# Null energy condition and superluminal propagation

Abstract: We study whether a violation of the null energy condition necessarily implies the presence of instabilities. We prove that this is the case in a large class of situations, including isotropic solids and fluids relevant for cosmology. On the other hand we present several counter-examples of consistent effective field theories possessing a stable background where the null energy condition is violated. Two necessary features of these counter-examples are the lack of isotropy of the background and the presence of superluminal modes. We argue that many of the properties of massive gravity can be understood by associating it to a solid at the edge of violating the null energy condition. We briefly analyze the difficulties of mimicking u H > 0 in scalar tensor theories of gravity.

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##### Citations

1,937 citations

### Cites background from "Null energy condition and superlumi..."

...In a broad technical sense we may define a modification of gravity as a field theory possessing solutions over which new degrees of freedom affect the propagation of gravity while the background is not producing any sizable energy momentum tensor [7]....

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1,099 citations

### Cites background or methods from "Null energy condition and superlumi..."

...It would also be interesting to use our approach for the study of fluctuations in fluids like in radiation or matter dominance [8]....

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...In appendix A we prove (1)Indeed, as shown for example in [8], non-vorticous excitations of a perfect fluid may be described by a derivatively coupled scalar....

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...This is an example of the well studied relationship between violation of the null energy condition, which in a FRW Universe is equivalent to Ḣ < 0, and the presence of instabilities in the system [17, 8]....

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^{1}, Korea Institute for Advanced Study

^{2}, University of Nottingham

^{3}, Institute of Cosmology and Gravitation, University of Portsmouth

^{4}, University of Oxford

^{5}, INAF

^{6}, Istituto Nazionale di Fisica Nucleare

^{7}, University of Bologna

^{8}, University of Padua

^{9}, University of Toulouse

^{10}, University of Geneva

^{11}, University of Trieste

^{12}, Roma Tre University

^{13}, University of Milan

^{14}, University of Oslo

^{15}, Federal University of Rio Grande do Norte

^{16}, University College London

^{17}, Imperial College London

^{18}, Ludwig Maximilian University of Munich

^{19}, Autonomous University of Madrid

^{20}, ETH Zurich

^{21}, University of Edinburgh

^{22}, Leiden University

^{23}, Sun Yat-sen University

^{24}, Max Planck Society

^{25}, Royal Institute of Technology

^{26}, University of Milano-Bicocca

^{27}, University of California, Berkeley

^{28}, University of Pennsylvania

^{29}, Universidade Federal do Espírito Santo

^{30}, University of Porto

^{31}, University of Portsmouth

^{32}, King's College London

^{33}, Durham University

^{34}, Institut d'Astrophysique de Paris

^{35}, Helsinki Institute of Physics

^{36}, University of Lisbon

^{37}, Université Paris-Saclay

^{38}, Paris Diderot University

^{39}, University of Surrey

^{40}, University of Trento

^{41}, University of Chile

^{42}, Academy of Sciences of the Czech Republic

^{43}, University of Cyprus

^{44}, University of Barcelona

^{45}, California Institute of Technology

^{46}, Perimeter Institute for Theoretical Physics

^{47}

1,036 citations

999 citations

914 citations

### Cites background from "Null energy condition and superlumi..."

...Conversely, as soon as superluminal modes are allowed, the null energy condition is lost, even in the absence of instabilities within the matter dynamics [12], and CTC’s can in principle appear with respect to the gravitational metric gμν as well....

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...While our arguments do not directly apply to theories in which the vacuum spontaneously breaks Lorentz invariance, such as Higgs phases of gravity [6, 7, 8] or the models studied in [12], it would be interesting to ask whether there are any analogous constraints to those we have discussed....

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...Notice that a violation of the Null Energy Condition under very broad assumptions leads either to instabilities at arbitrarily short time-scales or to superluminal propagation in the matter sector [12]....

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...It is a remarkable fact that if the matter dynamics do not feature either instabilities or superluminal modes then the energy momentum tensor corresponding to the effective metric satisfies the null energy condition [12]....

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##### References

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