11 research outputs found
On avoiding Ostrogradski instabilities within Asymptotic Safety
We study the renormalization group flow of gravity coupled to scalar matter
using functional renormalization group techniques. The novel feature is the
inclusion of higher-derivative terms in the scalar propagator. Such terms give
rise to Ostrogradski ghosts which signal an instability of the system and are
therefore dangerous for the consistency of the theory. Since it is expected
that such terms are generated dynamically by the renormalization group flow
they provide a potential threat when constructing a theory of quantum gravity
based on Asymptotic Safety. Our work then establishes the following picture:
upon incorporating higher-derivative terms in the scalar propagator the flow of
the gravity-matter system possesses a fixed point structure suitable for
Asymptotic Safety. This structure includes an interacting renormalization group
fixed point where the Ostrogradski ghosts acquire an infinite mass and decouple
from the system. Tracing the flow towards the infrared it is found that there
is a subset of complete renormalization group trajectories which lead to stable
renormalized propagators. This subset is in one-to-one correspondence to the
complete renormalization group trajectories obtained in computations which do
not track of the higher-derivative terms. Thus our asymptotically safe
gravity-matter systems are not haunted by Ostrogradski ghosts.Comment: 35 pages, 10 figure
De Sitter scattering amplitudes in the Born approximation
We present a covariant framework to compute scattering amplitudes and
potentials in a de Sitter background. In this setting, we compute the potential
of a graviton-mediated scattering process involving two very massive scalars at
tree level. Although the obtained scattering potential reproduces the Newtonian
potential at short distances, on Hubble-size length scales it is affected by
the constant curvature: effectively, it yields a repulsive force at sub-Hubble
distances. This can be attributed to the expansion of the de Sitter universe.
Beyond the de Sitter horizon, the potential vanishes identically. Hence, the
scattering amplitude unveils the geometric properties of de Sitter spacetime in
a novel and nontrivial way
Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams
We employ a manifestly covariant formalism to compute the tree-level
amputated Green's function of non-minimally coupled scalar fields in quadratic
gravity in a de Sitter background. We study this Green's function in the
adiabatic limit, and construct the classical Newtonian potential. At short
distances, the flat-spacetime Yukawa potential is reproduced, while the
curvature gives rise to corrections to the potential at large distances. Beyond
the Hubble radius, the potential vanishes identically, in agreement with the
causal structure of de Sitter spacetime. For sub-Hubble distances, we
investigate whether the modifications to the potential reproduce Modified
Newtonian Dynamics.Comment: 34 pages, 9 figure
Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
Over the last years the Asymptotic Safety program has matured into a serious
candidate for a quantum theory of gravity compatible with observations. The
rapid technical progress in computing renormalisation group flows for gravity
and gravity-matter systems in the non-perturbative regime has put many
interesting physical questions within reach. In particular, the construction of
the non-perturbative quantum corrections to the propagation of fields on a
fluctuating spacetime allows addressing the effective propagation of matter on
a quantum spacetime or the possible resolution of spacetime singularities based
on first principle computations. In this article, we assemble a technical
toolbox for carrying out investigations on this promising research frontier. As
a specific example we present results for the momentum-dependent two-point
function for a scalar field induced by the quantum fluctuations of the
underlying geometry in a self-consistent way.Comment: 48 pages, 2 Mathematica notebook
Reflection positivity in higher derivative scalar theories
Reflection positivity constitutes an integral prerequisite in the
Osterwalder-Schrader reconstruction theorem which relates quantum field
theories defined on Euclidean space to their Lorentzian signature counterparts.
In this work we rigorously prove the violation of reflection positivity in a
large class of free scalar fields with a rational propagator. This covers in
particular higher-derivative theories where the propagator admits a partial
fraction decomposition as well as degenerate cases including e.g. p^4 -type
propagators.Comment: 9 pages, 1 figur
Consistent early and late time cosmology from the RG flow of gravity
We investigate the compatibility of cosmological constraints on inflation and
the cosmological constant with the asymptotic safety scenario of quantum
gravity. The effective action is taken to be of form, truncated to
second order. The flow generated by the Functional Renormalisation Group
Equation is analysed and it is found to allow for trajectories that are
compatible with the observational constraints on the parameters of the action,
both at early and late cosmological times. In particular, the gravitational
effective dynamics generated in the trans-Planckian regime flows to Starobinsky
inflation at early times and to standard Einstein Gravity with a cosmological
constant at late times. Moreover, the cosmological constant acquires an energy
dependence at eV, increasing from its current value of on Hubble scale to a value of at
inflation scale.Comment: v2 matches the JCAP accepted versio
Graviton-Mediated Scattering Amplitudes from the Quantum Effective Action
We employ the curvature expansion of the quantum effective action for
gravity-matter systems to construct graviton-mediated scattering amplitudes for
non-minimally coupled scalar fields in a Minkowski background. By design, the
formalism parameterises all quantum corrections to these processes and is
manifestly gauge-invariant. The conditions resulting from UV-finiteness,
unitarity, and causality are analysed in detail and it is shown by explicit
construction that the quantum effective action provides sufficient room to meet
these structural requirements without introducing non-localities or higher-spin
degrees of freedom. Our framework provides a bottom-up approach to all quantum
gravity programs seeking for the quantisation of gravity within the framework
of quantum field theory. Its scope is illustrated by specific examples,
including effective field theory, Stelle gravity, infinite derivative gravity,
and Asymptotic Safety
Finite Quantum Gravity Amplitudes -- no strings attached
We study the gravity-mediated scattering of scalar fields based on a
parameterisation of the Lorentzian quantum effective action. We demonstrate
that the interplay of infinite towers of spin zero and spin two poles at
imaginary squared momentum leads to scattering amplitudes that are compatible
with unitarity bounds, causal, and scale-free at trans-Planckian energy. Our
construction avoids introducing non-localities or the massive higher-spin
particles that are characteristic in string theory.Comment: v2: various small improvements/clarifications, version accepted for
publicatio