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It has been intensively discussed if modifications in the dynamics of the Universe at late times is able or not to solve the $H_0$ tension. On the other hand, it has also been argued that the $H_0$ tension is actually a tension on the supernova absolute magnitude $M_B$. In this work, we robustly constraint $M_B$ using Pantheon Supernovae Ia (SN) sample, Baryon Acoustic Oscillations (BAO), and Big Bang Nucleosynthesis (BBN) data, and assess the $M_B$ tension by comparing three theoretical models, namely the standard $Lambda$CDM, the $w$CDM and a non-gravitational interaction (IDE) between dark energy (DE) and dark matter (DM). We find that the IDE model can solve the $M_B$ tension with a coupling different from zero at 95% CL, confirming the results obtained using a $H_0$ prior.
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A phenomenological attempt at alleviating the so-called coincidence problem is to allow the dark matter and dark energy to interact. By assuming a coupled quintessence scenario characterized by an interaction parameter $epsilon$, we investigate the precision in the measurements of the expansion rate $H(z)$ required by future experiments in order to detect a possible deviation from the standard $Lambda$CDM model ($epsilon = 0$). We perform our analyses at two levels, namely: through Monte Carlo simulations based on $epsilon$CDM models, in which $H(z)$ samples with different accuracies are generated and through an analytic method that calculates the error propagation of $epsilon$ as a function of the error in $H(z)$. We show that our analytical approach traces simulations accurately and find that to detect an interaction {using $H(z)$ data only, these must reach an accuracy better than 1%.
It is possible that there exist some interactions between dark energy (DE) and dark matter (DM), and a suitable interaction can alleviate the coincidence problem. Several phenomenological interacting forms are proposed and are fitted with observations in the literature. In this paper we investigate the possible interaction in a way independent of specific interacting forms by use of observational data (SNe, BAO, CMB and Hubble parameter). We divide the whole range of redshift into a few bins and set the interacting term $delta(z)$ to be a constant in each redshift bin. We consider four parameterizations of the equation of state $w_{de}$ for DE and find that $delta(z)$ is likely to cross the non-interacting ($delta=0$) and have an oscillation form. It suggests that to study the interaction between DE and DM, more general phenomenological forms of the interacting term should be considered.
We show that a general late-time interaction between cold dark matter and vacuum energy is favoured by current cosmological datasets. We characterize the strength of the coupling by a dimensionless parameter $q_V$ that is free to take different values in four redshift bins from the primordial epoch up to today. This interacting scenario is in agreement with measurements of cosmic microwave background temperature anisotropies from the Planck satellite, supernovae Ia from Union 2.1 and redshift space distortions from a number of surveys, as well as with combinations of these different datasets. We show that a non-zero interaction is very likely at late times. We then focus on the case $q_V ot=0$ in a single low-redshift bin, obtaining a nested one parameter extension of the standard $Lambda$CDM model. We study the Bayesian evidence, with respect to $Lambda$CDM, of this late-time interaction model, finding moderate evidence for an interaction starting at $z=0.9$, dependent upon the prior range chosen for the interaction strength parameter $q_V$. For this case the null interaction ($q_V=0$, i.e.$Lambda$CDM) is excluded at 99% c.l..
In this paper we explore possible extensions of Interacting Dark Energy cosmologies, where Dark Energy and Dark Matter interact non-gravitationally with one another. In particular, we focus on the neutrino sector, analyzing the effect of both neutrino masses and the effective number of neutrino species. We consider the Planck 2018 legacy release data combined with several other cosmological probes, finding no evidence for new physics in the dark radiation sector. The current neutrino constraints from cosmology should be therefore regarded as robust, as they are not strongly dependent on the dark sector physics, once all the available observations are combined. Namely, we find a total neutrino mass $M_ u<0.15$ eV and a number of effective relativistic degrees of freedom of $N_{rm eff}=3.03^{+0.33}_{-0.33}$, both at 95% CL, which are close to those obtained within the $Lambda$CDM cosmology, $M_ u<0.12$ eV and $N_{rm eff}=3.00^{+0.36}_{-0.35}$ for the same data combination.
Phantom dark energy can produce amplified cosmic acceleration at late times, thus increasing the value of $H_0$ favored by CMB data and releasing the tension with local measurements of $H_0$. 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 $H_0 + 30.93; w - 36.47 = 0$ ($H_0$ in $km ; sec^{-1} ; Mpc^{-1}$). This equation is derived by assuming that both $Omega_{0 rm m}h^2$ and $d_A=int_0^{z_{rec}}frac{dz}{H(z)}$ remain constant (for invariant CMB spectrum) and equal to their best fit Planck/$Lambda$CDM values as $H_0$, $Omega_{0 rm m}$ and $w$ vary. 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 while the best fit matter density parameter is predicted to decrease since $Omega_{0 rm m}h^2$ is fixed. We verify the above $H_0-w$ degeneracy equation by fitting a $w$CDM model with fixed values of $w$ to the Planck TT spectrum showing also that the quality of fit ($chi^2$) is similar to that of $Lambda$CDM. However, when including SnIa, BAO or growth data the quality of fit becomes worse than $Lambda$CDM when $w< -1$. Finally, we generalize the $H_0-w(z)$ degeneracy equation for $w(z)=w_0+w_1; z/(1+z)$ 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. This exploitation of $H_0-w(z)$ degeneracy can lead to immediate identification of all parameter values of a given $w(z)$ parametrization that can potentially resolve the $H_0$ tension.
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