Large-scale peculiar velocities in the universe

Abstract

Observations have repeatedly confirmed the presence of large-scale peculiar motions in the universe, commonly referred to as ``bulk flows''. These are vast regions of the observable universe, typically spanning scales of several hundred Mpc, that move coherently with speeds of the order of several hundred km/sec. While there is a general consensus on the direction of these motions, discrepancies persist in their reported sizes and velocities, with some of them exceeding the predictions of the standard $Λ$CDM model. The observed large-scale peculiar-velocity fields are believed to have originated as weak peculiar-velocity perturbations soon after equipartition, which have subsequently grown by structure formation and by the increasing inhomogeneity of the post-recombination universe. However, the evolution and the implications of these bulk velocity fields remain poorly understood and they are still a matter of debate. For instance, it remains a challenge for the theoreticians to explain the high velocities measured by several bulk-flow surveys, like those recently reported using the CosmicFlows-4 data. Such extensive and fast velocity fields could have played a non-negligible role during structure formation and they might have also ``contaminated'' our observations. After all, in the history of astronomy, there are examples where relative-motion effects have led us to a serious misinterpretation of reality (shortened abstract due to length limits).

Figures (21)

• Figure 1: In a multi-component system, the 4-velocity $\tilde{u}_a^{(i)}$ of the $i$-th fluid makes a hyperbolic angle $\beta^{(i)}$ with the reference 4-velocity field $u_a$, normal to the hypersurfaces of homogeneity $S(t)$. The unit vectors $e_a$ and $\tilde{e}_a^{(i)}$ are orthogonal to $u_a$ and $\tilde{u}_a^{(i)}$ respectively. Following definition (\ref{['Lboost']}), the peculiar velocity of the $i$-th species is $\tilde{v}_a^{(i)}= \tilde{v}^{(i)}e_a$, with $\tilde{v}_{(i)}^2= \tilde{v}_a^{(i)}\tilde{v}_{(i)}^a$1973CMaPh..31..209K.
• Figure 2: Typical tilted cosmologies equipped with two families of observers in relative motion, with peculiar velocity $\tilde{v}_a$. The associated 4-velocities ($u_a$ and $\tilde{u}_a$), which form a hyperbolic tilt angle ($\beta$) between them, are normal to their corresponding spatial hypersurfaces ($S$ and $\tilde{S}$).
• Figure 3: Tilted spacetimes allow for two families of relatively moving observers, with 4-velocities $u_a$ and $\tilde{u}_a$, at every event ($O$). Assuming that the $u_a$-field defines the reference frame of the universe, $\tilde{u}_a$ is the 4-velocity of the tilted (the realistic) observers, "drifting" with peculiar velocity $\tilde{v}_a$ relative to the CMB (see Eq. (\ref{['4vels4vels']}a) and Fig. \ref{['fig:f1']} above). Alternatively, one may turn to Fig. \ref{['fig:f2']} and adopt the $\tilde{u}_a$-field as their frame of reference. In that case, the idealised CMB observers are assumed to "move" relative to the tilted frame of a typical galaxy with (effective) "peculiar" velocity $v_a$. It goes without saying that both approaches are physically equivalent and both lead to the same results. Also note that in either case $\beta$ (with $\cosh\beta=-u_a\tilde{u}^a$) is the hyperbolic (tilt) angle between $u_a$ and $\tilde{u}_a$, while $S$ and $\tilde{S}$ are the 3-D rest-spaces of the aforementioned two groups of observers.
• Figure 4: Realistic observers ($O_1$, $O_2$) inside a bulk-flow domain ($D$), moving with peculiar velocity $\tilde{v}_a$ relative to their idealised CMB counterparts. The 4-velocities $u_a$ and $\tilde{u}_a$, with a hyperbolic "tilt" angle ($\beta$) between them, define the reference (CMB) frame of the universe and that of the bulk peculiar motion respectively (see Eqs. (\ref{['4vels4vels']})).
• Figure 5: The transition length $\lambda_T$ on an Einstein-de Sitter background with $q=1/2$. On scales much larger than $\lambda_T$ the relative-motion effects are negligible and $\tilde{q}^{\,\pm}\rightarrow1/2$. Scales close and inside the transition scale, on the other hand, are heavily contaminated by the observers peculiar motion. There, $\tilde{q}^{\,+}$ becomes increasingly more positive (dashed curve), while $\tilde{q}^{\,-}$ turns negative at $\lambda_T$ and keeps decreasing on progressively smaller wavelengths (solid curve). The vertical line marks the nonlinear cutoff, where the linear approximation is expected to break down 2021EPJC...81..753T. In both cases the (unsuspecting) observer is located at the $\lambda=0$ point.