Minimal theory of massive gravity in the light of CMB data and the $S_8$ tension

Abstract

We investigate the Minimal Theory of Massive Gravity (MTMG) in the light of different observational data sets which are in tension within the ΛCDM cosmology. In particular, we analyze MTMG model, for the first time, with the Planck-CMB data, and how these precise measurements affect the free parameters of the theory. The MTMG model can affect the CMB power spectrum at large angular scales and cause a suppression on the amplitude of the matter power spectrum. We find that on adding Planck-CMB data, the graviton has a small, positive, but non-zero mass at 68% confidence level, and from this perspective, we show that the tension between redshift space distortions measurements and Planck-CMB data in the parametric space S8 − Ωm can be resolved within the MTMG scenario. Through a robust and accurate analysis, we find that the H0 tension between the CMB and the local distance ladder measurements still remains but can be reduced to ∼ 3.5σ within the MTMG theory. The MTMG is very well consistent with the CMB observations, and undoubtedly, it can serve as a viable candidate amongst other modified gravity theories.

Minimal theory of massive gravity and constraints on the graviton mass

“…Although this transition is still a special dynamics among all the possible ones, we think it captures the observationally relevant possibilities of the whole MTMG model for several reasons: (i) the background corresponds to a transition between two ΛCDM backgrounds (which differ by their effective cosmological constant), and we know that ΛCDM has still an extremely good fit to the data 4 , and, although not impossible, it is quite hard to outperform it (see e.g. [24]); (ii) the final results on today's value of the graviton mass µ 0 closely agree with the ones recently shown in [20] for the simplest possible choice that X(t) = constant, namely the case where the background (but not the perturbations) is exactly the same as in ΛCDM. For these reasons we believe that the constraints we have found for the today's graviton mass for the normal branch of MTMG will hold even for other dynamics of X(t), after we impose all the constraints coming from the data.…”

Minimal theory of massive gravity and constraints on the graviton mass

“…Although this transition is still a special dynamics among all the possible ones, we think it captures the observationally relevant possibilities of the whole MTMG model for several reasons: (i) the background corresponds to a transition between two ΛCDM backgrounds (which differ by their effective cosmological constant), and we know that ΛCDM has still an extremely good fit to the data, 4 and, although not impossible, it is quite hard to outperform it (see e.g. [25]); (ii) the final results on today's value of the graviton mass µ 0 closely agree with the ones recently shown in [20] for the simplest possible choice that X(t) = constant, namely the case where the background (but not the perturbations) is exactly the same as in ΛCDM. For these reasons we believe that the constraints we have found for the today's graviton mass for the normal branch of MTMG will hold even for other dynamics of X(t), after we impose all the constraints coming from the data.…”

“…Let us first define all the perturbation variables which enter in the theory, keeping in mind we have already fixed a gauge for the perturbations, namely the unitary gauge. This study has been already performed in [20], and thus we will only summarize here the results. In any case, the equations of motion to be inserted in the Boltzmann solver appear here, as far as we know, for the first time in the literature.…”

“…On top of that, without introducing any new propagating degrees of freedom, the normal branch of MTMG allows the presence of a dynamical dark energy component, and such a dynamics can be set by appropriately choosing the fiducial metric to match essentially any desired profile. Recently the simplest possible dynamics for the normal branch (that reproduces the background dynamics of ΛCDM) has been studied in [20] and led to the surprising feature that the Planck data tend to set the squared mass of the tensor modes, µ 2 , to be a positive quantity (at 1-sigma). In fact, although this result was consistent with late time data only, still the data were allowing a large region of µ 2 < 0 (i.e.…”

The Hubble Tension, The $M$ Crisis of Late Time $H(z)$ Deformation Models and the Reconstruction of Quintessence Lagrangians

“…However, if the constraints from the CMB on the ΛCDM background are not taken into account, leaving only the constraints from the SNIa data, the tension decreases to a level below 2σ [68]. The tension also decreases when marginalized confidence contours are used [69] and can be resolved completely within the Minimal theory of massive gravity scenario [70]. A brief analysis of the growth tension along with some proposed solutions can be found in [71].…”