A $w-M$ phantom transition at $z_t<0.1$ as a resolution of the Hubble tension

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 $w(z)=-1+\Delta w\Theta (z_t-z)$ with $\Delta w<0$ can lead to a higher value of the Hubble constant while closely mimicking a Planck18/$\Lambda$CDM form of the comoving distance $r(z)={\int }_0^z\frac{d{z}^{\prime }}{H(z^{\prime })}$ 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 $M(z)=M_C+\Delta M\Theta (z-z_t)$ with $\Delta M<0$. This is a Late $w-M$ phantom transition ($LwMPT$). It may be achieved by a sudden reduction of the value of the normalized effective Newton constant $\mu =G_{\mathrm{eff}}/G_{\mathrm{N}}$ by about $6\%$ assuming that the absolute luminosity of SnIa is proportional to the Chandrasekhar mass which varies as ${\mu }^{-3/2}$. We demonstrate that such an ultra low $z$ abrupt feature of $w-M$ 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 $\Delta w\simeq -4$, $\Delta M\simeq -0.1$. This model also addresses the growth tension due to the predicted lower value of $\mu$ at $z>z_t$. A prior of $\Delta w=0$ (no $w$ transition) can still resolve the $H_0$ tension with a larger amplitude $M$ transition with $\Delta M\simeq -0.2$ at $z_t\simeq 0.01$. This implies a larger reduction of $\mu$ for $z>0.01$ (about $12\%$). The $LwMPT$ can be generically induced by a scalar field non-minimally coupled to gravity with no need of a screening mechanism since in this model $\mu =1$ at $z<0.01$.

14 pages, 9 Figures. Accepted in Physical Review D (to appear). Typos corrected, a new figure and references added. The Mathematica files used for the construction of the figures may be downloaded from https://github.com/GeorgeAlestas/LwMPT

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