Research PapersNo Access

A new $f (R)$ model in the light of local gravity test and late-time cosmology

Akhilesh Nautiyal

Department of Physics, Malaviya National Institute of Technology Jaipur, Jaipur 302 017, India

E-mail Address: akhilesh.phy@mnit.ac.in

Search for more papers by this author

Sukanta Panda

Indian Institute of Science Education and Research, Bhauri, Bhopal 462066, Madhya Pradesh, India

E-mail Address: sukanta@iiserb.ac.in

Search for more papers by this author

, and

Avani Patel

Indian Institute of Science Education and Research, Bhauri, Bhopal 462066, Madhya Pradesh, India

E-mail Address: avani@iiserb.ac.in

Search for more papers by this author

https://doi.org/10.1142/S0218271817501851Cited by:1 (Source: Crossref)

Abstract

We propose a new model of $f (R)$ gravity containing Arctan function in the Lagrangian. We show here that this model satisfies fifth force constraint unlike a similar model in 2013 by Kruglov. In addition to this, we carry out the fixed point analysis as well as comment on the existence of curvature singularity in this model. The cosmological evolution for this $f (R)$ gravity model is also analyzed in the Friedmann–Robertson–Walker (FRW) background. To understand observational significance of the model, cosmological parameters are obtained numerically and compared with those of Lambda cold dark matter ( $Λ$ CDM) model. We also scrutinize the model with supernova data. We apply $O m$ diagnostic given by Sahni et al. in 2008 to the model. Using this diagnostic, we detect the distinction between cosmic evolution caused by the $f (R)$ model and $Λ$ CDM. We find best-fit parameter values of the model using baryon acoustic oscillations data.

Keywords:

PACS: 04.50.Kd, 98.80.−k, 98.80.Es

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. Supernova Search Team Collab. (A. G. Riess et al.), Astron. J. 116 (1998) 1009, arXiv:astro-ph/9805201; Supernova Cosmology Project Collab. (S. Perlmutter et al.), Nature 391 (1998) 51, arXiv:astro-ph/9712212; Supernova Search Team Collab. (B. P. Schmidt et al.), Astrophys. J. 507 (1998) 46, arXiv:astro-ph/9805200; Supernova Cosmology Project Collab. (S. Perlmutter et al.), Astrophys. J. 517 (1999) 565, arXiv:astro-ph/9812133; Supernova Search Team Collab. (A. G. Riess et al.), Astrophys. J. 607 (2004) 665, arXiv:astro-ph/0402512. Google Scholar
2. A. Padilla, arXiv:1502.05296 [hep-th]. Google Scholar
3. A. D. Felice and S. Tsujikawa , Living Rev. Rel. 13 (2010) 3. Web of Science, Google Scholar
4. T. P. Sotiriou and V. Faraoni , Rev. Mod. Phys. 82 (2010) 451, arXiv:0805.1726 [gr-qc]. Web of Science, ADS, Google Scholar
5. A. Starobinsky , JETP Lett. 86 (2007) 157, arXiv:0706.2041. Web of Science, ADS, Google Scholar
6. W. Hu and I. Sawicki , Phys. Rev. D 76 (2007) 064004, arXiv:0705.1158 [astro-ph]. Web of Science, ADS, Google Scholar
7. S. A. Appleby and R. A. Battye , Phys. Lett. B 654 (2007) 7, arXiv:0705.3199 [astro-ph]. Web of Science, ADS, Google Scholar
8. S. Appleby, R. Battye and A. Starobinsky , J. Cosmol. Astropart. Phys. 1006 (2010) 005, arXiv:astro-ph/0909.1737. Web of Science, ADS, Google Scholar
9. S. Tsujikawa , Phys. Rev. D 77 (2008) 023507, arXiv:0709.1391 [astro-ph]. Web of Science, ADS, Google Scholar
10. P. Zhang , Phys. Rev. D 73 (2006) 123504, arXiv:astro-ph/0511218. Web of Science, ADS, Google Scholar
11. G. Cognola, E. Elizalde, S. Nojiri, S. D. Odintsov, L. Sebastiani and S. Zerbini , Phys. Rev. D 77 (2008) 046009, arXiv:0712.4017 [hep-th]. Web of Science, ADS, Google Scholar
12. V. Miranda, S. E. Joras, I. Waga and M. Quartin , Phys. Rev. Lett. 102 (2009) 221101, arXiv:0905.1941 [astro-ph.CO]. Web of Science, ADS, Google Scholar
13. E. V. Linder , Phys. Rev. D 80 (2009) 123528, arXiv:0905.2962 [astro-ph.CO]. Web of Science, ADS, Google Scholar
14. K. Bamba, C. Q. Geng and C. C. Lee , J. Cosmol. Astropart. Phys. 1008 (2010) 021, arXiv:1005.4574 [astro-ph.CO]. Web of Science, ADS, Google Scholar
15. K. Bamba, C. Q. Geng and C. C. Lee , Int. J. Mod. Phys. D 20 (2011) 1339, arXiv:1108.2557 [gr-qc]. Link, Web of Science, ADS, Google Scholar
16. S. I. Kruglov , Phys. Rev. D 89 (2014) 064004, arXiv:1310.6915 [gr-qc]. Web of Science, ADS, Google Scholar
17. L. Amendola, R. Gannouji, D. Polarski and S. Tsujikawa , Phys. Rev. D 75 (2007) 083504, arXiv:gr-qc/0612180. Web of Science, ADS, Google Scholar
18. S. Carloni , J. Cosmol. Astropart. Phys. 1509 (2015) 013, arXiv:1505.06015 [gr-qc]. Web of Science, ADS, Google Scholar
19. S. Kandhai and P. K. S. Dunsby, arXiv:1511.00101 [gr-qc]. Google Scholar
20. G. J. Olmo , Phys. Rev. D 72 (2005) 083505, arXiv:gr-qc/0505135. Web of Science, ADS, Google Scholar
21. G. J. Olmo , Phys. Rev. Lett. 95 (2005) 261102, arXiv:gr-qc/0505101. Web of Science, ADS, Google Scholar
22. C. M. Will , Living Rev. Rel. 17 (2014) 4, arXiv:1403.7377 [gr-qc]. Web of Science, ADS, Google Scholar
23. K. Dutta, S. Panda and A. Patel , Phys. Rev. D 94 (2016) 024016, arXiv:1601.07928 [gr-qc]. Web of Science, ADS, Google Scholar
24. S. A. Appleby and R. A. Battye , J. Cosmol. Astropart. Phys. 0805 (2008) 019, arXiv:0803.1081 [astro-ph]. Web of Science, ADS, Google Scholar
25. A. Frolov , Phys. Rev. Lett. 101 (2008) 061103, arXiv:astro-ph/0803.2500. Web of Science, ADS, Google Scholar
26. K. Dutta, S. Panda and A. Patel , Phys. Rev. D 92 (2015) 063503, arXiv:1504.05790 [gr-qc]. Web of Science, ADS, Google Scholar
27. S. Nojiri and S. D. Odintsov , Phys. Rev. D 78 (2008) 046006, arXiv:0804.3519 [hep-th]. Web of Science, ADS, Google Scholar
28. K. Bamba, S. Nojiri and S. D. Odintsov , J. Cosmol. Astropart. Phys. 0810 (2008) 045, arXiv:0807.2575 [hep-th]. Web of Science, ADS, Google Scholar
29. A. Dev, D. Jain, S. Jhingan, S. Nojiri, M. Sami and I. Thongkool , Phys. Rev. D 78 (2008) 083515, arXiv:hep-th/0807.3445. Web of Science, ADS, Google Scholar
30. I. Thongkool, M. Sami, R. Gannouji and S. Jhingan , Phys. Rev. D 80 (2009) 043523, arXiv:0906.2460 [hep-th]. Web of Science, ADS, Google Scholar
31. S. Capozziello, M. De Laurentis, S. Nojiri and S. D. Odintsov , Phys. Rev. D 79 (2009) 124007, arXiv:0903.2753 [hep-th]. Web of Science, ADS, Google Scholar
32. A. de la Cruz-Dombriz, P. K. S. Dunsby, S. Kandhai and D. Saez-Gomez , Phys. Rev. D 93 (2016) 084016, arXiv:1511.00102 [gr-qc]. Web of Science, ADS, Google Scholar
33. E. Arbuzova and S. Dolgov , Phys. Lett. B 700 (2011) 289, arXiv:astro-ph/1012.1963. Web of Science, ADS, Google Scholar
34. C. Lee, C. Geng and L. Yang , Prog. Theor. Phys. 128 (2012) 415, arXiv:astro-ph/1201.4546. Web of Science, ADS, Google Scholar
35. L. Reverberi , Phys. Rev. D 87 (2013) 084005, arXiv:gr-qc/1212.2870. Web of Science, ADS, Google Scholar
36. T. Kobayashi and K. i. Maeda , Phys. Rev. D 78 (2008) 064019, arXiv:0807.2503 [astro-ph]. Web of Science, ADS, Google Scholar
37. A. Upadhye and W. Hu , Phys. Rev. D 80 (2009) 064002, arXiv:0905.4055 [astro-ph.CO]. Web of Science, ADS, Google Scholar
38. E. Babichev and D. Langlois , Phys. Rev. D 81 (2010) 124051, arXiv:0911.1297 [gr-qc]. Web of Science, ADS, Google Scholar
39. A. Shafieloo, V. Sahni and A. A. Starobinsky , Phys. Rev. D 86 (2012) 103527, arXiv:1205.2870 [astro-ph.CO]. Web of Science, ADS, Google Scholar
40. V. Sahni, A. Shafieloo and A. A. Starobinsky , Phys. Rev. D 78 (2008) 103502, arXiv:0807.3548 [astro-ph]. Web of Science, ADS, Google Scholar
41. V. Sahni, A. Shafieloo and A. A. Starobinsky , Astrophys. J. 793 (2014) L40, arXiv:1406.2209 [astro-ph.CO]. Web of Science, ADS, Google Scholar
42. L. G. Jaime , Phys. Rev. D 91 (2015) 124070, arXiv:1506.03618 [gr-qc]. Web of Science, ADS, Google Scholar
43. R. C. Nunes, S. Pan, E. N. Saridakis and E. M. C. Abreu, arXiv:1610.07518 [astro-ph.CO]. Google Scholar
44. L. G. Jaime, L. Patino and M. Salgado, arXiv:1206.1642 [gr-qc]. Google Scholar
45. Supernova Cosmology Project (R. Amanullah et al.), Astrophys. J. 716 (2010) 712. Web of Science, ADS, Google Scholar
46. J. Khoury and A. Weltman, Phys. Rev. Lett. 93 (2004) 171104, arXiv:astro-ph/0309300; J. Khoury and A. Weltman, Phys. Rev. D 69 (2004) 044026, arXiv:astro-ph/0309411. Google Scholar
47. S. Capozziello and S. Tsujikawa , Phys. Rev. D 77 (2008) 107501, arXiv:gr-qc/0712.2268. Web of Science, ADS, Google Scholar
48. Planck Collab. (P. A. R. Ade et al.), Astron. Astrophys. 571 (2014) A16, arXiv:1303.5076 [astro-ph.CO]. Web of Science, Google Scholar
49. L. Samushia et al., Mon. Not. R. Astron. Soc. 429 (2013) 1514, arXiv:1206.5309 [astro-ph.CO]. Web of Science, ADS, Google Scholar
50. L. Anderson et al., Mon. Not. R. Astron. Soc. 441 (2014) 24. Web of Science, ADS, Google Scholar
51. BOSS Collab. (T. Delubac et al.), Astron. Astrophys. 574 (2015) A59, arXiv:1404.1801 [astro-ph.CO]. Web of Science, Google Scholar
52. G. Efstathiou et al., Mon. Not. R. Astron. Soc. 440 (2014) 1138. Web of Science, ADS, Google Scholar