Chin. Phys. Lett.  2016, Vol. 33 Issue (03): 039801    DOI: 10.1088/0256-307X/33/3/039801
Consistency Conditions and Constraints on Generalized $f(R)$ Gravity with Arbitrary Geometry-Matter Coupling
Si-Yu Wu1, Ya-Bo Wu1**, Yue-Yue Zhao2, Xue Zhang1, Cheng-Yuan Zhang1, Bo-Hai Chen1
1Department of Physics, Liaoning Normal University, Dalian 116029
2Department of Basic, Dalian Naval Academy, Dalian 116018
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Si-Yu Wu, Ya-Bo Wu, Yue-Yue Zhao et al  2016 Chin. Phys. Lett. 33 039801
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Abstract We study the consistency conditions of the generalized $f(R)$ gravity by extending $f(R)$ gravity with non-minimal coupling to the generalized $f(R)$ with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized $f(R)$ by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov–Kawasaki stability criterion, and give the value ranges of the parameters in the first model. It is worth stressing that our results include the ones in $f(R)$ gravity with non-minimal coupling as the special case of $Q(L_{\rm m})=L_{\rm m}$.
Received: 07 December 2015      Published: 31 March 2016
PACS:  98.80.-k (Cosmology)  
  98.80.Jk (Mathematical and relativistic aspects of cosmology)  
  04.20.-q (Classical general relativity)  
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Si-Yu Wu
Ya-Bo Wu
Yue-Yue Zhao
Xue Zhang
Cheng-Yuan Zhang
Bo-Hai Chen
[1]Riess A G, Filippenko A V, Challis P et al 1998 Astron. J. 116 1009
[2]Perlmutter S, Aldering G, Goldhaber G et al 1999 Astron. J. 517 565
[3]Caldwell R R, Dave R and Steinhardt P J 1998 Phys. Rev. Lett. 80 1582
[4]Sen A 2002 J. High Energy Phys. 0207 065
[5]Li M 2004 Phys. Lett. B 603 1
[6]Huang Q G and Li M 2004 J. Cosmol. Astropart. Phys. 2004 013
[7]Gong Y G 2004 Phys. Rev. D 70 064029
[8]Zhu Z 2004 Astron. Astrophys. 423 421
[9]Cai R G and Wang A 2005 J. Cosmol. Astropart. Phys. 0503 002
[10]Cai R G 2007 Phys. Lett. B 657 228
[11]Wang B, Gong Y and Su R K 2005 Phys. Lett. B 605 9
[12]Zhao W and Zhang Y 2006 Phys. Rev. D 73 123509
[13]Hu B and Ling Y 2006 Phys. Rev. D 73 123510
[14]Zhang X 2007 Phys. Lett. B 648 1
[15]Wei H and Cai R G 2008 Phys. Lett. B 660 113
[16]Zhu W T, Wu P X and Yu H W 2013 Chin. Phys. Lett. 30 059501
[17]Wu Y B et al 2014 Chin. Phys. Lett. 31 029801
[18]Brans C and Dicke R H 1961 Phys. Rev. 124 925
[19]Randall L and Sundrum R 1999 Phys. Rev. Lett. 83 4690
[20]Randall L and Sundrum R 1999 Phys. Rev. Lett. 83 3370
[21]Dvali G et al 2000 Phys. Lett. B 485 208
[22]Carroll S M 2001 Living Rev. Relativ. 4 1
[23]Maartens R 2004 Living Rev. Relativ. 7 7
[24]Carroll S M et al 2005 Phys. Rev. D 71 063513
[25]Zhang X and Ma Y 2011 Phys. Rev. Lett. 106 171301
[26]Meng X H and Wang Y B 2011 Eur. Phys. J. C 71 1755
[27]Huang Q G, Zhang K C and Zhou S Y 2013 J. Cosmol. Astropart. Phys. 1308 050
[28]Cai R G, Yang Q and Zhang Y L 2014 J. High Energy Phys. 1412 147
[29]Wu Y B et al 2013 Chin. Phys. Lett. 30 069801
[30]Sotiriou T P and Faraoni V 2010 Rev. Mod. Phys. 82 451
[31]Nojiri S and Odintsov S D 2006 Phys. Rev. D 74 086005
[32]Santos J et al 2007 Phys. Rev. D 76 083513
[33]Bertolami O et al 2007 Phys. Rev. D 75 104016
[34]Koivisto T 2006 Class. Quantum Grav. 23 4289
[35]Harko T 2008 Phys. Lett. B 669 376
[36]Bergliaffa S E P 2006 Phys. Lett. B 642 311
[37]Wang J et al 2010 Phys. Lett. B 689 133
[38]Wang J et al 2010 Eur. Phys. J. C 69 541
[39]Harko T and Lobo F S N 2010 Eur. Phys. J. C 70 373
[40]Harko T and Lobo F S N 2012 Phys. Rev. D 86 124034
[41]Harko T, Lobo F S N and Minazzoli O 2013 Phys. Rev. D 87 047501
[42]Wang J and Liao K 2012 Class. Quantum Grav. 29 215016
[43]Wu Y B et al 2014 Mod. Phys. Lett. A 29 1450089
[44]Tamanini N and Koivisto T S 2013 arXiv:1308.3401v1 [gr-qc]
[45]Bertolami O and Paramos J 2008 Class. Quantum Grav. 25 245017
[46]Garriga J and Mukhanov V F 1999 Phys. Lett. B 458 219
[47]Armendariz-Picon C, Mukhanov V and Steinhardt P J 2001 Phys. Rev. D 63 103510
[48]Albareti F D et al 2013 J. Cosmol. Astropart. Phys. 2013 009
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