# On the Hartle-Hawking state for loop quantum gravity

Dhandhukiya S, Sahlmann H (2016)

**Publication Type:** Thesis

**Publication year:** 2016

### Abstract

The dynamical laws of an evolving system determine how the system will look at later times, given some initial state the system started from. In quantum cosmology, one ap- plies this idea to the earliest moments of the universe, which requires one to have some idea about the intial conditions at the beginning of time. One proposal describing these initial conditions in the context of canonical quantum gravity is due to Hartle and Hawk- ing. Their proposal entails a preferred initial state for the universe which is based on a Euclidean path integral over all compact positive definite four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the constraint equations of general relativity in ADM variables in a formal sense.

Following the connection formulation, general relativity can be equivalently recast using the so-called Ashtekar-Barbero variables. The idea followed in this thesis is to mimic Hartle’s and Hawking’s procedure to construct an initial state in terms of these new variables. We observe that the wave function constructed this way does not satisfy the constraint equations of loop quantum gravity, even in a formal sense. We investigate this issue in the simple case of a relativistic particle. We finally suggest a modification of the proposal that does satisfy the constraints at least in a formal sense and start to consider its implications in quantum cosmology.

### Authors with CRIS profile

### How to cite

**APA:**

Dhandhukiya, S., & Sahlmann, H. (2016). *On the Hartle-Hawking state for loop quantum gravity* (Master thesis).

**MLA:**

Dhandhukiya, Satya, and Hanno Sahlmann. *On the Hartle-Hawking state for loop quantum gravity.* Master thesis, 2016.

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