This thesis deals primarily with the phenomenology associated to quantum
aspects of spacetime. In particular, it aims at exploring the phenomenological
consequences of a fundamental discreteness of the spacetime fabric,
as predicted by several quantum gravity models and strongly hinted by
many theoretical insights.
The first part of this work considers a toy-model of emergent spacetime
in the context of analogue gravity. The way in which a relativistic Bose–
Einstein condensate can mimic, under specific configurations, the dynamics
of a scalar theory of gravity will be investigated. This constitutes proof-ofconcept
that a legitimate dynamical Lorentzian spacetime may emerge from
non-gravitational (discrete) degrees of freedom. Remarkably, this model
will emphasize the fact that in general, even when arising from a relativistic
system, any emergent spacetime is prone to show deviations from exact
Lorentz invariance. This will lead us to consider Lorentz Invariance Violations
as first candidate for a discrete spacetime phenomenology.
Having reviewed the current constraints on Lorentz Violations and studied
in depth viable resolutions of their apparent naturalness problem, the
second part of this thesis focusses on models based on Lorentz invariance.
In the context of Casual Set theory, the coexistence of Lorentz invariance
and discreteness leads to an inherently nonlocal scalar field theory over
causal sets well approximating a continuum spacetime. The quantum aspects
of the theory in flat spacetime will be studied and the consequences
of its non-locality will be spelled out. Noticeably, these studies will lend
support to a possible dimensional reduction at small scales and, in a classical
setting, show that the scalar field is characterized by a universal nonminimal
coupling when considered in curved spacetimes.
Finally, the phenomenological possibilities for detecting this non-locality
will be investigated. First, by considering the related spontaneous emission
of particle detectors, then by developing a phenomenological model to test
nonlocal effects using opto-mechanical, non-relativistic systems. In both
cases, one could be able to cast in the near future stringent bounds on the
non-locality scale.
