Cosmological constraints on Hořava gravity revised in light of GW170817 and GRB170817A and the degeneracy with massive neutrinos

We revise the cosmological bounds on Hořava gravity, taking into account the stringent constraint on the speed of propagation of gravitational waves from GW170817 and GRB170817A. In light of this, we also investigate the degeneracy between massive neutrinos and Hořava gravity. We show that a luminal propagation of gravitational waves suppresses the large-scale cosmic microwave background (CMB) radiation temperature anisotropies, and the presence of massive neutrinos increases this effect. On the contrary, large neutrinos mass can compensate the modifications induced by Hořava gravity in the lensing, matter, and primordial B-mode power spectra. Another degeneracy is found, at a theoretical level, between the tensor-to-scalar ratio $r$ and massive neutrinos, as well as with the model’s parameters. We analyze these effects using CMB, supernovae type Ia (SNIa), galaxy clustering, and weak gravitational lensing measurements, and we show how such degeneracies are removed. We find that the model’s parameters are constrained to be very close to their general relativity limits, and we get a 2 orders of magnitude improved upper bound, with respect to the big bang nucleosynthesis constraint, on the deviation of the effective gravitational constant from the Newtonian one. The deviance information criterion suggests that in Hořava gravity, $\mathrm{\Sigma }{m}_{\nu }>0$ is favored when CMB data only are considered, while the joint analysis of all datasets prefers zero neutrinos mass.

Figure 1

Power spectra of different cosmological observables for the Hořava gravity models in Table 1 and $\mathrm{\Lambda }\mathrm{CDM}$. Top panels: CMB temperature-temperature power spectrum at low $\ell$ (left) and high $\ell$ (right). Central panels: Lensing potential autocorrelation power spectrum (left) and E-modes power spectra (right). Bottom panels: Cross-power spectra of the temperature anisotropies and E-mode polarization (left) and matter power spectra (right).

Figure 2

The tensor contribution to the primordial BB power spectra for the Hořava gravity models in Table 1 and $\mathrm{\Lambda }\mathrm{CDM}$. We have set $r_{0.002}=0.05$. We define $D_{\ell }^{BB}=\ell (\ell +1)C_{\ell }^{BB}/2\pi$ and the relative difference as $\mathrm{\Delta }{D}_{\ell }^{BB}/D_{\ell }^{BB}$, i.e., the difference between the Hořava gravity model and $\mathrm{\Lambda }\mathrm{CDM}$, divided by the standard cosmological model.

Figure 3

The primordial total BB spectra, including lensing for the Hořava gravity models in Table 1 and $\mathrm{\Lambda }\mathrm{CDM}$. We also include the data points from BICEP2 and Keck Array (BK15) [92]. We have set $r_{0.002}=0.05$.

Figure 4

The primordial total BB spectra, including lensing for the Hořava gravity models is Table 1 and $\mathrm{\Lambda }\mathrm{CDM}$. We show the impact of different values of the ratio of the tensor-to-scalar power spectra, $r$, on the total BB spectra. We have chosen at the pivot scale, $k_{*}=0.002\mathrm{h}/\mathrm{Mpc}$, two values for $r_{0.002}$: $r_{0.002}=0.05$ and $r_{0.002}=0.1$.

Figure 5

Comparison between the $\mathrm{\Lambda }\mathrm{CDM}$ (top panel) and Hořava gravity (bottom panel) marginalized cosmological parameters. Solid lines indicate the massless neutrino assumption, while dashed lines indicate the massive neutrinos extensions. The 68% C.L. are reported in Table 2.

Figure 6

$H_0-{\mathrm{\Omega }}_m^0$ plane for $\mathrm{\Lambda }\mathrm{CDM}$ analysis (right panels) and Horava gravity model (left panels).

Figure 7

$H_0-{\sigma }_8^0$ plane for $\mathrm{\Lambda }\mathrm{CDM}$ analysis (right panel) and Horava gravity model (left panel).

Figure 8

The marginalized likelihood of ${\log }_{10}(\lambda -1)$ and ${\log }_{10}\eta$. Solid lines correspond to the case without massive neutrinos, dashed lines to the case with massive neutrinos.