The construction of a quantum theory of gravity
remains an open problem despite decades of efforts.
In time, the very perspective on this problem evolved.
From quantising General Relativity, the goal is now
mostly understood to be unraveling a more
fundamental microstructure of spacetime, based on
non-geometric building blocks, and to show how
spacetime and matter emerge as effective, approximate
notions. Given some candidate building blocks, the task
becomes analogous to that of extracting the
macroscopic, collective behaviour of the atoms of a
condensed matter system, but even more challenging
since we cannot use the usual spacetime intuition and
no direct observational input is available to guide
theory construction.
Lacking a fundamental theory of quantum gravity,
existing cosmological models which have proven
extremely successful in accounting for the observed
features of the very early universe (via CMB data)
remain without a solid foundation, having to make a
number of assumptions about a physical regime (close
to the big bang), where the quantum nature of gravity
and spacetime is expected to be relevant. This is all the
LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN SEITE 2 VON 2
more unfortunate, since the very early universe is also
where any proposed quantum theory of gravity has the
highest chance of finding its observational test-bed.
The gap needs to be bridged.
In this talk I will first of all review the basic aspects of
the problem of quantum gravity, and of some current
approaches. I will then focus on one specific formalism
for quantum gravity, so-called group field theories
(strictly related to a number of other modern
approaches). I will introduce its main features, trying to
clarify the nature of the suggested building blocks of
spacetime and their mathematical description. Next, I
will outline a general strategy to extract an effective
cosmological dynamics from quantum gravity, within
this formalism. In this setting, the universe emerges as
a quantum condensate of the fundamental “atoms of
spacetime”, and cosmology is its corresponding
hydrodynamics. Finally, I will summarize the recent
results obtained along this research direction.