Quantum Break-Time of de Sitter
  The quantum break-time of a system is the time-scale after which its true
quantum evolution departs from the classical mean field evolution. For
capturing it, a quantum resolution of the classical background - e.g., in terms
of a coherent state - is required. In this paper, we first consider a simple
scalar model with anharmonic oscillations and derive its quantum break-time.
Next, we apply these ideas to de Sitter space. We formulate a simple model of a
spin-2 field, which for some time reproduces the de Sitter metric and
simultaneously allows for its well-defined representation as quantum coherent
state of gravitons. The mean occupation number $N$ of background gravitons
turns out to be equal to the de Sitter horizon area in Planck units, while
their frequency is given by the de Sitter Hubble parameter. In the
semi-classical limit, we show that the model reproduces all the known
properties of de Sitter, such as the redshift of probe particles and thermal
Gibbons-Hawking radiation, all in the language of quantum $S$-matrix
scatterings and decays of coherent state gravitons. Most importantly, this
framework allows to capture the $1/N$-effects to which the usual semi-classical
treatment is blind. They violate the de Sitter symmetry and lead to a finite
quantum break-time of the de Sitter state equal to the de Sitter radius times
$N$. We also point out that the quantum-break time is inversely proportional to
the number of particle species in the theory. Thus, the quantum break-time
imposes the following consistency condition: Older and species-richer universes
must have smaller cosmological constants. For the maximal, phenomenologically
acceptable number of species, the observed cosmological constant would saturate
this bound if our Universe were $10^{100}$ years old in its entire classical
history.
