TY - JOUR

T1 - Dark energy survivals in massive gravity after GW170817

T2 - SO(3) invariant

AU - Heisenberg, Lavinia

AU - Tsujikawa, Shinji

N1 - Funding Information:
We thank Antonio De Felice for useful discussions. L.H. thanks financial support from Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation. S.T. is supported by the Grant-in-Aid for Scientific Research Fund of the JSPS No. 16K05359 and the MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Cosmic Acceleration” (No. 15H05890).

PY - 2018/1

Y1 - 2018/1

N2 - The recent detection of the gravitational wave signal GW170817 together with an electromagnetic counterpart GRB 170817A from the merger of two neutron stars puts a stringent bound on the tensor propagation speed. This constraint can be automatically satisfied in the framework of massive gravity. In this work, we consider a general SO(3)-invariant massive gravity with five propagating degrees of freedom and derive the conditions for the absence of ghosts and Laplacian instabilities in the presence of a matter perfect fluid on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological background. The graviton potential containing the dependence of three-dimensional metrics and a fiducial metric coupled to a temporal scalar field gives rise to a scenario of the late-time cosmic acceleration in which the dark energy equation of state wDE is equivalent to -1 or varies in time. We find that the deviation from the value wDE=-1 provides important contributions to the quantities associated with the stability conditions of tensor, vector, and scalar perturbations. In concrete models, we study the dynamics of dark energy arising from the graviton potential and show that there exist viable parameter spaces in which neither ghosts nor Laplacian instabilities are present for both wDE>-1 and wDE<-1. We also generally obtain the effective gravitational coupling Geff with non-relativistic matter as well as the gravitational slip parameter ηs associated with the observations of large-scale structures and weak lensing. We show that, apart from a specific case, the two quantities Geff and ηs are similar to those in general relativity for scalar perturbations deep inside the sound horizon.

AB - The recent detection of the gravitational wave signal GW170817 together with an electromagnetic counterpart GRB 170817A from the merger of two neutron stars puts a stringent bound on the tensor propagation speed. This constraint can be automatically satisfied in the framework of massive gravity. In this work, we consider a general SO(3)-invariant massive gravity with five propagating degrees of freedom and derive the conditions for the absence of ghosts and Laplacian instabilities in the presence of a matter perfect fluid on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological background. The graviton potential containing the dependence of three-dimensional metrics and a fiducial metric coupled to a temporal scalar field gives rise to a scenario of the late-time cosmic acceleration in which the dark energy equation of state wDE is equivalent to -1 or varies in time. We find that the deviation from the value wDE=-1 provides important contributions to the quantities associated with the stability conditions of tensor, vector, and scalar perturbations. In concrete models, we study the dynamics of dark energy arising from the graviton potential and show that there exist viable parameter spaces in which neither ghosts nor Laplacian instabilities are present for both wDE>-1 and wDE<-1. We also generally obtain the effective gravitational coupling Geff with non-relativistic matter as well as the gravitational slip parameter ηs associated with the observations of large-scale structures and weak lensing. We show that, apart from a specific case, the two quantities Geff and ηs are similar to those in general relativity for scalar perturbations deep inside the sound horizon.

KW - cosmological perturbation theory

KW - dark energy theory

KW - gravity

KW - modified gravity

UR - http://www.scopus.com/inward/record.url?scp=85041590725&partnerID=8YFLogxK

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U2 - 10.1088/1475-7516/2018/01/044

DO - 10.1088/1475-7516/2018/01/044

M3 - Article

AN - SCOPUS:85041590725

VL - 2018

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 1

M1 - 044

ER -