In general relativity, a gravitational horizon (more commonly known as the “apparent horizon”) is an imaginary surface beyond which all null geodesics recede from the observer. The Universe has an apparent (gravitational) horizon, but unlike its counterpart in the Schwarzschild and Kerr metrics, it is not static. It may eventually turn into an event horizon—an asymptotically defined membrane that forever separates causally connected events from those that are not—depending on the equation of state of the cosmic fluid. In this paper, we examine how and why an apparent (gravitational) horizon is manifested in the Friedmann–Robertson–Walker metric, and why it is becoming so pivotal to our correct interpretation of the cosmological data. We discuss its observational signature and demonstrate how it alone defines the proper size of our visible Universe. In so doing, we affirm its physical reality and its impact on cosmological models.
References
As demonstrated by these authors, the mass M(R) emerging from the grr coefficient of the FRW metric is defined in terms of the comoving density ρ and the proper radius R = a(t)r, where a(t) is the expansion factor and r is the (unchanging) comoving radius (see Eq. (3)). Therefore, as one can see in Eq. (15), Eqs. (1) and (2) lead to an identification of Rh as the Hubble radius only if Rh is itself a proper distance, in contrast to the claim in Ref. 16 that Rh is not a proper radius.
Of course, H is necessarily “constant” at every position only on a given time slice t, but may change with time, depending on the expansion dynamics.