Peculiar velocity field: Constraining the tilt of the Universe

A large bulk flow, which is in tension with the Lambda cold dark matter ($\Lambda \mathrm{CDM}$) cosmological model, has been observed. In this paper, we provide a physically plausible explanation of this bulk flow, based on the assumption that some fraction of the observed dipole in the cosmic microwave background is due to an intrinsic fluctuation, so that the subtraction of the observed dipole leads to a mismatch between the cosmic microwave background defined rest frame and the matter rest frame. We investigate a model that takes into account the relative velocity (hereafter the tilted velocity) between the two frames, and develop a Bayesian statistic to explore the likelihood of this tilted velocity. By studying various independent peculiar velocity catalogs, we find that (1) the magnitude of the tilted velocity $u$ is around $400\mathrm{km}/\mathrm{s}$, and its direction is close to what is found from previous bulk flow analyses; for most catalogs analyzed, $u=0$ is excluded at about the $2.5\sigma$ level; (2) constraints on the magnitude of the tilted velocity can result in constraints on the duration of inflation, due to the fact that inflation can neither be too long (no dipole effect) nor too short (very large dipole effect); (3) under the assumption of a superhorizon isocurvature fluctuation, the constraints on the tilted velocity require that inflation lasts at least 6 e-folds longer (at the 95% confidence interval) than that required to solve the horizon problem. This opens a new window for testing inflation and models of the early universe from observations of large scale structure.

Figure 1

The SN data plotted in Galactic coordinates. The red points are moving away from us and the blue ones are moving towards us. The size of the points is proportional to the magnitude of the line-of-sight peculiar velocity. “X” is our estimate of the direction of the tilted velocity estimated from the SN data.

Figure 2

The 1-D marginalized posterior probability distribution functions of the parameters are shown: (a) ${\sigma }_{*}$, (b) magnitude of $\mathbf{u}$, (c) $\cos (\theta )$, (d) $\varphi$.

Figure 3

(a) The 68%, 95%, and 99.7% Bayesian confidence interval contours for parameters ${\sigma }_{*}$-$u$. (b) The 68% contours for $\cos (\theta )-\varphi$. The black dot is the direction of the bulk flow found by 1.