Eur. Phys. J. C (2018) 78: 73
https://doi.org/10.1140/epjc/s10052-018-5535-4

Regular Article - Theoretical Physics

Quantum spreading of a self-gravitating wave-packet in singularity free gravity

¹ Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, 84084, Fisciano (SA), Italy
² INFN-Sezione di Napoli, Gruppo collegato di Salerno, 84084, Fisciano (SA), Italy
³ Van Swinderen Institute, University of Groningen, 9747 AG, Groningen, The Netherlands
⁴ Kapteyn Astronomical Institute, University of Groningen, 9700 AV, Groningen, The Netherlands

^* e-mail: lambiase@sa.infn.it

Received: 24 November 2017
Accepted: 8 January 2018
Published online: 25 January 2018

Abstract

In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein’s general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1 / r singularity in the potential – such that the gradient of the potential vanishes within the scale of non-locality. We will show that a quantum wave-packet spreads faster for a ghost-free and singularity-free gravity as compared to the Newtonian case, therefore providing us a unique scenario for testing classical and quantum properties of short-distance gravity in a laboratory in the near future.