Pre-big-bang cosmology and circles in the cosmic microwave background

We examine the possibility that circles in the cosmic microwave background could be formed by the interaction of a gravitational wave pulse emitted in some pre-big-bang phase of the universe with the last scattering surface. We derive the expected size distribution of such circles, as well as their typical ring width and (for concentric circles) angular separation. We apply these results, in particular, to conformal cyclic cosmology, ekpyrotic cosmology as well as loop quantum cosmology with and without inflation in order to determine how the predicted geometric properties of these circles would vary from one model to the other, and thus, if detected, could allow us to differentiate between various pre-big-bang cosmological models. We also obtain a relation between the angular ring width and the angular radius of such circles that can be used in order to determine whether or not circles observed in the cosmic microwave background are due to energetic pre-big-bang events.

Figure 1

The conformal diagram of the expanding (null) pulse, intersecting the last scattering surface (LSS). The CMB sphere as seen today is also pictured. The time $t=0$ corresponds to the transition between the pre-big-bang and post-big-bang epochs. The detailed dynamics near the transition point are of course model-specific.

Figure 2

The geometric properties of the circles we are interested in: their angular radius (Sec. 3a), the typical angular separation between concentric circles (Sec. 3b) and the angular ring width of the circles (Sec. 3c).

Figure 3

A pair of spherical pulses with coordinate radii $r_p$ and $r_p-\delta r_p$, intersecting the observed CMB sphere of radius $r_o$.