Constraints on linear-negative potentials in quintessence and phantom models fromrecent supernova data

Constraints on linear-negative potentials in quintessence and phantom models from recent supernova data

L. Perivolaropoulos
Department of Physics, University of Ioannina, Greece

Abstract

Evolving phantom or quintessence scalar fields in linear-negative potentials of the form V(f)=s f are favored by anthropic principle considerations and produce an evolving equation of state parameter at late times. We investigate the predicted redshift dependence w(z) for a wide range of slopes s in both quintessence and phantom models. We show that w(z) does not cross the phantom divide line w=-1 (hereafter PDL). This is a generic feature of all phantom and quintessence models with fixed sign of the kinetic term independent of the sign of the potential energy. We then use the gold dataset of 157 SnIa and place constraints on the allowed range of slopes s. We find s=0±1.6 for quintessence and s=±0.7±1 for phantom models (the range is at the 2s level and the units of s are in Φ3M_p H₀² @ 10^-38eV³ where M_p is the Planck mass). In both cases the best fit is very close to s @ 0 corresponding to a cosmological constant. We also show that specific model independent parametrizations of w(z) which allow crossing of the PDL (w=-1) provide significantly better fits to the data. Unfortunately such crossings are not allowed in any phantom or quintessence single field model minimally coupled to gravity. Mixed models (coupled phantom-quintessence fields) can in principle lead to a w(z) crossing the PDL but a preliminary investigation indicates that this does not happen for natural initial conditions.

Best Fits of the Equation of State Parameter w(z) predicted by Field Theories (Phantom and Quintessence) and Arbitrary Parametrizations
(Δχ² indicates the difference in χ² with respect to the fit of the cosmological constant for each w(z))

Numerical Analysis

The file numerics.nb has been used for the numerical analysis of the paper and is based on Mathematica 4. It takes about 20min to run on P4 2.6GHz and it produces all the 7 figures of the paper. The code is fairly simple and some explanatory comments are included in the file.

It can be downloaded using the link below in a zip file (less than 0.5Mb). The 157 SnIa data file of the Gold dataset is also included within the zip file. The data-file should be placed in a directory called c:\mathfiles under the name datar-g.txt before runing numerics.nb.

Download the numerics.nb file along with the data file

References

[1a] Riess A , et al., 1998 aj 116 1009
[1b] Perlmutter S J , et al., 1999 Astroph.\@ J. 517 565
[1c] S. Perlmutter et al, Nature (London) 391 , 51(1998) [ADS]
[1d] Bull.Am.Astron.Soc 29 ,1351(1997)
[1e] P.Garnavich et al, Astrophys.J. 493 L53 (1998) [ADS]
[1f] B.P.Schmidt et al, Astrophys. J. 507 ,46 (1998) [ADS]
[1g] Tonry, J L , et al., 2003 Astroph. J. 594 1
[1h] Barris, B , et al., 2004 Astroph. J. 602 571
[1i] Knop R , et al., 2003 Astroph. J. 598 102
[2a] A. G. Riess et al. [Supernova Search Team Collaboration], Astrophys. J. 607 , 665 (2004) [ADS]
[2b] astro-ph/0402512 . [ARXIV]
[3a] N.A.Bahcall et al, Science 284 ,1481 (1999) [ADS]
[3b] Percival, W.J., et al., Mon. Not. Roy. Ast.\@ Soc. 327 , 1297 (2001)
[3c] M. Tegmark et al. , Phys. Rev. D 69 , 103501 (2004) [APS]
[3d] astro-ph/0310723 . [ARXIV]
[4a] D.N.Spergel et al, arXiv.astro-ph/0302209 [ARXIV]
[4b] D. Miller et al. , Astrophys. J. 524 , L1 (1999) [ADS]
[4c] astro-ph/9906421 [ARXIV]
[4d] C. Bennett et al, astro-ph/0302207 [ARXIV]
[4e] P. de Bernardis et al. , Nature 404 , 955 (2000) [ADS]
[4f] astro-ph/0004404 [ARXIV]
[4g] S. Hanany et al. , Astrophys. J. 545 , L5 (2000) [ADS]
[4h] astro-ph/0005123 [ARXIV]
[4i] T. J. Pearson et al. , Astrophys. J. 591 , 556 (2003) [ADS]
[4j] astro-ph/0205388 [ARXIV]
[4k] B. S. Mason et al. , Astrophys. J. 591 , 540 (2003) [ADS]
[4l] astro-ph/0205384 [ARXIV]
[4m] A. Benoit et al. , Astron. Astrophys. 399 , L25 (2003)
[4n] astro-ph/0210306 . [ARXIV]
[5a] V. Sahni and Y. Shtanov, IJMP D 11, 1515 (2002)
[5b] JCAP 0311 , 014 (2003)
[5c] L. Perivolaropoulos and C. Sourdis, Phys. Rev. D 66 , 084018 (2002) [APS]
[5d] hep-ph/0204155 [ARXIV]
[5e] C. Deffayet, G. Dvali and G. Gabadadze, Phys. Rev. D 65, 044023 (2002) [APS]
[5f] J. S. Alcaniz, Phys. Rev. D 65 , 123514 (2002) [APS]
[5g] astro-ph/0202492 [ARXIV]
[5h] E. V. Linder, Phys. Rev. Lett. 90 , 091301 (2003) [APS]
[5i] L. Perivolaropoulos, Phys. Rev. D 67 , 123516 (2003) [APS]
[5j] hep-ph/0301237 [ARXIV]
[5k] D.F.Torres, Phys. Rev. D 66 ,043522(2002) [APS]
[5l] B. Boisseau, G. Esposito-Farese, D. Polarski and A. A. Starobinsky, Phys. Rev. Lett. 85 , 2236 (2000) [APS]
[5m] gr-qc/0001066 . [ARXIV]
[6a] M. S. Turner and M. White, Phys. Rev. D56 , R4439 (1997) [APS]
[6b] T. Padmanabhan, astro-ph/0411044 [ARXIV]
[6c] P. H. Frampton, astro-ph/0409166. [ARXIV]
[7a] U. Alam, V. Sahni, T. D. Saini and A. A. Starobinsky, Mon. Not. Roy. Astron. Soc. 354 , 275 (2004)
[7b] astro-ph/0311364 [ARXIV]
[7c] T. R. Choudhury, T. Padmanabhan, astro-ph/0311622 [ARXIV]
[7d] Y. Wang and P. Mukherjee, Astrophys. J. 606 , 654 (2004) [ADS]
[7e] astro-ph/0312192 [ARXIV]
[7f] Huterer D and Cooray A, 2004 astro-ph/0404062 [ARXIV]
[7g] R. A. Daly and S. G. Djorgovski, Astrophys. J. 597 , 9 (2003) [ADS]
[7h] astro-ph/0305197 [ARXIV]
[7i] J. S. Alcaniz, Phys. Rev. D 69, 083521 (2004) [APS]
[7j] astro-ph/0312424 [ARXIV]
[7k] J. A. S. Lima, J. V. Cunha and J. S. Alcaniz, Phys. Rev. D 68 , 023510 (2003) [APS]
[7l] astro-ph/0303388 [ARXIV]
[7m] A. Upadhye, M. Ishak and P. J. Steinhardt, astro-ph/0411803. [ARXIV]
[8a] S. Nesseris and L. Perivolaropoulos, Phys. Rev. D 70 , 043531 (2004) [APS]
[8b] astro-ph/0401556 . [ARXIV]
[9a] B.Ratra and P.J.E.Peebles, Phys.Rev. D 37 ,3406(1988) [APS]
[9b] astro-ph/0207347 [ARXIV]
[9c] C.Wetterich, Nucl. Phys. B 302 ,668(1988) [ADS]
[9d] P.G.Ferreira and M.Joyce, Phys. Rev. D. 58 ,023503(1998) [APS]
[9e] P.Brax and J.Martin, Phys. Rev. D. 61 ,103502(2000) [APS]
[9f] L.A.Urena-Lopez and T.Matos, Phys. Rev. D. 62 ,081302(2000) [APS]
[9g] T.Barreiro, E.J.Copeland and N.J.Nunes, Phys. Rev. D. 61 ,127301(2000) [APS]
[9h] D.Wands, E.J.Copeland and A.R.Liddle, Phys. Rev. D. 57 ,4686 (1998) [APS]
[9i] A.R. Liddle and R.J. Scherrer, Phys. Rev. D 59 , 023509 (1998) [APS]
[9j] R.R. Caldwell, R. Dave and P. Steinhardt, Phys. Rev. Lett 80 , 1582 (1998) [APS]
[9k] I. Zlatev, L. Wang and P. Steinhardt, Phys. Rev. Lett. 82 , 896 (1999) [APS]
[9l] S. Dodelson, M. Kaplinghat and E. Stewart, Phys. Rev. Lett. 85 , 5276(2000) [APS]
[9m] V.B.Johri, Phys. Rev. D. 63 ,103504(2001) [APS]
[9n] V.B.Johri, Class. Quant. Grav. 19 ,5959 (2002) [ADS]
[9o] V.Sahni and L.Wang, Phys. Rev. D. 62 ,103517(2000) [APS]
[9p] M. Axenides and K. Dimopoulos, JCAP 0407 , 010 (2004)
[9q] hep-ph/0401238 . [ARXIV]
[10a] R. R. Caldwell, Phys. Lett. B 545 , 23 (2002) [ADS]
[10b] astro-ph/9908168 [ARXIV]
[10c] P. F. Gonzalez-Diaz, Phys. Lett. B 586 , 1 (2004) [ADS]
[10d] astro-ph/0312579 [ARXIV]
[10e] P. Singh, M. Sami and N. Dadhich, Phys. Rev. D 68 , 023522 (2003) [APS]
[10f] hep-th/0305110 . V. B. Johri, Phys. Rev. D 70 , 041303 (2004) [ARXIV]
[10g] astro-ph/0311293 [ARXIV]
[10h] V.K.Onemli and R.P.Woodard, Class. Quant. Grav. 19 , 4607 (2000) [ADS]
[10i] S. Hannestad and E. Mortsell, Phys. Rev. D 66 ,063508(2002) [APS]
[10j] S. M. Carroll, M. Hoffman and M. Trodden, Phys. Rev. D 68 , 023509 (2003) [APS]
[10k] astro-ph/0301273 [ARXIV]
[10l] P.H.Frampton, hep-th/0302007 [ARXIV]
[10m] P. F. Gonzalez-Diaz and C. L. Siguenza, Nucl. Phys. B 697 , 363 (2004) [ADS]
[10n] astro-ph/0407421 [ARXIV]
[10o] G.W.Gibbons, hep-th/0302199 [ARXIV]
[10p] B.Mcinnes, astro-ph/0210321 [ARXIV]
[10q] L. P. Chimento and R. Lazkoz, Phys. Rev. Lett. 91 , 211301 (2003) [APS]
[10r] gr-qc/0307111 [ARXIV]
[10s] H. Stefancic,Phys. Lett. B 586 , 5 (2004) [ADS]
[10t] astro-ph/0310904 [ARXIV]
[10] H. Stefancic,Eur. Phys. J. C 36 , 523 (2004) [EDPS]
[10] astro-ph/0312484 [ARXIV]
[10] P. F. Gonzalez-Diaz, Phys. Rev. D 69 , 063522 (2004) [APS]
[10] hep-th/0401082 . [ARXIV]
[11a] J. Garriga, L. Pogosian and T. Vachaspati, Phys. Rev. D 69 , 063511 (2004) [APS]
[11b] astro-ph/0311412 . [ARXIV]
[12a] J. Garriga and A. Vilenkin, Phys. Rev. D 61 , 083502 (2000) [APS]
[12b] astro-ph/9908115 [ARXIV]
[12c] J. Garriga and A. Vilenkin, Phys. Rev. D 67 , 043503 (2003) [APS]
[12d] astro-ph/0210358 [ARXIV]
[12e] J. Garriga, A. Linde and A. Vilenkin, Phys. Rev. D 69 , 063521 (2004) [APS]
[12f] hep-th/0310034 . [ARXIV]
[13a] S. Dimopoulos and S. Thomas, Phys. Lett. B 573 , 13 (2003) [ADS]
[13b] hep-th/0307004 . [ARXIV]
[14a] R. Kallosh, J. Kratochvil, A. Linde, E. V. Linder and M. Shmakova, JCAP 0310 , 015 (2003)
[14b] astro-ph/0307185 . [ARXIV]
[15] Y. Wang, J. M. Kratochvil, A. Linde and M. Shmakova, astro-ph/0409264. [ARXIV]
[16a] R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, Phys. Rev. Lett. 91 , 071301 (2003) [APS]
[16b] astro-ph/0302506 [ARXIV]
[16c] S. Nesseris and L. Perivolaropoulos,
[16d] astro-ph/0410309 . [ARXIV]
[17] The mathematica file with the numerical analysis and the figures of the paper can be downloaded from http://leandros.physics.uoi.gr/negpot.htm [URL]
[18] Press, W.H., et. al., `Numerical Recipes', Cambridge University Press (1994)
[19] Z. K. Guo, Y. S. Piao, X. M. Zhang and Y. Z. Zhang, astro-ph/0410654. [ARXIV]
[20] L. Perivolaropoulos (in preparation).
[21a] A. Melchiorri, L. Mersini, C. J. Odman and M. Trodden, Phys. Rev. D 68 , 043509 (2003) [APS]
[21b] astro-ph/0211522 . [ARXIV]