TY - JOUR

T1 - Infrared scaling for a graviton condensate

AU - Bose, Sougato

AU - Mazumdar, Anupam

AU - Toroš, Marko

N1 - Funding Information:
We would like to thank Samir Mathur for helpful discussions. MT and SB would like to acknowledge EPSRC grant No. EP/N031105/1 , SB the EPSRC grant EP/S000267/1 , and MT funding by the Leverhulme Trust ( RPG-2020-197 ). AM's research is funded by the Netherlands Organisation for Science and Research ( NWO ) grant number 680-91-119 .
Publisher Copyright:
© 2022 The Author(s)

PY - 2022/4

Y1 - 2022/4

N2 - The coupling between gravity and matter provides an intriguing length scale in the infrared for theories of gravity within Einstein-Hilbert action and beyond. In particular, we will show that such an infrared length scale is determined by the number of gravitons Ng≫1 associated to a given mass in the non-relativistic limit. After tracing out the matter degrees of freedom, the graviton vacuum is found to be in a displaced vacuum with an occupation number of gravitons Ng≫1. In the infrared, the length scale appears to be L=Ngℓp, where L is the new infrared length scale, and ℓp is the Planck length. In a specific example, we have found that the infrared length scale is greater than the Schwarzschild radius for a slowly moving in-falling thin shell of matter. We will argue that the appearance of such an infrared length scale in higher curvature theories of gravity, such as in quadratic and cubic curvature theories of gravity, is also expected. Furthermore, we will show that gravity is fundamentally different from the electromagnetic interaction where the number of photons, Np, is the fine structure constant after tracing out an electron wave function.

AB - The coupling between gravity and matter provides an intriguing length scale in the infrared for theories of gravity within Einstein-Hilbert action and beyond. In particular, we will show that such an infrared length scale is determined by the number of gravitons Ng≫1 associated to a given mass in the non-relativistic limit. After tracing out the matter degrees of freedom, the graviton vacuum is found to be in a displaced vacuum with an occupation number of gravitons Ng≫1. In the infrared, the length scale appears to be L=Ngℓp, where L is the new infrared length scale, and ℓp is the Planck length. In a specific example, we have found that the infrared length scale is greater than the Schwarzschild radius for a slowly moving in-falling thin shell of matter. We will argue that the appearance of such an infrared length scale in higher curvature theories of gravity, such as in quadratic and cubic curvature theories of gravity, is also expected. Furthermore, we will show that gravity is fundamentally different from the electromagnetic interaction where the number of photons, Np, is the fine structure constant after tracing out an electron wave function.

UR - http://www.scopus.com/inward/record.url?scp=85126611243&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2022.115730

DO - 10.1016/j.nuclphysb.2022.115730

M3 - Article

AN - SCOPUS:85126611243

SN - 0550-3213

VL - 977

JO - Nuclear Physics B

JF - Nuclear Physics B

M1 - 115730

ER -