Abstract
The latest Planck results are in excellent agreement with the theoretical expectations predicted from standard normal inflation based on slow-roll approximation which assumes equation-of-state \(\omega \geq-1\). In this work, we study the phantom inflation (\(\omega<-1\)) as an alternative cosmological model within the slow-climb approximation using two hybrid inflationary fields. We perform Chain Monte Carlo analysis to determine the posterior distribution and best fit values for the cosmological parameters using Planck data and show that current CMB data does not discriminate between normal and phantom inflation. Interestingly, unlike in normal inflation, \(\omega\) in phantom induced inflation evolves very slowly away from −1 during the inflation. Furthermore, in contrast to the standard normal inflation for which only upper bound on tensor-to-scalar ratio \(r\) are possible, we obtain both upper and lower bounds for the two hybrid fields in the phantom scenario. Finally, we discuss prospects of future high precision polarization measurements and show that it may be possible to establish the dominance of one model over the other.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Since the latest Planck results (PLANCK Collaboration et al. 2018) (which came after the completion of this work) remarkably agree with earlier data releases we do not expect any significant changes in our results.
References
Aich, M., Souradeep, T.: Phys. Rev. D. 81, 083008 (2010). https://doi.org/10.1103/PhysRevD.81.083008. 1001.1723
Armendáriz-Picón, C., Damour, T., Mukhanov, V.: Phys. Lett. B 458, 209 (1999). https://doi.org/10.1016/S0370-2693(99)00603-6. hep-th/9904075
Baldi, M., Finelli, F., Matarrese, S.: Phys. Rev. D. 72, 083504 (2005). https://doi.org/10.1103/PhysRevD.72.083504. astro-ph/0505552
Bond, J.R., Jaffe, A.H., Knox, L.: Phys. Rev. D. 57, 2117 (1998). https://doi.org/10.1103/PhysRevD.57.2117. astro-ph/9708203
Cai, Y., Wang, Y.-T., Piao, Y.-S.: Phys. Rev. D. 93, 063005 (2016). https://doi.org/10.1103/PhysRevD.93.063005. 1510.08716
Calabrese, E., Alonso, D., Dunkley, J.: Phys. Rev. D. 95, 063504 (2017). https://doi.org/10.1103/PhysRevD.95.063504. 1611.10269
Caldwell, R.R.: Phys. Lett. B 545, 23 (2002). https://doi.org/10.1016/S0370-2693(02)02589-3. astro-ph/9908168
Capozziello, S., Nojiri, S., Odintsov, S.D.: Phys. Lett. B 632(597), 0507182 (2006). https://doi.org/10.1016/j.physletb.2005.11.012
Carroll, S.M., Hoffman, M., Trodden, M.: Phys. Rev. D. 68(023509), 03012732 (2003). https://doi.org/10.1103/PhysRevD.68.023509
Dodelson, S., Kinney, W.H., Kolb, E.W.: Phys. Rev. D. 56(3207), 9702166 (1997). https://doi.org/10.1103/PhysRevD.56.3207
Elizalde, E., Nojiri, S., Odintsov, S.D.: Phys. Rev. D. 70, 043539 (2004). https://doi.org/10.1103/PhysRevD.70.043539. hep-th/0405034
Eriksen, H.K., Hansen, F.K., Banday, A.J., Gorski, K.M., Lilje, P.B.: Astrophys. J. 605, 14 (2004). https://doi.org/10.1086/382267. astro-ph/0307507
Guth, A.H.: Phys. Rev. D. 23, 347 (1981). https://doi.org/10.1103/PhysRevD.23.347
Hajian, A., Souradeep, T.: Astrophys. J. Lett. 597, 5 (2003). https://doi.org/10.1086/379757. astro-ph/0308001
Hamann, J., Covi, L., Melchiorri, A., Slosar, A.: Phys. Rev. D. 76, 023503 (2007). https://doi.org/10.1103/PhysRevD.76.023503. astro-ph/0701380
Hansen, F.K., Banday, A.J., Górski, K.M.: Mon. Not. R. Astron. Soc. 354, 641 (2004). https://doi.org/10.1111/j.1365-2966.2004.08229.x. astro-ph/0404206
Hawking, S.W.: Phys. Lett. B 115, 295 (1982). https://doi.org/10.1016/0370-2693(82)90373-2
Hazra, D.K., Sriramkumar, L., Martin, J.: J. Cosmol. Astropart. Phys. 05, 026 (2013). https://doi.org/10.1088/1475-7516/2013/05/026. 1201.0926
Huang, Q.-G., Wang, S., Zhao, W.: J. Cosmol. Astropart. Phys. 10, 035 (2015). https://doi.org/10.1088/1475-7516/2015/10/035. 1509.02676
Ilić, S., Kunz, M., Liddle, A.R., Frieman, J.A.: Phys. Rev. D. 81, 103502 (2010). https://doi.org/10.1103/PhysRevD.81.103502. 1002.4196
Iqbal, A., Prasad, J., Souradeep, T., Malik, M.A.: J. Cosmol. Astropart. Phys. 06, 14 (2015). https://doi.org/10.1088/1475-7516/2015/06/014. 1501.02647
Kinney, W.H.: Phys. Rev. D. 56, 2002 (1997). https://doi.org/10.1103/PhysRevD.56.2002. hep-ph/9702427
Lewis, A., Bridle, S.: Phys. Rev. D. 66(10), 103511 (2002). https://doi.org/10.1103/PhysRevD.66.103511. astro-ph/0205436
Lewis, A., Challinor, A.: Phys. Rev. D. 66(2), 023531 (2002). https://doi.org/10.1103/PhysRevD.66.023531. astro-ph/0203507
Lewis, A., Challinor, A., Lasenby, A.: Astrophys. J. 538, 473 (2000). https://doi.org/10.1086/309179. astro-ph/9911177
Liddle, A.R., Lyth, D.H.: Phys. Rep. 231, 1 (1993). https://doi.org/10.1016/0370-1573(93)90114-S. astro-ph/9303019
Liddle, A.R., Lyth, D.H.: Cosmological Inflation and Large-Scale Structure. Cambridge University Press, Cambridge (2000)
Liddle, A.R., Parsons, P., Barrow, J.D.: Phys. Rev. D. 50, 7222 (1994). https://doi.org/10.1103/PhysRevD.50.7222. astro-ph/9408015
Lidsey, J.E., Mulryne, D.J., Nunes, N.J., Tavakol, R.: Phys. Rev. D. 70, 063521 (2004). https://doi.org/10.1103/PhysRevD.70.063521. gr-qc/0406042
Liu, Z.-G., Guo, Z.-K., Piao, Y.-S.: Phys. Lett. B 697, 407 (2010). https://doi.org/10.1016/j.physletb.2010.12.055. 1012.0673
Liu, Z.-G., Guo, Z.-K., Piao, Y.-S.: Eur. Phys. J. C 74, 3006 (2014). https://doi.org/10.1140/epjc/s10052-014-3006-0. 1311.1599
Ludwick, K.J.: Phys. Rev. D. 92, 063019 (2015). https://doi.org/10.1103/PhysRevD.92.063019. 1507.06492
Mortonson, M.J., Dvorkin, C., Peiris, H.V., Hu, W.: Phys. Rev. D. 79, 103519 (2009). https://doi.org/10.1103/PhysRevD.79.103519. 0903.4920
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 562, 147 (2003). https://doi.org/10.1016/S0370-2693(03)00594-X. hep-th/0303117
Nojiri, S., Odintsov, S.D.: Gen. Relativ. Gravit. 38, 1285 (2006). https://doi.org/10.1007/s10714-006-0301-6. hep-ph/0506212
Novosyadlyj, B., Sergijenko, O., Durrer, R., Pelykh, V.: Phys. Rev. D. 86, 083008 (2012). https://doi.org/10.1103/PhysRevD.86.083008. 0712.3328
Piao, Y.-S.: Phys. Rev. D. 78, 023518 (2008). https://doi.org/10.1103/PhysRevD.78.023518. 0712.3328
Piao, Y.-S., Zhang, Y.-Z.: Phys. Rev. D. 70, 063513 (2004). https://doi.org/10.1103/PhysRevD.70.063513. astro-ph/0401231
Piao, Y.-S., Zhou, E.: Phys. Rev. D. 68, 083515 (2003). https://doi.org/10.1103/PhysRevD.68.083515. hep-th/0308080
PLANCK Collaboration, Ade, P.A.R., et al.: Astron. Astrophys. 571, 16 (2014a). https://doi.org/10.1051/0004-6361/201321591. 1303.5076
PLANCK Collaboration, Ade, P.A.R., et al.: Astron. Astrophys. 571, 22 (2014b). https://doi.org/10.1051/0004-6361/201321569. 1303.5082
PLANCK Collaboration, Ade, P.A.R., et al.: Astron. Astrophys. 571, 23 (2014c). https://doi.org/10.1051/0004-6361/201321534. 1303.5083
PLANCK Collaboration, Ade, P.A.R., et al.: Astron. Astrophys. 594, 13 (2016a). https://doi.org/10.1051/0004-6361/201525898. 1502.01589
PLANCK Collaboration, Ade, P.A.R., et al.: Astron. Astrophys. 594, 16 (2016b). https://doi.org/10.1051/0004-6361/201526681. 1506.07135
PLANCK Collaboration, Ade, P.A.R., et al.: Astron. Astrophys. 594, 20 (2016c). 1502.02114
PLANCK Collaboration, Ade, P.A.R., et al.: Planck 2018 results. VI. Cosmological parameters (2018). 1807.06209
Pollock, M.D.: Phys. Lett. B 215, 635 (1988). https://doi.org/10.1016/0370-2693(88)90034-2
Qureshi, M.H., Iqbal, A., Malik, M.A., Souradeep, T.: J. Cosmol. Astropart. Phys. 04, 013 (2017). https://doi.org/10.1088/1475-7516/2017/04/013. 1610.05776
Richarte, M.G., Kremer, G.M.: Eur. Phys. J. C 77, 51 (2017). https://doi.org/10.1140/epjc/s10052-017-4629-8. 1612.03822
Sahni, V., Shtanov, Y.: J. Cosmol. Astropart. Phys. 11, 014 (2003). https://doi.org/10.1088/1475-7516/2003/11/014. astro-ph/0202346
Sami, M., Toporensky, A.: Phys. Lett. A 19(1509), 0312009 (2004). https://doi.org/10.1142/S0217732304013921
Seljak, U., Zaldarriaga, M.: Astrophys. J. 469, 437 (1996). https://doi.org/10.1086/177793. astro-ph/9603033
Singh, P., Sami, M., Dadhich, N.: Phys. Rev. D. 68, 023522 (2003). https://doi.org/10.1103/PhysRevD.68.023522. hep-th/0305110
Smoot, G.F., et al.: Astrophys. J. Lett. 396, 1 (1992). https://doi.org/10.1086/186504
Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972)
WMAP Collaboration Hinshaw, G., et al.: Astrophys. J. Lett. 208, 19 (2013). https://doi.org/10.1088/0067-0049/208/2/19. 1212.5226
Wu, P., Yu, H.: J. Cosmol. Astropart. Phys. 05, 08 (2006). https://doi.org/10.1088/1475-7516/2006/05/008. gr-qc/0604117
Acknowledgements
AI and MM would like to thank IUCAA, Pune for its hospitality. The authors would like to thank Professor Tarun Souradeep (IUCAA) for a critical scrutiny of the manuscript. We acknowledge the use of IUCAA’s high performance computing facility for carrying out this work.
