Cosmology in warped massive gravity

Abstract

We study the cosmological dynamics and predictions in the theory of warped massive gravity. This set-up postulates a five-dimensional ghost-free massive graviton with a brane-localized four-dimensional massive gravity potential, and has the virtue of raising the strong-coupling scale of the 4D theory. We identify two classes of models that lead to decoupled equations for the scale factor on the brane: one characterized by a particular choice of boundary conditions for the Stückelberg fields and one characterized by a special tuning between the coefficients of the 5D and 4D potentials. In the first case, we find interesting solutions including a cosmological bounce without the need of exotic matter. The second case leads to a modified Friedmann equation, and comparison with data shows the potential of the model to alleviate the Hubble tension.

Figures (8)

• Figure 1: Phase diagram of the modified Raychaudhuri equation. The parameter setting is $\kappa=3$, $\Omega_{\rm m}=1/4$, $m_4=m_5=1$, $\mathcal{A}=\mathcal{B}_1=1$, $\Lambda_{\rm eff}=0$ and $K=10^{-3}$, all in units of $\mu=1$. The colored curves are examples of the three classes of solutions that we identify in this model: Big Bang (green), Big Crunch (orange) and non-singular bounce (red). The right panel is a zoomed-in section near the bounce.
• Figure 2: Graph of $a(t)$ for the bounce solution (red curve) of Fig. \ref{['fig:neumann-stream']}. The right panel is a zoomed-in section near the bounce.
• Figure 3: Graph of $a(t)$ in the special model for different choices of $\kappa$ (left panel) and $\Lambda_{\rm eff}$ (right). Other parameters are fixed as $m_4=1/10$, $\Omega_{\rm r}=1/2$ and $\mathcal{A}=\pm1/10$ (respectively for the $\pm$ branch), all in units of $\mu=1$. When varying $\kappa$, $\Lambda_{\rm eff}=1/10$; when varying $\Lambda_{\rm eff}$, $\kappa=170$. In each case, $\mathcal{C}$ is chosen such that the slope matches the corresponding GR result at $t=10$.
• Figure 4: Constraints on parameters for $\Lambda$CDM and the WMG special "M" model assuming a flat prior $M\in[-1,1]$. Shown are $1\sigma$ and $2\sigma$ contours obtained from the CMB and PPS datasets.
• Figure 5: Same as Fig. \ref{['fig:dataM']} but assuming a flat prior $M\in[0,1]$ for the special "M" model.