Abdelwahab, MohamedCruz Dombriz, Álvaro de laDunsby, P.K.S.2023-06-192023-06-1920131. S. Nojiri, S. D. Odintsov, Int. J. Geom. Meth. Mod. Phys., 4, 115 (2007) -- T. P. Sotiriou, V. Faraoni, Rev. Mod. Phys., 82, 451 (2010) -- F. S. N. Lobo, arXiv:0807.1640 [gr-qc] -- S. Capozziello, V. Faraoni, Beyond Einstein Gravity, Springer Ed., Dordrecht (2011) -- A. Dobado, A. L. Maroto, Phys. Rev. D, 52, 1895 (1995) -- G. Dvali, G. Gabadadze, M. Porrati, Phys. Lett. B, 485, 208 (2000) -- J.Beltrán, A. L. Maroto, Phys. Rev. D, 78, 063005 (2008) --- JCAP 0903 016 (2009) --- Phys. Rev. D, 80, 063512 (2009) --- Int. J. Mod. Phys. D, 18, 2243-2248 (2009). 2. S. Nojiri, S. D. Odintsov, Phys. Rev. D, 74, 086005 (2006) -- E. Elizalde, D. Sáez-Gómez, Phys. Rev. D, 80, 044030 (2009) -- S. Nojiri, S. D. Odintsov, D. SáezGómez, Phys. Lett. B, 681, 74 (2009) -- S. A. Appleby, R. A. Battye, A. A. Starobinsky, JCAP, 1006, 005 (2010) 3. J. M. Bardeen, Phys. Rev., D22, 1882 (1980) -- S. M. Carroll, I. Sawicki, A. Silvestri, M. Trodden, New J. Phys., 8, 323, (2006) -- Y. S. Song, W. Hu, I. Sawicki, Phys. Rev. D, 75, 044004, (2007) -- A. A. Starobinsky, JETP Lett., 86, 157 (2007) -- A. de la Cruz-Dombriz, A. Dobado, A. L. Maroto, Phys. Rev. D, 77, 123515 (2008) --- Phys. Rev. Lett. D, 103, 179001 (2009) -- A. Abebe, M. Abdelwahab, A. de la Cruz-Dombriz, P. K. S. Dunsby, Class. Quant. Grav., 29, 135011 (2012). 4. A. de la Cruz-Dombriz, D. Sáez-Gómez, Class. Quant. Grav., 29, 245014, 2012. 5. G. J. Olmo, Phys. Rev. D, 75, 023511 (2007) -- A. M. Nzioki, S. Carloni, R. Goswami, P. K. S. Dunsby, Phys. Rev. D, 81, 084028 (2010) -- A. de la Cruz-Dombriz, A. Dobado, A. L. Maroto, Phys. Rev. D, 80, 124011 (2009) [Erratum: Phys. Rev. D, 83, 029903(E) (2011)] --- J. Phys. Conf. Ser., 229, (2010) 012033 -- J. A. R. Cembranos, A. de la Cruz-Dombriz, P. Jimeno Romero, e-Print: arXiv:1109.4519 [gr-qc] --- AIP Conf. Proc., 1458, 439 (2012). 6. A. A. Starobinsky, Phys. Lett., 91B, 99 (1980) -- S. Nojiri, S. Odintsov, Phys. Rev. D, 68, 123512 (2003) ---- Gen. Rel. Grav., 36, 1765 (2004) -- S. M. Carroll, et al, Phys. Rev., D71,63513 (2005) -- S. Carloni, P. K. S. Dunsby, S. Capozziello, A. Troisi, Class. Quant. Grav., 22 4839 (2005) -- J. A. R. Cembranos, Phys. Rev. D, 73, 064029 (2006) --- Phys. Rev. Lett., 102, 141301 (2009) -- T. Clifton, J. D. Barrow, Phys. Rev. D, 72, 103005 (2005) -- D. Sáez-Gómez, Gen. Rel. Grav., 41, 1527 (2009) -- P. K. S. Dunsby, et al., Phys. Rev. D, 82, 023519 (2010). 7. T. Clifton, et al., Phys. Rept., 513, 1 (2012). 8. A. de la Cruz-Dombriz, A. Dobado, Phys. Rev. D, 74, 087501 (2006). 9. W. Hu, I. Sawicki, Phys. Rev. D, 76, 064004 (2007) -- L. Pogosian, A. Silvestri, Phys. Rev. D, 77, 023503 (2008) -- S. Capozziello, S. Tsujikawa, Phys. Rev. D, 77, 107501 (2008). 10. A. Lewis, A. Challinor, A. Lasenby, Astrophys. J., 538, 473 (2000) -- A. Lewis, PhD Thesis, University of Cambridge (2000). 11. U. Seljak, M. Zaldarriaga, ApJ, 469, 437, 1996 -- M. Zaldarriaga, U. Seljak, E. Bertschinger, ApJ, 494, 491, 1998 -- M. Zaldarriaga, U. Seljak, ApJS, 129, pp 431-434, 2000. 12. N. Bevis, M. Hindmarsh, M. Kunz, J. Urrestilla, Phys. Rev. D, 75, 065015 (2007) -- S. Foreman, A. Moss, D. Scott, Phys. Rev. D, 84, 043522 (2011) -- J. Urrestilla, N. Bevis, M. Hindmarsh, M. Kunz, JCAP, 1112, 021 (2011) --- Phys. Rev. D, 82, 065004 (2010) -- C. Ringeval, Adv. Astron., 2010, 380507 (2010) -- C. Ringeval, F. R. Bouchet, Phys. Rev. D, 86, 023513 (2012). 13. R. A. Battye, C. Van de Bruck, A. Mennim, Phys. Rev. D, 69, 064040 (2004) -- R. Easther, D. Langlois, R. Maartens, D. Wands, JCAP, 0310, 014 (2003). 14. B. Leong, A. Challinor, R. Maartens, A. Lasenby, Phys. Rev. D, 66, 104010 (2002). 15. Y. Zhong, Y. -X. Liu, K. Yang, Phys. Lett. B, 699, 398 (2011). 16. M. Abdelwahab, H. Bourhrous, A. de la Cruz-Dombriz, P. K. S. Dunsby, in preparation. 17. K. N. Ananda, S. Carloni, P. K. S. Dunsby, Phys. Rev. D, 77, 024033 (2008) -- A. Challinor, Class. Quant. Grav., 17, 871 (2000) -- P. K. S. Dunsby, B. A. C. C. Bassett, G. F. R. Ellis, Class. Quant. Grav., 14, 1215 (1997). 18. H. Bourhrous, A. de la Cruz-Dombriz, P. K. S. Dunsby, AIP Conf. Proc., 1458, 343 (2012). 19. S. Carloni, P. K. S. Dunsby, A. Troisi, Phys. Rev. D, 77, 024024, 2008. 20. S. Capozziello, M. Francaviglia, Gen. Rel. Grav., 40, 357, 420 (2008). 21. http : //camb.info/ppf/0094-243x10.1063/1.4791747https://hdl.handle.net/20.500.14352/35118© 2013 American Institute of Physics. Conference on Multiverse and Fundamental Cosmology (Multicosmofun) (12. 2013. Szczecin, POLAND). AdlCD acknowledges financial support from URC and NRF (South Africa), MICINN (Spain) projects numbers FIS2011-23000, FPA2011-27853-C02-01 and Consolider-Ingenio MULTIDARK CSD2009-00064.We study for the first time a complete analysis of the imprint of tensor anisotropies on the Cosmic Microwave Background for a class of f(R) gravity theories within the CAMB-PPF framework. Herein we present the most relevant equations, both for the cosmological background and gravitational wave perturbations, taking care to include all effects which arise from f(R) modifications. We find that that the dominant contribution to deviations from General Relativity in the temperature and polarization spectra can be attributed to modifications in the background. This demonstrates the importance of using the correct background in perturbative studies of f(R) gravity.engCosmological tensor perturbations in theories beyond Lambda CDMjournal articlehttp://dx.doi.org/10.1063/1.4791747http://scitation.aip.org/open access53Microwave background anisotropiesModified gravityGravitional-wavesF(R) gravityUniversesModels.Física (Física)22 Física