*Article* **On the Geometry of No-Boundary Instantons in Loop Quantum Cosmology**

### **Suddhasattwa Brahma 1,\* and Dong-han Yeom 1,2**


Received: 5 November 2018; Accepted: 7 January 2019; Published: 10 January 2019

**Abstract:** We study the geometry of Euclidean instantons in loop quantum cosmology (LQC) such as those relevant for the no-boundary proposal. Confining ourselves to the simplest case of a cosmological constant in minisuperspace cosmologies, we analyze solutions of the semiclassical (Euclidean) path integral in LQC. We find that the geometry of LQC instantons have the peculiar feature of an infinite tail which distinguishes them from Einstein gravity. Moreover, due to quantum-geometry corrections, the small-*a* behaviour of these instantons seem to naturally favor a closing-off of the geometry in a regular fashion, as was originally proposed for the no-boundary wavefunction.

**Keywords:** no-boundary proposal; loop quantum cosmology; LQC instanton
