Looking the void in the eyes—the kinematic Sunyaev–Zeldovich effect in Lemaître–Tolman–Bondimodels

Abstract

As an alternative explanation of the dimming of distant supernovae it has recently beenadvocated that we live in a special place in the Universe near the centre of a large voiddescribed by a Lemaître–Tolman–Bondi (LTB) metric. The Universe is no longerhomogeneous and isotropic and the apparent late time acceleration is actually aconsequence of spatial gradients in the metric. If we did not live close to the centre of thevoid, we would have observed a cosmic microwave background (CMB) dipole much largerthan that allowed by observations. Hence, until now it has been argued, for the modelto be consistent with observations, that by coincidence we happen to live veryclose to the centre of the void or we are moving towards it. However, even if weare at the centre of the void, we can observe distant galaxy clusters, which areoff-centre. In their frame of reference there should be a large CMB dipole, whichmanifests itself observationally for us as a kinematic Sunyaev–Zeldovich (kSZ) effect.kSZ observations give far stronger constraints on the LTB model compared toother observational probes such as type Ia supernovae, the CMB, and baryonacoustic oscillations. We show that current observations of only nine clusterswith large error bars already rule out LTB models with void sizes greater than∼1.5 Gpc and a significant underdensity, and that near future kSZ surveys like the AtacamaCosmology Telescope (ACT), South Pole Telescope (SPT), APEX telescope, and thePlanck satellite will be able to strongly rule out or confirm LTB models with gigaparsecsized voids. On the other hand, if the LTB model is confirmed by observations, a kSZsurvey gives a unique possibility of directly reconstructing the expansion rate andunderdensity profile of the void.