Past exam of the short options paper of the physics Prelims of the University of Oxford / 2022 / S02 / 3 / d

The angle estimates the largest transverse region at decoupling that could have established causal contact after the big bang in the assumed decelerating model. The cosmic microwave background has nearly the same temperature in directions separated by much larger angles. This is the horizon problem: those regions have no shared causal history in that simple model, yet their thermodynamic conditions are strikingly alike. The particle horizon should be distinguished from the smaller sound horizon, which controls acoustic propagation in the primordial fluid.

An early epoch dominated by a sufficiently large positive effective cosmological constant gives $\ddot{R}>0$ and approximately $R\propto e^{Ht}$. During this cosmic inflation, the comoving Hubble length $c/(RH)$ shrinks. A patch that was initially in causal contact can expand to contain the whole presently observable cosmic microwave background surface, while expansion suppresses spatial curvature. A finite period of cosmic inflation followed by reheating and the usual hot expansion therefore explains the uniformity without superluminal local signals. An eternally large unchanged cosmological constant would prevent the later matter-dominated history; an exit from cosmic inflation and reheating are required. Sufficient duration and a suitable pre-inflationary causal patch are part of this explanation.