= Solution
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.
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