# Seminario de Ilya L. Shapiro (Universidade Federal de Juiz de Fora, Brasil)

Title:
Anomaly-induced effective action of gravity and some important applications

Ilya L. Shapiro
Universidade Federal de Juiz de Fora.

Abstract:
The effective action of gravity is supposed to contain the main
information about quantum corrections to gravity. However, in many
cases, it can not be calculated exactly. A remarkable and important
exception is the effective action of a vacuum for massless and
conformal-invariant matter fields. In this case, effective action
can be easily derived by integrating trace anomaly. The integration
constant is an unknown conformal functional of the background metric,
but for zero-order cosmology this functional is irrelevant and the
solution becomes exact. Until recently the integrated anomaly was
known only in dimensions d=2 and d=4, but recently we achieved the
explicit result for d=6, which confirms the universal functional
structure of the effective action. The most important applications
in d=4 include systematic classification of vacuum states in the
vicinity of the black hole and the Starobinsky model of inflation.
In the seminar, I will give a non-technical introduction to the
subject and also discuss our recent works on the transition from
stable to unstable (Starobinsky model) branches of anomaly-induced
inflation.

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