We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.

In this paper we use and extend the results present in [1,2,3,4] and in particular in [4] to obtain a statistical description of the cosmological constant in a cosmological de Sitter universe in terms of massless excitations with Planckian effects. First of all, we show that at a classical level, the cosmological constant Λ > 0 can be obtained only for T → 0. Similarly to the black hole case, when quantum effects are taken into account, a representation for Λ is possible in terms of massless excitations, provided that quantum corrections to the Misner-Sharp mass are considered. Moreover, thanks to quantum fluctuations, an effective cosmological constant arises depending on the physical scale under consideration, thus representing a possible solution to the cosmological constant problem without introducing a quintessence field. The smalness of the actual value for Λ can be due to the existence of a quantum decoherence scale above the Planck length such that the spacetime evolves as a pure de Sitter universe with a small averaged cosmological constant frozen in the lowest energy state. Number(s): 95.36.+x, 04.60.Bc, PACS

We derive new spacetime uncertainty relations (STUR) at the fundamental Planck length L P from quantum mechanics and general relativity (GR), both in flat and curved backgrounds. Contrary to claims present in the literature, our approach suggests that no minimal uncertainty appears for lengths, but instead for minimal space and fourvolumes. Moreover, we derive a maximal absolute value for the energy density. Finally, some considerations on possible commutators among quantum operators implying our STUR are done.

This paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index ℓ similar to the harmonic oscillator one is obtained and a statistical study is performed. The mean energy < E > results as a sum of two discrete Planck distributions with different dependent frequencies. As an important application, we derive the semiclassical Bekenstein-Hawking entropy formula for a static Schwarzschild black hole by only requiring that the black hole internal energy U is provided by its ADM rest energy, without invoking particular quantum gravity theories. This seriously suggests that the interior of a black hole can be composed of trapped gravitons at a thermodynamical temperature proportional by a factor ≃ 2 to the horizon temperature T h .

Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. In this letter, we begin the study of this new formula to obtain the first law of thermodynamics for dynamical apparent horizons. In this regard we obtain a generalized expression for the internal energy U together with a distinction between the dynamical temperature T D of apparent horizons and the related one due to thermodynamics formulas. Remarkable, when the expression for U is applied to the apparent horizon of the universe, we found that this internal energy is a constant of motion. Our calculations thus show that the total energy of our spatially flat universe including the gravitational contribution, when calculated at the apparent horizon, is an universal constant that can be set to zero from simple dimensional considerations. This strongly support the holographic principle.