Constraining Lorentz Violation with Cosmology

The Einstein-aether theory provides a simple, dynamical mechanism for breaking Lorentz invariance. It does so within a generally covariant context and may emerge from quantum effects in more fundamental theories. The theory leads to a preferred frame and can have distinct experimental signatures. In this Letter, we perform a comprehensive study of the cosmological effects of the Einstein-aether theory and use observational data to constrain it. Allied to previously determined consistency and experimental constraints, we find that an Einstein-aether universe can fit experimental data over a wide range of its parameter space, but requires a specific rescaling of the other cosmological densities.

Figure 1

The angular power spectrum of the CMB (bottom) and the power spectrum of galaxies (top) for a sample of class $\mathcal{C}$ Einstein-aether models, with different $c_{+}$ (with $c_{-}$ chosen to satisfy the weak-field binary pulsar constraint—the dashed line of Fig. 4) The other parameters have their $\Lambda \mathrm{CDM}$ best-fit values, with the ${\Omega }_i$ rescaled as described in the text. Superposed are the WMAP and SDSS data sets.

Figure 2

The angular power spectrum of the CMB (bottom) and the power spectrum of galaxies (top) for a sample of exotic class $\mathcal{E}$ Einstein-aether models where $c_1=c_2=c_3=0$. The other parameters have their $\Lambda \mathrm{CDM}$ best-fit values, with the radiation density modified to account for the change in the gravitational constant. Superposed are the WMAP and SDSS datasets.

Figure 3

Joint constraints on the fractional aether density ${\Omega }_{AE}$, with the physical dark matter density ${\Omega }_c{h}^2$, the physical baryon density ${\Omega }_b{h}^2$, and the fractional $\Lambda$ density ${\Omega }_{\Lambda }$. The contours are 1 and $2\sigma$.

Figure 4

Joint constraints on the parameters $-c_{+}$ and $-c_{-}$. The black lines are the 1 and $2\sigma$ contours, where we have marginalized over the values of the parameters. The hatched region is excluded by Čerenkov constraints; the dashed line indicates where weak-field constraints from binary pulsars are met. Both are taken from [4].