Measuring our Peculiar Velocity by "Pre-deboosting" the CMB

It was recently shown that our peculiar velocity \beta with respect to the CMB induces mixing among multipoles and off-diagonal correlations at all scales which can be used as a measurement of \beta, which is independent of the standard measurement using the CMB temperature dipole. The proposed techniques rely however on a perturbative expansion which breaks down for \ell \gtrsim 1/(\beta) \approx 800. Here we propose a technique which consists of deboosting the CMB temperature in the time-ordered data and show that it extends the validity of the perturbation analysis multipoles up to \ell \sim 10000. We also obtain accurate fitting functions for the mixing between multipoles valid in a full non-linear treatment. Finally we forecast the achievable precision with which these correlations can be measured in a number of current and future CMB missions. We show that Planck could measure the velocity with a precision of around 60 km/s, ACTPol in 4 years around 40 km/s, while proposed future experiments could further shrink this error bar by over a factor of around 2.