# Unimodular loop quantum gravity and the problems of time

@article{Smolin2010UnimodularLQ, title={Unimodular loop quantum gravity and the problems of time}, author={Lee Smolin}, journal={Physical Review D}, year={2010}, volume={84}, pages={044047} }

We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not couple to terms in the expectation value of energy proportional to the metric tensor. The path integral takes the same form as is used to define spin foam models, with the additional constraint that the determinant of the four metric is constrained to be a…

## 37 Citations

### UV structure of quantum unimodular gravity

- Physics
- 2014

It is a well known result that any formulation of unimodular gravity is classically equivalent to General Relativity (GR), however a debate exists in the literature about this equivalence at the…

### Can quantum fluctuations differentiate between standard and unimodular gravity?

- MathematicsJournal of High Energy Physics
- 2021

We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that…

### How unimodular gravity theories differ from general relativity at quantum level

- Physics, Mathematics
- 2015

We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is analyzed, which does not include a unimodular condition on the…

### How unimodular gravity theories differ from general relativity at quantum level

- Physics, MathematicsThe European Physical Journal C
- 2015

We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is analyzed, which does not include a unimodular condition on the…

### The Renormalization Group flow of unimodular f(R) gravity

- Physics
- 2015

A bstractUnimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could…

### Topological features of the quantum vacuum

- PhysicsPhysical Review D
- 2020

A central aspect of the cosmological constant problem is to understand why vacuum energy does not gravitate. In order to account for this observation, while allowing for nontrivial dynamics of the…

### Unimodular quantum gravity: steps beyond perturbation theory

- PhysicsJournal of High Energy Physics
- 2020

The renormalization group flow of unimodular quantum gravity is computed by taking into account the graviton and Faddeev-Popov ghosts anomalous dimensions. In this setting, a ultraviolet attractive…

### Unitarity and Information in Quantum Gravity: A Simple Example

- PhysicsFrontiers in Astronomy and Space Sciences
- 2021

In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any effective smooth field theoretical description would miss part…

### Quantum Corrections to Unimodular Gravity To the memory of Raymond Stora

- Physics
- 2019

The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter…

### The landscape of polymer quantum cosmology

- Physics
- 2022

We show that the quantization ambiguities of loop quantum cosmology, when considered in wider generality, can be used to produce discretionary dynamical behaviour. There is an inﬁnite dimensional…

## References

SHOWING 1-10 OF 21 REFERENCES

### Quantization of unimodular gravity and the cosmological constant problems

- Physics
- 2009

A quantization of unimodular gravity is described, which results in a quantum effective action which is also unimodular, ie a function of a metric with fixed determinant. A consequence is that…

### Unimodular loop quantum cosmology

- Physics
- 2010

Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has the interesting…

### Unimodular theory of gravity and the cosmological constant

- Physics
- 1991

The unimodular theory of gravity with a constrained determinant gμν is equivalent to general relativity with an arbitrary cosmological constant Λ. Within this framework Λ appears as an integration…

### Quantum gravity with a positive cosmological constant

- Physics
- 2002

A quantum theory of gravity is described in the case of a positive cosmological constant in 3 + 1 dimensions. Both old and new results are described, which support the case that loop quantum gravity…

### Time as spacetime four-volume and the Ashtekar variables.

- PhysicsPhysical review. D, Particles and fields
- 1991

We consider a recently proposed theory of gravity, classically equivalent to Einstein's theory with the cosmological constant as an additional variable, in which spacetime volume plays the role of…

### Holomorphic wave function of the Universe.

- Physics, MathematicsPhysical review. D, Particles and fields
- 1990

The analysis of the quantum Robertson-Walker universe indicates that if the superspace is extended to such a classically forbidden region, the holomorphic representation picks up some restricted class of solutions in general, which leads to a new ansatz on the boundary condition of the Universe.

### Time and the interpretation of canonical quantum gravity.

- PhysicsPhysical review. D, Particles and fields
- 1989

It is argued that the interpretive problems of quantum gravity are not alleviated by the incorporation of observers into the theory, and a proposal for a formulation of canonical quantum gravity in which an appropriate nondynamical time parameter is present is made.

### Role of time in the sum-over-histories framework for gravity

- Physics
- 1994

I sketch a self-contained framework for quantum mechanics based on its path-integral or “sum-over-histories” formulation. The framework is very close to that for classical stochastic processes like…

### Possible solution to the cosmological-constant problem.

- PhysicsPhysical review letters
- 1990

A modified-gravity-type model of two hypothetical massless vector fields are presented, which give rise to a standard Friedmann-Robertson-Walker universe and standard Newtonian gravitational dynamics of small systems.

### On the Role of Time in the Sum-over-histories Framework for Gravity, paper presented to the conference on The History of Modern Gauge The- ories, held Logan, Utah

- published in Int. J. Theor. Phys
- 1987