Multigravity and the cosmological constant

TL;DR

This paper investigates the existence of flat metric solutions in multigravity theories with cosmological constants, finding that flat solutions generally require fine-tuning, but an infinite number of fields can admit such solutions without fine-tuning.

Contribution

It demonstrates that flat solutions in ghost-free multigravity theories are generally absent for finite N, but can exist in the limit of infinite fields without fine-tuning.

Findings

No flat solutions without fine-tuning for any finite N.

Flat solutions exist in an infinite-dimensional parameter space for infinite N.

Ground state with infinite fields acts as a collective state.

Abstract

The possibility of flat metric solutions in the presence of arbitrary, in particular, Planck mass sized cosmological constants is investigated within multigravity theory, the ghost-free theory of $(N+1)$ rank-2 tensor fields comprising one massless and $N$ massive spin-2 fields. It is found that, indeed, for any $N$, no matter how large, no flat solutions exist without fine-tuning parameters in the potential. For an infinite number of fields, however, flat solutions exist within an infinite-dimensional parameter space. Such a ground state may be viewed as a collective state that cannot be approximated by any finite $N$.