Positive signs in massive gravity
Here, we derive new constraints on massive gravity from unitarity and analyticity of scattering amplitudes. Our results apply to a general effective theory defined by Einstein gravity plus the leading soft diffeomorphismbreaking corrections. We calculate scattering amplitudes for all combinations of tensor, vector, and scalar polarizations. Furthermore, the highenergy behavior of these amplitudes prescribes a specific choice of couplings that ameliorates the ultraviolet cutoff, in agreement with existing literature. We then derive consistency conditions from analytic dispersion relations, which dictate positivity of certain combinations of parameters appearing in the forward scattering amplitudes. These constraints exclude all but a small island in the parameter space of ghostfree massive gravity. And while the theory of the "Galileon" scalar mode alone is known to be inconsistent with positivity constraints, this is remedied in the full massive gravity theory.
 Authors:

^{[1]};
^{[1]}
 California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
 Publication Date:
 Grant/Contract Number:
 SC0010255; DGE1144469
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; E ective eld theories; Models of Quantum Gravity
 OSTI Identifier:
 1327304
Cheung, Clifford, and Remmen, Grant N. Positive signs in massive gravity. United States: N. p.,
Web. doi:10.1007/JHEP04(2016)002.
Cheung, Clifford, & Remmen, Grant N. Positive signs in massive gravity. United States. doi:10.1007/JHEP04(2016)002.
Cheung, Clifford, and Remmen, Grant N. 2016.
"Positive signs in massive gravity". United States.
doi:10.1007/JHEP04(2016)002. https://www.osti.gov/servlets/purl/1327304.
@article{osti_1327304,
title = {Positive signs in massive gravity},
author = {Cheung, Clifford and Remmen, Grant N.},
abstractNote = {Here, we derive new constraints on massive gravity from unitarity and analyticity of scattering amplitudes. Our results apply to a general effective theory defined by Einstein gravity plus the leading soft diffeomorphismbreaking corrections. We calculate scattering amplitudes for all combinations of tensor, vector, and scalar polarizations. Furthermore, the highenergy behavior of these amplitudes prescribes a specific choice of couplings that ameliorates the ultraviolet cutoff, in agreement with existing literature. We then derive consistency conditions from analytic dispersion relations, which dictate positivity of certain combinations of parameters appearing in the forward scattering amplitudes. These constraints exclude all but a small island in the parameter space of ghostfree massive gravity. And while the theory of the "Galileon" scalar mode alone is known to be inconsistent with positivity constraints, this is remedied in the full massive gravity theory.},
doi = {10.1007/JHEP04(2016)002},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2016,
place = {United States},
year = {2016},
month = {4}
}