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Dissipative universe-inflation with soft singularity

Iver Brevik

Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

E-mail Address: iver.h.brevik@ntnu.no

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and

Alexander V. Timoshkin

Tomsk State Pedagogical University, Kievskaja Street 60, 634050 Tomsk, Russia

Tomsk State University of Control Systems and Radioelectronics, Lenin Avenue 40, 634050 Tomsk, Russia

E-mail Address: alex.timosh@rambler.ru

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https://doi.org/10.1142/S021988781750061XCited by:20 (Source: Crossref)

Abstract

We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann–Robertson–Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data, while for the scalar-to-tensor ratio, there are minor deviations.

Keywords:

PACS: 98.80.-k, 95.36.+x

References

1. Supernova Search Team Collab. (A. G. Riess et al.), Observation evidence from super-novae for an accelerating, Astron. J. 116 (1998) 1009, arXiv:astro-ph/9805201. Crossref, Web of Science, Google Scholar
2. SNCP Collab. (S. Perlmutter et al.), Measurements of Omega and Lambda from 42 high-redshift, Astrophys. J. 517 (1999) 565–586, arXiv:astro-ph/9812133. Crossref, Web of Science, Google Scholar
3. R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, Phantom energy and cosmic doomsday, Phys. Rev. Lett. 91 (2003) 071301, arXiv:astro-ph/0302506. Crossref, Web of Science, Google Scholar
4. S. Nojiri and S. D. Odintsov, Quantum de Sitter cosmology and phantom matter, Phys. Lett. B 562 (2003) 147–152, arXiv:hep-th/0303117. Crossref, Web of Science, Google Scholar
5. H. Frampton, K. J. Ludwick and R. J. Scherrer, The little Rip, Phys. Rev. D 84 (2011) 063003, arXiv:1106.4996v1 [astro-ph. CO]. Crossref, Web of Science, Google Scholar
6. I. Brevik, E. Elizalde, S. Nojiri and S. D. Odintsov, Viscous Little Rip cosmology, Phys. Rev. D 84 (2011) 103508, arXiv:1107.4642 [hep-th]. Crossref, Web of Science, Google Scholar
7. P. H. Frampton, K. J. Ludwick, S. Nojiri, S. D. Odintsov and R. J. Scherrer, Models for little Rip dark energy, Phys. Lett. B 708 (2012) 204–211, arXiv:1108.0067v2 [hep-th]. Crossref, Web of Science, Google Scholar
8. P. H. Frampton, K. J. Ludwick and R. J. Scherrer, Pseudo-rip: Cosmological models intermediate between the cosmological constant and the little rip, Phys. Rev. D 85 (2012) 083001, arXiv:1112.2964v2 [astro-ph. CO]. Crossref, Web of Science, Google Scholar
9. H. Wei, L. F. Wang and X. J. Guo, Quasi-Rip: A new type of rip model without cosmic doomsday, Phys. Rev. D 86 (2012) 083003, arXiv:1207.2898.v1 [gr-qc]. Crossref, Web of Science, Google Scholar
10. R. H. Brandenberger, Alternatives to cosmological inflation, Int. J. Mod. Phys. Conf. Ser. 01 (2011) 67, arXiv:0902.4731 [hep-th]. Link, Google Scholar
11. M. Novello and S. E. Perez Bergliaffa, Bouncing cosmologies, Phys. Rep. 463 (2008) 127–213. Crossref, Web of Science, Google Scholar
12. K. Bamba, A. N. Makarenko, A. N. Myagky, S. Nojiri and S. D. Odintsov, Bounce cosmology from $F (R)$ gravity and $F (R)$ bigravity, J. Cosmol. Astropart. Phys. 008 (2014) 01, arXiv:1309.3748v1 [hep-th]. Google Scholar
13. Y.-F. Cai, S.-H. Chen, J. B. Dent, S. Dutta and E. N. Saridakis, Matter bounce cosmology with the $f (T)$ gravity, Class. Quantum Grav. 28 (2011) 215011, arXiv:1104.4349[astro-ph.CO]. Crossref, Web of Science, Google Scholar
14. A. D. Linde, Inflationary cosmology, Lect. Notes Phys. 738 (2008) 1, arXiv:0705.0164 [hep-th]. Crossref, Google Scholar
15. D. S. Gorbunov and V. A. Rubakov, Introduction to the Theory of the Early Universe: Hot Big Bang Theory (World Scientific, Singapore, 2011). Crossref, Google Scholar
16. R. H. Brandenberger, Introduction to early universe cosmology, PoS ICFI 001 (2010) 1–70, arXiv:1103.2271v1 [astro-ph.CO]. Google Scholar
17. S. Nojiri and S. D. Odintsov, Inhomogeneous equation of state of the universe: Phantom era, future singularity and crossing the phantom barrier, Phys. Rev. D 72 (2005) 023003, arXiv:hep-th/0505215. Crossref, Web of Science, Google Scholar
18. S. Capozziello, S. Nojiri, S. D. Odintsov and A. Troisi, Cosmological viability of $f (R)$ -gravity as an ideal fluid and its compatibility with a matter dominated phase, Phys. Lett. B 639 (2006) 135–143, arXiv:astro-ph/0604431; S. Nojiri and S. D. Odintsov, Introduction to modified gravity and gravitational alternative for dark energy, Phys. Rev. D 70 (2004) 103522; Phys. Lett. B 562 (2003) 147–152; S. Nojiri and S. D. Odintsov, Introduction to modified gravity and gravitational alternative for dark energy, eConf. C 0602061 (2006) 06; Int. J. Geom. Methods Mod. Phys. 4 (2007) 115–145, arXiv:hep-th/061213; S. Nojiri and S. D. Odintsov, Modified gravity with negative and positive powers of the curvature: Verification of the inflation and of the cosmic acceleration, Phys. Rev. D 68 (2003) 123512, hep-th/0307288. Google Scholar
19. S. Nojiri, S. D. Odintsov and S. Tsujikawa, Properties of singularities in (phantom) dark energy universe, Phys. Rev. D 71 (2005) 063004, arXiv:0501025[hep-th]; J. D. Barrow, More general sudden singularities, Class. Quant. Grav. 21 (2004) 5619–5622, arXiv:gr-qc/0409062. Google Scholar
20. S. Nojiri, S. D. Odintsov and V. K. Oikonomou, Singular inflation from generalized equation of state fluids, Phys. Lett. B 747 (2015) 310–320, arXiv:1506.03307 [gr-qc]. Crossref, Web of Science, Google Scholar
21. I. Brevik, V. V. Obukhov and A. V. Timoshkin, Inflationary cosmology leading to a soft type singularity, Mod. Phys. Lett. A 31 (2016) 1650105, arXiv:1604.04748 [gr-qc]. Link, Web of Science, Google Scholar
22. S. Nojiri, S. D. Odintsov and V. K. Oikonomou, A quantitative analysis of singular inflation with scalar-tensor and modified gravity, Phys. Rev. D 91 (2015) 084059, arXiv:1502.07005 [gr-qc]. Crossref, Web of Science, Google Scholar
23. S. Nojiri, S. D. Odintsov, V. K. Oikonomou and E. N. Saridakis, Singular cosmological evolution using canonical and phantom scalar fields, J. Cosmol. Astropart. Phys. 1509 (2015) 044, arXiv:1503.08443 [gr-qc]; S. D. Odintsov and V. K. Oikonomou, Singular $F (R)$ cosmology unifying early and late-time acceleration with matter and radiation domination era, Class. Quantum Grav. 33 (2016) 125029, arXiv:1602.03309 [gr-qc]; S. D. Odintsov and V. K. Oikonomou, Inflation in exponential scalar model and finite-time singularity induced instability, Phys. Rev. D 92 (2015) 024058, arXiv:1507.05273 [gr-qc]. Google Scholar
24. S. D. Odintsov and V. K. Oikonomou, Singular deformations of nearly R2 inflation potentials, Class. Quantum Grav. 32 (2015) 23, 235011, arXiv:1504.01772 [gr-qc]. Crossref, Web of Science, Google Scholar
25. I. Brevik, J. M. Børven and S. Ng, Crossing of the $w = - 1$ barrier in two-fluid viscous modified gravity, Gen. Relativ. Grav. 38 (2006) 907–915. Crossref, Web of Science, Google Scholar
26. S. Caapozzielli, V. F. Cardone, E. Elizalde, S. Nojiri and S. D. Odintsov, Observational constraints on dark energy with generalized equation of state, Phys. Rev. D 73 (2006) 043512, arXiv:astro-ph/0508350. Crossref, Web of Science, Google Scholar
27. I. Brevik, S. Nojiri, S. D. Odintsov and D. Saez-Gomez, Eur. Phys. J. C 69 (2010) 563–574. Crossref, Web of Science, Google Scholar
28. I. Brevik, V. V. Obukhov and A. V. Timoshkin, Dark energy coupled with dark matter in viscous fluid cosmology, Astrophys. Space Sci. 355 (2015) 399–403. Crossref, Web of Science, Google Scholar
29. N. Komatsu and S. Kimura, Entropic cosmology in a dissipative universe, Phys. Rev. D 90 (2014) 123516, arXiv:1408.4836v1 [astro-ph.CO]. Crossref, Web of Science, Google Scholar
30. I. Brevik, V. V. Obukhov and A. V. Timoshkin, Cosmological models coupled with dark matter in a dissipative universe, Astrophys. Space Sci. 359 (2015) 11. Crossref, Web of Science, Google Scholar
31. I. Brevik, E. Elizalde, O. Gorbunova and A. V. Timoshkin, A FRW dark fluid with a non-linear inhomogeneous equation of state, Eur. Phys. J. C 52 (2007) 223–228. Crossref, Web of Science, Google Scholar
32. R. Myrzakulov and S. Sebastiani, Inhomogeneous viscous fluids for inflation, Astrophys. Space Sci. 356 (2015) 205–213. Crossref, Web of Science, Google Scholar
33. Planck Collab. (P. A. R. Ade et al.), Planck 2013 results. XXII. Constraints on inflation, Astron. Astrophys. 571 (2014) 1–43, arXiv:1303.5082 [astro-ph. CO]. Crossref, Web of Science, Google Scholar
34. K. Bamba, S. Nojiri, S. D. Odintsov and D. Saez-Gomez, Inflationary universe from perfect fluid and $F (R)$ gravity and its comparison with observational data, Phys. Rev. D 90 (2014) 124061, arXiv:1410.3993 [hep-th]. Crossref, Web of Science, Google Scholar
35. BICEP2 Collab. (P. A. R. Ade et al.), BICEP2 I: Detection of B-mode polarization at degree angular scales, Phys. Rev. Lett. 112 (2014) 1–26, arXiv:1403. 3985 [astro-ph. CO]. Web of Science, Google Scholar
36. J. B. Jimenez, R. Lazkoz, D. Saez-Gomes and V. Salzano, Observational constraints on cosmological future singularities, Eur. Phys. J. C 76 (2016) 631, arXiv:1602.06211 [gr-qc]. Crossref, Web of Science, Google Scholar