THE CONFORMAL FACTOR AND THE COSMOLOGICAL CONSTANT

1990 ◽  
Vol 05 (19) ◽  
pp. 3811-3829 ◽  
Author(s):  
STEVEN B. GIDDINGS

The issue of the conformal factor in quantum gravity is examined for Lorentzian signature spacetimes. In Euclidean signature, the “wrong” sign of the conformal action makes the path integral undefined, but in Lorentzian signature this sign is tied to the instability of gravity and once this is accounted for the path integral should be well-defined. In this approach it is not obvious that the Baum-Hawking-Coleman mechanism for suppression of the cosmological constant functions. It is conceivable that since the multiuniverse system exhibits an instability for positive cosmological constant, the dynamics should force the system to zero cosmological constant.

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Dionysios Anninos ◽  
Teresa Bautista ◽  
Beatrix Mühlmann

Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.


2018 ◽  
Vol 27 (14) ◽  
pp. 1847003 ◽  
Author(s):  
Tim R. Morris

The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. In particular, around the Gaussian fixed point, it supports a Hilbert space of renormalizable interactions involving arbitrarily high powers of the gravitational fluctuations. These interactions are characterized by being exponentially suppressed for large field amplitude, perturbative in Newton’s constant but nonperturbative in Planck’s constant. By taking a limit to the boundary of the Hilbert space, diffeomorphism invariance is recovered whilst retaining renormalizability. Thus the so-called conformal factor instability points the way to constructing a perturbatively renormalizable theory of quantum gravity.


1995 ◽  
Vol 10 (09) ◽  
pp. 733-739 ◽  
Author(s):  
E. ELIZALDE ◽  
S. D. ODINTSOV

We suggest to consider conformal factor dynamics as applying to composite bound states, in the framework of the 1/N expansion. In this way, a new model of effective theory for quantum gravity is obtained. The renormalization group (RG) analysis of this model provides a framework to solve the cosmological constant problem, since the value of this constant turns out to be suppressed, as a result of the RG contributions. The effective potential for the conformal factor is also found.


2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jerzy Kowalski-Glikman ◽  
Jerzy Lukierski ◽  
Tomasz Trześniewski

Abstract Following the recently obtained complete classification of quantum-deformed $$ \mathfrak{o} $$ o (4), $$ \mathfrak{o} $$ o (1, 3) and $$ \mathfrak{o} $$ o (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail.


2019 ◽  
Vol 28 (02) ◽  
pp. 1930005 ◽  
Author(s):  
Jean-Luc Lehners

In this paper, I will review an obstruction for theories of the beginning of the universe which can be formulated as semiclassical path integrals. Hartle and Hawking’s no boundary proposal and Vilenkin’s tunneling proposal are examples of such theories. Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries. The result is obtained using a new mathematical tool — Picard–Lefschetz theory — for defining the semiclassical path integral for gravity. The Lorentzian path integral for quantum cosmology with a positive cosmological constant is mathematically meaningful in this approach, but the Euclidean version is not. Framed in this way, the resulting framework and predictions are unique. Unfortunately, the outcome is that primordial gravitational wave fluctuations are unsuppressed.


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
J. Gutowski ◽  
W. A. Sabra

Abstract We classify all supersymmetric solutions of minimal D = 4 gauged supergravity with (2) signature and a positive cosmological constant which admit exactly one Killing spinor. This classification produces a geometric structure which is more general than that found for previous classifications of N = 2 supersymmetric solutions of this theory. We illustrate how the N = 2 solutions which consist of a fibration over a 3-dimensional Lorentzian Gauduchon-Tod base space can be written in terms of this more generic geometric structure.


2012 ◽  
Vol 27 (28) ◽  
pp. 1250164
Author(s):  
J. MANUEL GARCÍA-ISLAS

In the three-dimensional spin foam model of quantum gravity with a cosmological constant, there exists a set of observables associated with spin network graphs. A set of probabilities is calculated from these observables, and hence the associated Shannon entropy can be defined. We present the Shannon entropy associated with these observables and find some interesting bounded inequalities. The problem relates measurements, entropy and information theory in a simple way which we explain.


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