Abstract
Field theories that violate the null energy condition (NEC) are of interest both for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter w < −1. We consider two recently proposed models that violate the NEC. The ghost condensate model requires higher-derivative terms in the action, and this leads to a heavy ghost field and energy unbounded from below. We estimate the rates of particle decay and discuss possible mass limitations to protect the stability of matter in the ghost condensate model. The nonlocal stringy model that arises from a cubic string field theory and exhibits a phantom behavior also leads to energy unbounded from below. In this case, the energy spectrum is continuous, and there are no particle-like excitations. This model admits a natural UV completion because it comes from superstring theory.
Similar content being viewed by others
References
S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge Univ. Press, London (1973).
M. Gasperini and G. Veneziano, Phys. Rep., 373, 1–212 (2003); arXiv:hep-th/0207130v1 (2002).
S. M. Carroll, M. Hoffman, and M. Trodden, Phys. Rev. D, 68, 023509 (2003); arXiv:astro-ph/0301273v2 (2003).
J. M. Cline, S. Jeon, and G. D. Moore, Phys. Rev. D, 70, 043543 (2004); arXiv:hep-ph/0311312v4 (2003).
S. D. H. Hsu, A. Jenkins, and M. B. Wise, Phys. Lett. B, 597, 270–274 (2004); arXiv:astro-ph/0406043v3 (2004).
B. McInnes, Nucl. Phys. B, 718, 55–82 (2005); arXiv:hep-th/0502209v2 (2005).
R. V. Buniy, S. D. H. Hsu, and B. M. Murray, Phys. Rev. D, 74, 063518 (2006); arXiv:hep-th/0606091v1 (2006).
E. J. Copeland, M. Sami, and Sh. Tsujikawa, Internat. J. Mod. Phys. D, 15, 1753–1935 (2006); arXiv:hep-th/0603057v3 (2006).
T. Padmanabhan, “Dark energy: Mystery of the millennium,” in: Albert Einstein Century International Conference (AIP Conf. Proc., Vol. 861), Amer. Inst. Phys., Melville, N.Y. (2006), pp. 179–196; arXiv:astro-ph/0603114v4 (2006).
M. Kaplinghat and S. Bridle, Phys. Rev. D, 71, 123003 (2005); arXiv:astro-ph/0312430v2 (2003).
G. Veneziano, JCAP, 0403, 004 (2004); arXiv:hep-th/0312182v1 (2003).
S. Dubovsky, T. Gregoire, A. Nicolis, and R. Rattazzi, JHEP, 0603, 025 (2006); arXiv:hep-th/0512260v2 (2005).
N. Arkani-Hamed, H. C. Cheng, M. A. Luty, and S. Mukohyama, JHEP, 0405, 074 (2004); arXiv:hep-th/0312099v1 (2003).
F. Piazza and S. Tsujikawa, JCAP, 0407, 004 (2004); arXiv:hep-th/0405054v2 (2004).
A. Adams et al., JHEP, 0610, 014 (2006); arXiv:hep-th/0602178v2 (2006).
P. Creminelli, M. A. Luty, A. Nicolis, and L. Senatore, JHEP, 0612, 080 (2006); arXiv:hep-th/0606090v2 (2006).
I. Ya. Aref’eva, “Nonlocal string tachyon as a model for cosmological dark energy,” in: p-Adic Mathematical Physics (AIP Conf. Proc., Vol. 826), Amer. Inst. Phys., Melville, N. Y. (2006), pp. 301–311; arXiv:astro-ph/0410443v2 (2004).
I. Ya. Aref’eva and L. V. Joukovskaya, JHEP, 0510, 087 (2005); arXiv:hep-th/0504200v2 (2005).
G. Calcagni, JHEP, 0605, 012 (2006); arXiv:hep-th/0512259v4 (2005).
I. Ya. Aref’eva and A. S. Koshelev, JHEP, 0702, 041 (2007); arXiv:hep-th/0605085v3 (2006); I. Ya. Aref’eva, “D-brane as a model for cosmological dark energy,” in: Contents and Structures of the Universe (Proc. 41st Rencontres de Moriond, La Thuile, Italy, March 18–25, 2006, C. Magneville, R. Ansari, J. Dumarchez, and J. T. T. Van, eds.), NXB The Gioi, Hanoi (2006), pp. 131–135.
I. Ya. Aref’eva, P. B. Medvedev, and A. P. Zubarev, Phys. Lett. B, 240, 356–362 (1990); Nucl. Phys. B, 341, 464–498 (1990); C. R. Preitschopf, C. B. Thorn, and S. A. Yost, Nucl. Phys. B, 337, 363–433 (1990); I. Ya. Arefeva, D. M. Belov, A. S. Koshelev, and P. B. Medvedev, Nucl. Phys. B, 638, 3–20 (2002); arXiv:hep-th/0011117v3 (2000).
I. Ya. Aref’eva, L. V. Joukovskaya, and A. S. Koshelev, JHEP, 0309, 012 (2003); arXiv:hep-th/0301137v2 (2003); Ya. I. Volovich, J. Phys. A, 36, 8685–8701 (2003); arXiv:math-ph/0301028v1 (2003).
A. Sen, Internat. J. Mod. Phys. A, 20, 5513–5656 (2005); arXiv:hep-th/0410103v2 (2004).
K. Ohmori, “A review on tachyon condensation in open string field theories,” arXiv:hep-th/0102085v4 (2001); I. Ya. Aref’eva et al., “Noncommutative field theories and (super)string field theories,” arXiv:hep-th/0111208v2 (2001); W. Taylor, “Lectures on D-branes, tachyon condensation, and string field theory,” arXiv:hep-th/0301094v1 (2003).
V. A. Rubakov, Theor. Math. Phys., 149, 1651–1664 (2006); arXiv:hep-th/0604153v2 (2006).
R. Gannouji, D. Polarski, A. Ranquet, and A. A. Starobinsky, JCAP, 0609, 016 (2006); arXiv:astro-ph/0606287v2 (2006).
R. Lazkoz, R. Maartens, and E. Majerotto, Phys. Rev. D, 74, 083510 (2006); arXiv:astro-ph/0605701v2 (2006).
I. P. Neupane, “Towards inflation and accelerating cosmologies in string-generated gravity models,” arXiv:hep-th/0605265v1 (2006).
S. Nojiri, S. D. Odintsov, and M. Sami, Phys. Rev. D, 74, 046004 (2006); arXiv:hep-th/0605039v3 (2006).
M. Ostrogradski, Memoires sur les equations differentielles relatives au probleme des isoperimetres (Mem. Ac. St. Petersburg, Vol. VI 4) (1850).
T. Nakamura and S. Hamamoto, Progr. Theoret. Phys., 95, 469–484 (1996); arXiv:hep-th/9511219v1 (1995).
A. Pais and G. E. Uhlenbeck, Phys. Rev., 79, 145–165 (1950).
I. V. Volovich, “Gauge invariance in the axiomatic approach,” Dissertation, Moscow State Univ., Moscow (1969).
V. S. Vladimirov and Ya. I. Volovich, Theor. Math. Phys., 138, 297–309 (2004); arXiv:math-ph/0306018v1 (2003); V. S. Vladimirov, Izv. RAN. Ser. Mat., 69, 487–512 (2005); arXiv:math-ph/0507018v1 (2005); L. V. Zhukovskaya, Theor. Math. Phys., 146, 335–342 (2006); D. V. Prokhorenko, “On some nonlinear integral equation in the (super)string theory,” arXiv:math-ph/0611068v1 (2006).
I. V. Volovich, Class. Q. Grav., 4, L83–L87 (1987); I. V. Volovich, Theor. Math. Phys., 71, 574–576 (1987).
L. Brekke, P. G. O. Freund, M. Olson, and E. Witten, Nucl. Phys. B, 302, 365–402 (1988); P. H. Frampton and Ya. Okada, Phys. Rev. D, 37, 3077–3079 (1988).
V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics [in Russian], Nauka, Moscow (1994); English transl.: (Ser. Soviet and East Eur. Math., Vol. 1), World Scientific, Singapore (1994).
I. Ya. Aref’eva, L. V. Joukovskaya, and S. Yu. Vernov, JHEP, 0707, 087 (2007); arXiv:hep-th/0701184v4 (2007).
I. V. Volovich and V. V. Kozlov, Dokl. Math., 73, 441–444 (2006); V. V. Kozlov and I. V. Volovich, Int. J. Geom. Meth. Mod. Phys., 3, 1349–1357 (2006); arXiv:gr-qc/0603111v1 (2006).
I. Ya. Aref’eva, S. Yu. Vernov, and A. S. Koshelev, Theor. Math. Phys., 148, 895–909 (2006); arXiv:astro-ph/0412619v5 (2004); I. Ya. Aref’eva, A. S. Koshelev, and S. Yu. Vernov, Phys. Lett. B, 628, 1–10 (2005); arXiv:astro-ph/0505605v2 (2005); Phys. Rev. D, 72, 064017 (2005); arXiv:astro-ph/0507067v2 (2005).
M. P. Dabrowski, C. Kiefer, and B. Sandhöfer, Phys. Rev. D, 74, 044022 (2006); arXiv:hep-th/0605229v1 (2006).
E. O. Kahya and V. K. Onemli, Phys. Rev. D, 76, 043512 (2007); arXiv:gr-qc/0612026v3 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 3–12, April, 2008.