The mass of our observable Universe

The standard cosmological model Lambda Cold Dark Matter (LCDM) assumes a global expanding space-time of infinite extent around us. But such idea is inconsistent with the observed cosmic acceleration unless we advocate for the existence of a mysterious dark energy (DE) or a cosmological constant (Λ). Here, we argue instead that our Universe has a very large but finite regular mass M, without the need to invoke DE or Λ. A system with a finite mass M has a finite gravitational radius rS = 2GM. When M is contained within rS, this is a black hole (BH). Nothing from inside can escape outside rS, which becomes a boundary for the inside dynamics. In the limit where there is nothing else outside, the inside corresponds then to a local isolated universe. Such boundary condition is equivalent to a Λ term: $\Lambda =3/r_{S}2$. We can therefore interpret cosmic acceleration as a measurement of the gravitational radius of our Universe, rS, with a mass M ≃ 6 × 1022 M⊙. Such BH Universe is observationally very similar to the LCDM, except for the lack of the largest scale perturbations, which are bounded by rS.