both Σ and µ are determined by a single variable, and consequently there is a unique trajectory in the (Σ, µ ) plane. 

• For interacting dark energy models, as there is no anisotropic stress induced by interactions, we have a simple relation, Σ = µ . Nevertheless, a non- trivial Σ is induced by the non-adiabatic scaling of the background dark matter density. 

Those investigations enrich our understanding of large scale structure formation, and provide theoretical priors 

[1] S. Perlmutter et al. (Supernova Cosmology Project), As- trophys. J. 517 , 565 (1999), astro-ph/9812133. 

[2] A. G. Riess et al. (Supernova Search Team), Astron. J. 116 , 1009 (1998), astro-ph/9805201. 

[3] M. Ishak, A. Upadhye, and D. N. Spergel, Phys. Rev. D74 , 043513 (2006), astro-ph/0507184. 

[4] Y.-S. Song, Phys. Rev. D71 , 024026 (2005), astro- ph/0407489. 

[5] S. Wang, L. Hui, M. May, and Z. Haiman, Phys. Rev. D76 , 063503 (2007), 0705.0165. 

[6] L. Knox, Y.-S. Song, and J. A. Tyson, Phys. Rev. D74 , 023512 (2006). 

[7] M. J. Mortonson, W. Hu, and D. Huterer, Phys. Rev. D79 , 023004 (2009), 0810.1744. 

[8] E. V. Linder, Phys. Rev. D72 , 043529 (2005), astro- ph/0507263. 

[9] E. V. Linder and R. N. Cahn, Astropart. Phys. 28 , 481 (2007), astro-ph/0701317. 

[10] D. Huterer and E. V. Linder, Phys. Rev. D75 , 023519 (2007), astro-ph/0608681. 

[11] D. Polarski and R. Gannouji, Phys. Lett. B660 , 439 (2008), 0710.1510. 

[12] C. Di Porto and L. Amendola, Phys. Rev. D77 , 083508 (2008), 0707.2686. 

[13] S. A. Thomas, F. B. Abdalla, and J. Weller, Mon. Not. Roy. Astron. Soc. 395 , 197 (2009), 0810.4863. 

[14] J. B. Dent and S. Dutta, Phys. Rev. D79 , 063516 (2009), 0808.2689. 

[15] J.-P. Uzan and F. Bernardeau, Phys. Rev. D64 , 083004 (2001), hep-ph/0012011. 

[16] Y.-S. Song (2006), astro-ph/0602598. 

[17] E. Bertschinger, Astrophys. J. 648 , 797 (2006), astro- ph/0604485. 

[18] T. Koivisto and D. F. Mota, Phys. Rev. D73 , 083502 (2006), astro-ph/0512135. 

[19] L. Amendola, M. Kunz, and D. Sapone, JCAP 0804 , 013 (2008), 0704.2421. 

[20] J.-P. Uzan, Gen. Rel. Grav. 39 , 307 (2007), astro- ph/0605313. 

[21] W. Hu and I. Sawicki, Phys. Rev. D76 , 104043 (2007), 0708.1190. 

[22] W. Hu, Phys. Rev. D77 , 103524 (2008), 0801.2433. 

[23] G.-B. Zhao, L. Pogosian, A. Silvestri, and J. Zylberberg, Phys. Rev. D79 , 083513 (2009), 0809.3791. 

[24] E. Bertschinger and P. Zukin, Phys. Rev. D78 , 024015 (2008), 0801.2431. 

[25] S. F. Daniel, R. R. Caldwell, A. Cooray, and A. Mel- 

on the modified growth parameter space spanned by Σ and µ . 

Y-S.S. is supported by the UK’s Science & Technol- ogy Facilities Council (STFC). K.K. is supported by the European Research Council, Research Councils UK and STFC. L.H. is supported by the Swiss National Science Foundation (SNSF). 

chiorri, Phys. Rev. D77 , 103513 (2008), 0802.1068. 

[26] R. Caldwell, A. Cooray, and A. Melchiorri, Phys. Rev. D76 , 023507 (2007), astro-ph/0703375. 

[27] O. Dore et al. (2007), 0712.1599. 

[28] B. Jain and P. Zhang, Phys. Rev. D78 , 063503 (2008), 0709.2375. 

[29] Y.-S. Song and K. Koyama, JCAP 0901 , 048 (2009), 0802.3897. 

[30] P. Zhang, M. Liguori, R. Bean, and S. Dodelson, Phys. Rev. Lett. 99 , 141302 (2007), 0704.1932. 

[31] P. Zhang, R. Bean, M. Liguori, and S. Dodelson (2008), 0809.2836. 

[32] Y.-S. Song and O. Dore, JCAP 0903 , 025 (2009), 0812.0002. 

[33] G. R. Dvali, G. Gabadadze, and M. Porrati, Phys. Lett. B485 , 208 (2000), hep-th/0005016. 

[34] S. M. Carroll, V. Duvvuri, M. Trodden, and M. S. Turner, Phys. Rev. D70 , 043528 (2004), astro-ph/0306438. 

[35] L. Amendola, Phys. Rev. D62 , 043511 (2000), astro- ph/9908023. 

[36] K. Koyama, A. Taruya, and T. Hiramatsu, Phys. Rev. D79 , 123512 (2009), 0902.0618. 

[37] K. Koyama, Class. Quant. Grav. 24 , R231 (2007), 0709.2399. 

[38] R. Bean and O. Dore, Phys. Rev. D69 , 083503 (2004), astro-ph/0307100. 

[39] J. Weller and A. M. Lewis, Mon. Not. Roy. Astron. Soc. 346 , 987 (2003), astro-ph/0307104. 

[40] W. Hu and R. Scranton, Phys. Rev. D70 , 123002 (2004), astro-ph/0408456. 

[41] M. Takada, Phys. Rev. D74 , 043505 (2006), astro- ph/0606533. 

[42] P. P. Avelino, L. M. G. Beca, and C. J. A. P. Martins, Phys. Rev. D77 , 101302 (2008), 0802.0174. 

[43] S. Unnikrishnan, H. K. Jassal, and T. R. Seshadri, Phys. Rev. D78 , 123504 (2008), 0801.2017. 

[44] L. R. Abramo, R. C. Batista, and R. Rosenfeld, JCAP 0907 , 040 (2009), 0902.3226. 

[45] R. Battye and A. Moss, Phys. Rev. D80 , 023531 (2009), 0905.3403. 

[46] D. Sapone, M. Kunz, and M. Kunz, Phys. Rev. D80 , 083519 (2009), 0909.0007. 

[47] A. Lewis, A. Challinor, and A. Lasenby, Astrophys. J. 538 , 473 (2000), astro-ph/9911177. 

[48] G. Caldera-Cabral, R. Maartens, and L. A. Urena-Lopez, Phys. Rev. D79 , 063518 (2009), 0812.1827. 

[49] J. Valiviita, E. Majerotto, and R. Maartens, JCAP 0807 , 

## Acknowledgments 

