Reiko Toriumi

Inconsistencies from a running cosmological constant

We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation, where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the nonlocal effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem.

Exact Renormalisation Group Equations and Loop Equations for Tensor Models

In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading order expectation values of observables in tensor models. Furthermore, we use the exact renormalisation group equations to establish a suitable scaling dimension for interactions in Abelian tensorial group field theories with a closure constraint. We also present analogues of the loop equations for tensor models.

Wheeler-DeWitt equation in2+1dimensions

The infrared structure of quantum gravity is explored by solving a lattice version of the WheelerDeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wave function solutions is such that a finite correlation length emerges and naturally cuts off any infrared divergences. Properties of the lattice vacuum are consistent with the existence of an ultraviolet fixed point in G located at the origin, thus precluding the existence of a weak coupling perturbative phase. The correlation length exponent is determined exactly and found to be ν = 6/11. The results obtained so far lend support to the claim that the Lorentzian and Euclidean formulations belong to the same field-theoretic universality class. e-mail address : HHamber@uci.edu e-mail address : RToriumi@uci.edu e-mail address : R.M.Williams@damtp.cam.ac.uk

Wheeler-DeWitt equation in 3+1 dimensions

The infrared structure of quantum gravity is explored by solving a lattice version of the WheelerDeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wave function solutions is such that a finite correlation length emerges and naturally cuts off any infrared divergences. Properties of the lattice vacuum are consistent with the existence of an ultraviolet fixed point in G located at the origin, thus precluding the existence of a weak coupling perturbative phase. The correlation length exponent is determined exactly and found to be ν = 6/11. The results obtained so far lend support to the claim that the Lorentzian and Euclidean formulations belong to the same field-theoretic universality class.

Cosmological density perturbations with a scale-dependent Newton's constant G

We explore possible cosmological consequences of a running Newtons constant

Scale-Dependent Newton's Constant G in the Conformal Newtonian Gauge

G(\ensuremath{\square})

Composite Leptons at the LHC

, as suggested by the nontrivial ultraviolet fixed point scenario in the quantum field-theoretic treatment of Einstein gravity with a cosmological constant term. In particular, we focus here on what possible effects the scale-dependent coupling might have on large scale cosmological density perturbations. Starting from a set of manifestly covariant effective field equations derived earlier, we systematically develop the linear theory of density perturbations for a nonrelativistic, pressureless fluid. The result is a modified equation for the matter density contrast, which can be solved and thus provides an estimate for the growth index parameter

Polchinski's equation for group field theory

\ensuremath{\gamma}

On the cosmological constant: its identification as renormalization group invariant scale corresponding to a gravitational condensate

in the presence of a running

Quantum field theory methods in the study of gravitation

G