Abstract
Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.
Similar content being viewed by others
References
Riess, A.G., et al.: Astron. J. 116, 1009 (1998)
Garnavich, P.M., et al.: Astrophys. J. 509, 74 (1998)
Filippenko, A.V., Riess, A.G.: Phys. Rep. 307, 31 (1998)
Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)
Perlmutter, S., et al.: Bull. Am. Astron. Soc. 29, 1351 (1997)
Riess, A.G., et al.: Astrophys. J. 536, 62 (2000)
Riess, A.G., et al.: Astrophys. J. 560, 49 (2001)
Tonry, J.L., et al.: Astrophys. J. 594, 1 (2003)
Knop, R.A., et al.: Astrophys. J. 598, 102 (2003)
Barris, B.J., et al.: Astrophys. J. 602, 571 (2004)
Riess, A.G., et al.: Astrophys. J. 607, 665 (2004)
Bennett, C.L., et al.: Astrophys. J. Suppl. 148, 1 (2003)
Netterfield, B., et al.: Astrophys. J. 571, 604 (2002)
de Bernardis, P., et al.: Nature 404, 955 (2000)
Spergel, D.N., et al.: Astrophys. J. Suppl. 148, 175 (2003)
Page, L., et al.: Astrophys. J. Suppl. 148, 233 (2003)
Tegmark, M., et al.: Astrophys. J. 606, 702 (2004)
Afshordi, N., Loh, Y.-S., Strauss, M.A.: Phys. Rev. D 69, 083524 (2004)
Carlberg, R., et al.: Astrophys. J. 478, 462 (1997)
Bahcall, N., et al.: Astrophys. J. 541, 1 (2000)
Freedman, W.L., et al.: Astrophys. J. 553, 47 (2001)
Fosalba, P., Gaztanaga, E., Castander, F.: Astrophys. J. 597, L89 (2003)
Fosalba, P., Gaztanaga, E.: Mon. Not. R. Astron. Soc. 350, L37 (2004)
Scranton, R., et al.: Preprint astro-ph/0307249 (2003)
Afshordi, N., Loh, Y.-S., Strauss, M.A.: Phys. Rev. D 69, 083524 (2004)
Boughn, S., Crittenden, R.: Nature 427, 6969 (2004)
Padmanabhan, N., et al.: Phys. Rev. D 70, 103501 (2004)
Weinberg, S.: Rev. Mod. Phys. 61, 1 (1989)
Carroll, S.M., Press, W.H., Turner, E.L.: Ann. Rev. Astron. Astrophys. 30, 499 (1992)
Turner, M.S.: Phys. Rep. 333, 619 (2000)
Sahni, V., Starobinsky, A.: Int. J. Mod. Phys. D 9, 373 (2000)
Carroll, S.M.: Living Rev. Relat. 4, 1 (2001)
Padmanabhan, T.: Phys. Rep. 380, 335 (2003)
Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003)
Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753–1936 (2006)
Peebles, P.J.E., Ratra, B.: Astrophys. J. Lett. 325, L17 (1988)
Ratra, B., Peebles, P.J.E.: Phys. Rev. D 37, 3406 (1988)
Wetterich, C.: Ncl. Phys. B 302, 668 (1988)
Zlatev, I., Wang, L., Steinhardt, P.J.: Phys. Rev. Lett. 82, 896 (1999)
Steinhardt, P.J., Wang, L., Zlatev, I.: Phys. Rev. D 59, 123504 (1999)
Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, San Francisco (1973)
Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972)
D’Inverno, R.A.: Introducing Einstein’s Relativity. Oxford University Press, New York (1996)
Rindler, W.: Relativity: Special, General, and Cosmological, 2nd edn. Oxford University Press, New York (2006)
Refregier, A.: Ann. Rev. Astron. Astrophys. 41, 645 (2003)
Bartelmann, M., Schneider, P.: Phys. Rep. 340, 291 (2001)
Mellier, Y.: Ann. Rev. Astron. Astrophys. 37, 127 (1999)
Mohr, J.J.: In: Wolff, S.C., Lauer, T.R. (eds.) Observing Dark Energy, Proceedings of a Meeting Held, Tucson, Arizona, 18–20 March 2004. ASP Conference Series, vol. 339, p. 140. Astronomical Society of the Pacific, San Francisco (2005), astro-ph/0408484
Wang, S., et al.: Phys. Rev. D 70, 123008 (2004)
Hu, W.: Phys. Rev. D 65, 023003 (2001)
Takada, M., Jain, B.: Mon. Not. R. Astron. Soc. 348, 897 (2004)
Ishak, M.: Mon. Not. R. Astron. Soc. 363, 469–478 (2005)
Hirata, C., Seljak, U.: Mon. Not. R. Astron. Soc. 343, 459 (2003)
Ishak, M., Hirata, C.M., McDonald, P., Seljak, U.: Phys. Rev. D 69, 083514 (2004)
Bennett, C.L., et al.: Astrophys. J. Suppl. 148, 1 (2003)
Spergel, D.N., et al.: Astrophys. J. Suppl. 170, 377 (2007)
Upadhye, A., Ishak, M., Steinhardt, P.J.: Phys. Rev. D 72, 063501 (2005)
Chevallier, M., Polarski, D., Starobinsky, A.: Int. J. Mod. Phys. D 10, 213 (2001)
Linder, E.: Phys. Rev. Lett. 90, 091301 (2003)
Wang, Y., Spergel, D.N., Strauss, M.A.: Astrophys. J. 510, 20 (1999)
Press, W.H., et al.: Numerical Recipes in C. Cambridge University Press, Cambridge (1992)
Dodelson, S.: Modern Cosmology. Academic Press, San Diego (2003)
Tegmark, M., Taylor, A.N., Heavens, A.F.: Astrophys. J. 480, 22 (1997)
Kaiser, N.: Astrophys. J. 388, 272 (1992)
Jain, B., Seljak, U.: Astrophys. J. 484, 560 (1997)
Kaiser, N.: Astrophys. J. 498, 26 (1998)
Cole, S., et al.: Mon. Not. R. Astron. Soc. 362, 505 (2005)
Montroy, T.E., et al.: Astrophys. J. 647, 799 (2006)
Kuo, C.-L., et al.: Astrophys. J. 600, 32 (2004)
Readhead, A.C.S., et al.: Astrophys. J. 609, 498 (2004)
Dickinson, C., et al.: Mon. Not. R. Astron. Soc. 353, 732 (2004)
Tegmark, M., et al.: Astrophys. J. 606, 702 (2004)
Eisenstein, D., et al.: Astrophys. J. 633, 560 (2005)
Riess, A., et al.: Astrophys. J. 607, 665 (2004)
Astier, P., et al.: Astron. Astrophys. 447, 31 (2006)
Erben, T., et al.: Astron. Astrophys. 366, 717 (2001)
Bacon, D.J., et al.: Mon. Not. R. Astron. Soc. 325, 1065 (2001)
Bernstein, G., Jarvis, M.: Astron. J. 123, 583 (2002)
Kaiser, N.: Astrophys. J. 537, 555 (2000)
Van Waerbeke, L., Mellier, Y.: Lecture given at the Aussois winter school, astro-ph/0305089 (2003)
Wittman, D., et al.: Nature 405, 143 (2000)
Ishak, M., Hirata, C.: Phys. Rev. D 71, 023002 (2005)
Tegmark, M., et al.: astro-ph/9805117 (1998)
Huterer, D., Turner, M.S.: Phys. Rev. D 64, 123527 (2001)
Aldering, G., et al., for the SNAP project collaboration, astro-ph/0405232 (2003)
Tonry, J.L., et al.: Astrophys. J. 594, 1 (2003)
Kim, A.G., et al.: Mon. Not. R. Astron. Soc. 347, 909 (2004)
Zlatev, I., Wang, L., Steinhardt, P.J.: Phys. Rev. Lett. 82, 896 (1999)
Brax, P., Martin, J.: Phys. Lett. B 468, 40 (1999)
Carroll, S., et al.: Phys. Rev. D 71, 063513 (2005)
Capozziello, S., Cardone, V.F., Troisi, A.: Phys. Rev. D 71, 043503 (2005)
Dvali, G.R., Gabadadzi, G., Porrati, M.: Phys. Lett. B 485, 208 (2000)
Deffayet, C., et al.: Phys. Rev. D 66, 024019 (2002)
Lue, A., Scoccimarro, R., Starkman, G.: Phys. Rev. D 69, 124015 (2004)
Lue, A.: Phys. Rep. 423, 1 (2006)
Deffayet, C., Landau, S.J., Raux, J., Zaldarriaga, M., Astier, P.: Phys. Rev. D 66, 024019 (2002)
Sawicki, I., Carroll, S.M.: Preprint astro-ph/0510364
Fairbairn, M., Goobar, A.: Preprint astro-ph/0511029
Deffayet, C., Dvali, G., Gabadadze, G.: Phys. Rev. D 65, 044023 (2002)
Deffayet, C.: Phys. Lett. B 502, 199–208 (2001)
Ma, C.P., Caldwell, R.R., Bode, P., Wang, L.: Astrophys. J. 521, L1 (1999)
Linder, E., Jenkins, A.: Mon. Not. R. Astron. Soc. 346, 573 (2003)
Koyama, K., Maartens, R.: J. Cosmol. Astropart. Phys. 601, 16 (2006)
Wang, Y., Tegmark, M.: Phys. Rev. Lett. 92, 241302 (2004)
Ishak, M., Upadhye, A., Spergel, D.N.: Phys. Rev. D 74, 043513 (2006), astro-ph/0507184
Knox, L., Song, Y., Tyson, J.A.: Phys. Rev. D 74, 023512 (2006), astro-ph/0503644
Linder, E.V.: Phys. Rev. D 72, 043529 (2005), astro-ph/0507263
Schimd, C., Uzan, J.P., Riazuelo, A.: Phys. Rev. D 71, 083512 (2005)
Cartan, E.: J. Math. Pure Appl. 1, 141 (1922)
Weyl, H.: Space, Time, Matter. Dover, New York (1922)
Vermeil, H.: Nachr. Ges. Wiss. Gottingen, 334 (1917)
Lovelock, D.: J. Math. Phys. 12, 498 (1971)
Lovelock, D.: J. Math. Phys. 13, 874 (1972)
Padmanadhan, T.: Class. Quantum Gravity 22, L107–L110 (2005)
Milton, K.A.: Grav. Cosmol. 8, 65 (2002)
Milton, K.A.: Grav. Cosmol. 9, 66 (2003)
Milton, K.A., Kantowski, R., Kao, C., Wang, Y.: Mod. Phys. Lett. A 16, 2281 (2001)
Mazur, P.O., Mottola, E.: Contributed talk at the Sixth Workshop on ‘Quantum Field Theory Under The Influence Of External Conditions’ held at the Univ. of Oklahoma, 15–19 September 2003, to be published in the Proceedings by Rinton Press (2004), gr-qc/0405111
Witten, E.. In: Cline, D.B. (ed.) Sources and Detection of Dark Matter and Dark Energy in the Universe, Fourth International Symposium, 23–25 February 2000, Marina del Rey, California, USA, p. 27. Springer, Berlin (2000), ISBN 3-540-41216-6, hep-ph/0002297
Casimir, H.: Proc. K. Ned. Akad. Wet. 51, 793 (1948)
Bordag, M., Mohideen, U., Mostepanenko, V.M.: Phys. Rep. 353, 1 (2001)
Lachieze-Rey, M., Luminet, J.P.: Phys. Rep. C 254, 135 (1995)
Zeldovich, Y.B., Starobinsky, A.A.: Pisma Astron. Zh. 10, 323 (1984)
Burgess, C.P.: THE NEW COSMOLOGY: Conference on Strings and Cosmology; The Mitchell Symposium on Observational Cosmology. AIP Conference Proceedings, vol. 743, pp. 417–449 (2004), hep-th/0411140
Caldwell, R.R.: astro-ph/0209312 (2002)
Calloni, E., Di Fiore, L., Esposito, G., Milano, L., Rosa, L.: Phys. Lett. A 297, 328 (2002)
Cornish, N.J., Spergel, D.N., Starkman, G.D., Komatsu, E.: Phys. Rev. Lett. 92, 201302 (2004)
Reynaud, S., Lambrecht, A., Genet, C., Jaekel, M.T.: C. R. Acad. Sci. Paris 2-IV, 1287–1298 (2001), quant-ph/0105053
Jaekel, M.T., Reynaud, S.: Rep. Prog. Phys. 60, 863 (1997)
Viola, L., Onofrio, R.: Phys. Rev. D 55, 455 (1997)
Papini, G.. In: De Sabbata, V., Zheltukhin, A. (eds.) Proceedings of the 17th Course of the International School of Cosmology and Gravitation “Advances in the Interplay between Quantum and Gravity Physics”. Kluwer Academic, Dordrecht (2001), gr-qc/0110056
Carot, J., da Costa: Class. Quantum Gravity 10, 461 (1993)
Santosuosso, K., Pollney, D., Pelavas, N., Musgrave, P., Lake, K.: Comput. Phys. Commun. 115, 381 (1998)
Author information
Authors and Affiliations
Corresponding author
Additional information
Part of this work was written when the author was a research associate at Princeton University.
Rights and permissions
About this article
Cite this article
Ishak, M. Remarks on the Formulation of the Cosmological Constant/Dark Energy Problems. Found Phys 37, 1470–1498 (2007). https://doi.org/10.1007/s10701-007-9175-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-007-9175-z