_{t}$. Such a transition however would imply a significantly lower value of the SnIa absolute magnitude $M$ than the value ${M}_{C}$ imposed by local Cepheid calibrators at $z<0.01$. Thus, in order to resolve the ${H}_{0}$ tension it would need to be accompanied by a similar transition in the value of the SnIa absolute magnitude $M$ as $M(z)={M}_{C}+\mathrm{\ensuremath{\Delta}}M\text{ }\mathrm{\ensuremath{\Theta}}(z\ensuremath{-}{z}_{t})$ with $\mathrm{\ensuremath{\Delta}}M<0$. This is a late $w\ensuremath{-}M$ phantom transition ($LwMPT$). It may be achieved by a sudden reduction of the value of the normalized effective Newton constant $\ensuremath{\mu}={G}_{\mathrm{eff}}/{G}_{\mathrm{N}}$ by about 6% assuming that the absolute luminosity of SnIa is proportional to the Chandrasekhar mass which varies as ${\ensuremath{\mu}}^{\ensuremath{-}3/2}$. We demonstrate that such an ultra low $z$ abrupt feature of $w\ensuremath{-}M$ provides a better fit to cosmological data compared to smooth late time deformations of $H(z)$ that also address the Hubble tension. For ${z}_{t}=0.02$ we find $\mathrm{\ensuremath{\Delta}}w\ensuremath{\simeq}\ensuremath{-}4$, $\mathrm{\ensuremath{\Delta}}M\ensuremath{\simeq}\ensuremath{-}0.1$. This model also addresses the growth tension due to the predicted lower value of $\ensuremath{\mu}$ at $z>{z}_{t}$. A prior of $\mathrm{\ensuremath{\Delta}}w=0$ (no $w$ transition) can still resolve the ${H}_{0}$ tension with a larger amplitude $M$ transition with $\mathrm{\ensuremath{\Delta}}M\ensuremath{\simeq}\ensuremath{-}0.2$ at ${z}_{t}\ensuremath{\simeq}0.01$. This implies a larger reduction of $\ensuremath{\mu}$ for $z>0.01$ (about 12%). The $LwMPT$ can be generically induced by a scalar field nonminimally coupled to gravity with no need of a screening mechanism since in this model $\ensuremath{\mu}=1$ at $z<0.01$.