75 research outputs found

### Ultraviolet properties of f(R)-Gravity

We discuss the existence and properties of a nontrivial fixed point in
f(R)-gravity, where f is a polynomial of order up to six. Within this
seven-parameter class of theories, the fixed point has three
ultraviolet-attractive and four ultraviolet-repulsive directions; this brings
further support to the hypothesis that gravity is nonperturbatively
renormalizabile.Comment: 4 page

### The Running Gravitational Couplings

We compute the running of the cosmological constant and Newton's constant
taking into account the effect of quantum fields with any spin between 0 and 2.
We find that Newton's constant does not vary appreciably but the cosmological
constant can change by many orders of magnitude when one goes from cosmological
scales to typical elementary particle scales. In the extreme infrared, zero
modes drive the cosmological constant to zero.Comment: 19 pages, TeX file, revised and expanded, some misprints correcte

### Deformed Special Relativity from Asymptotically Safe Gravity

By studying the notion of a fundamentally minimal length scale in
asymptotically safe gravity we find that a specific version of deformed special
relativity (DSR) naturally arises in this approach. We then consider two
thought experiments to examine the interpretation of the scenario and discuss
similarities and differences to other approaches to DSR.Comment: replaced with published versio

### Further Evidence for a Gravitational Fixed Point

A theory of gravity with a generic action functional and minimally coupled to
N matter fields has a nontrivial fixed point in the leading large N
approximation. At this fixed point, the cosmological constant and Newton's
constant are nonzero and UV relevant; the curvature squared terms are
asymptotically free with marginal behaviour; all higher order terms are
irrelevant and can be set to zero by a suitable choice of cutoff function.Comment: LaTEX, 4 pages. Relative to the published paper, a sign has been
corrected in equations (17) and (18

### Dynamical diffeomorphisms

We construct a general effective dynamics for diffeomorphisms of spacetime,
in a fixed external metric. Though related to familiar models of scalar fields
as coordinates, our models have subtly different properties, both at
kinematical and dynamical level. The energy-momentum tensor consists of two
independently conserved parts. The background solution is the identity
diffeomorphism and the energy-momentum tensor of this solution gives rise to an
effective cosmological constant

### Dynamical diffeomorphisms

We construct a general effective dynamics for diffeomorphisms of spacetime, in a fixed external metric. Though related to familiar models of scalar fields as coordinates, our models have subtly different properties, both at kinematical and dynamical level. The energy-momentum (EM) tensor consists of two independently conserved parts. The background solution is the identity diffeomorphism and the EM tensor of this solution gives rise to an effective cosmological constant

### Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation

We review and extend in several directions recent results on the asymptotic
safety approach to quantum gravity. The central issue in this approach is the
search of a Fixed Point having suitable properties, and the tool that is used
is a type of Wilsonian renormalization group equation. We begin by discussing
various cutoff schemes, i.e. ways of implementing the Wilsonian cutoff
procedure. We compare the beta functions of the gravitational couplings
obtained with different schemes, studying first the contribution of matter
fields and then the so-called Einstein-Hilbert truncation, where only the
cosmological constant and Newton's constant are retained. In this context we
make connection with old results, in particular we reproduce the results of the
epsilon expansion and the perturbative one loop divergences. We then apply the
Renormalization Group to higher derivative gravity. In the case of a general
action quadratic in curvature we recover, within certain approximations, the
known asymptotic freedom of the four-derivative terms, while Newton's constant
and the cosmological constant have a nontrivial fixed point. In the case of
actions that are polynomials in the scalar curvature of degree up to eight we
find that the theory has a fixed point with three UV-attractive directions, so
that the requirement of having a continuum limit constrains the couplings to
lie in a three-dimensional subspace, whose equation is explicitly given. We
emphasize throughout the difference between scheme-dependent and
scheme-independent results, and provide several examples of the fact that only
dimensionless couplings can have "universal" behavior.Comment: 86 pages, 13 figures, equation (71) corrected, references added, some
other minor changes. v.5: further minor corrections to eqs. (20), (76), (91),
(94), (A9), Tables II, III, Appendix

### On the Ultraviolet Behaviour of Newton's constant

We clarify a point concerning the ultraviolet behaviour of the Quantum Field
Theory of gravity, under the assumption of the existence of an ultraviolet
Fixed Point. We explain why Newton's constant should to scale like the inverse
of the square of the cutoff, even though it is technically inessential. As a
consequence of this behaviour, the existence of an UV Fixed Point would seem to
imply that gravity has a built-in UV cutoff when described in Planck units, but
not necessarily in other units.Comment: 8 pages; CQG class; minor changes and rearrangement

### Quantum fields without wick rotation

We discuss the calculation of one-loop effective actions in Lorentzian spacetimes, based on a very simple application of the method of steepest descent to the integral over the field. We show that for static spacetimes this procedure agrees with the analytic continuation of Euclidean calculations. We also discuss how to calculate the effective action by integrating a renormalization group equation. We show that the result is independent of arbitrary choices in the definition of the coarse-graining and we see again that the Lorentzian and Euclidean calculations agree. When applied to quantum gravity on static backgrounds, our procedure is equivalent to analytically continuing time and the integral over the conformal factor

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