49 research outputs found

### Frame (In)equivalence in Quantum Field Theory and Cosmology

We revisit the question of frame equivalence in Quantum Field Theory in the
presence of gravity, a situation of relevance for theories aiming to describe
the early Universe dynamics and Inflation in particular. We show that in those
cases, the path integral measure must be carefully defined and that the
requirement of diffeomorphism invariance forces it to depend non-trivially on
the fields. As a consequence, the measure will transform also non-trivially
between different frames and it will induce a new finite contribution to the
Quantum Effective Action that we name frame discriminant. This new contribution
must be taken into account in order to asses the dynamics and physical
consequences of a given theory. We apply our result to scalar-tensor theories
described in the Einstein and Jordan frame, where we find that the frame
discriminant can be thought as inducing a scale-invariant regularization scheme
in the Jordan frame.Comment: 33 pages, minor correction

### Background independent exact renormalisation

A geometric formulation of Wilson's exact renormalisation group is presented
based on a gauge invariant ultraviolet regularisation scheme without the
introduction of a background field. This allows for a manifestly background
independent approach to quantum gravity and gauge theories in the continuum.
The regularisation is a geometric variant of Slavnov's scheme consisting of a
modified action, which suppresses high momentum modes, supplemented by
Pauli-Villars determinants in the path integral measure. An exact
renormalisation group flow equation for the Wilsonian effective action is
derived by requiring that the path integral is invariant under a change in the
cutoff scale while preserving quasi-locality. The renormalisation group flow is
defined directly on the space of gauge invariant actions without the need to
fix the gauge. We show that the one-loop beta function in Yang-Mills and the
one-loop divergencies of General Relativity can be calculated without fixing
the gauge. As a first non-perturbative application we find the form of the
Yang-Mills beta function within a simple truncation of the Wilsonian effective
action.Comment: 34 pages, v2: One reference added, minor modifications and typos
fixe

### Black holes and asymptotically safe gravity

Quantum gravitational corrections to black holes are studied in four and
higher dimensions using a renormalisation group improvement of the metric. The
quantum effects are worked out in detail for asymptotically safe gravity, where
the short distance physics is characterized by a non-trivial fixed point of the
gravitational coupling. We find that a weakening of gravity implies a decrease
of the event horizon, and the existence of a Planck-size black hole remnant
with vanishing temperature and vanishing heat capacity. The absence of
curvature singularities is generic and discussed together with the conformal
structure and the Penrose diagram of asymptotically safe black holes. The
production cross section of mini-black holes in energetic particle collisions,
such as those at the Large Hadron Collider, is analysed within low-scale
quantum gravity models. Quantum gravity corrections imply that cross sections
display a threshold, are suppressed in the Planckian, and reproduce the
semi-classical result in the deep trans-Planckian region. Further implications
are discussed.Comment: 22 pages, 9 figures, Sec V G added to match published versio

### Aspects of asymptotic safety for quantum gravity

We study fixed points of quantum gravity with renormalisation group methods,
and a procedure to remove convergence-limiting poles from the flow. The setup
is tested within the $f(R)$ approximation for gravity by solving exact
recursive relations up to order $R^{70}$ in the Ricci scalar, combined with
resummations and numerical integration. Results include fixed points, scaling
exponents, gap in the eigenvalue spectrum, dimensionality of the UV critical
surface, fingerprints for weak coupling, and quantum equations of motion. Our
findings strengthen the view that ``most of quantum gravity'' is rather weakly
coupled. Another novelty are a pair of de Sitter solutions for quantum
cosmology, whose occurrence is traced back to the removal of poles. We also
address slight disparities of results in the literature, and give bounds on the
number of fundamentally free parameters of quantum gravity.Comment: 29 pages, 7 figures, v2: explanations added, to appear with PR

### Essential Quantum Einstein Gravity

The non-perturbative renormalisation of quantum gravity is investigated
allowing for the metric to be reparameterised along the RG flow such that only
the essential couplings constants are renormalised. This allows us to identify
a universality class of quantum gravity which is guaranteed to be unitary,
since the physical degrees of freedom are those of General Relativity with a
vanishing cosmological constant. Considering all diffeomorphism invariant
operators with up to four derivatives, only Newton's constant is essential at
the Gaussian infrared fixed point associated to perturbative gravity. The other
inessential couplings can then be fixed to the values they take at the Gaussian
fixed point along the RG flow. In the ultraviolet, the corresponding beta
function for Newton's constant vanishes at the interacting Reuter fixed point.
The properties of the Reuter fixed point are stable between the
Einstein-Hilbert approximation and the approximation including all
diffeomorphism invariant four derivative terms in the flow equation. Our
results suggest that Newton's constant is the only relevant essential coupling
at the Reuter fixed point. Therefore, we conjecture that Quantum Einstein
Gravity, the ultraviolet completion of Einstein's theory of General Relativity
in the asymptotic safety scenario, has no free parameters and in particular
predicts a vanishing cosmological constant