Summary
The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio r and tensor spectral index nT In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Huber S. J., Konstandin T., Nardini G. and Rues I., JCAP, 1603 (2016) 036.
Caprini C. et al., JCAP, 1604 (2016) 001.
Dev P. S. B. and Mazumdar A., Phys. Rev. D, 93 (2016) 104001.
Sanidas S. A., Battye R. A. and Stappers B. W., Phys. Rev. D, 85 (2012) 122003.
Figueroa D. G., Hindmarsh M. and Urrestilla J., Phys. Rev. Lett., 110 (2013) 101302.
Ade P. A. R. et al., Phys. Rev. Lett., 116 (2016) 031302.
Sorbo L., JCAP, 1106 (2011) 003.
Barnaby N., Moxon J., Namba R., Peloso M., Shiu G. and Zhou P., Phys. Rev. D, 86 (2012) 103508.
Senatore L., Silverstein E. and Zaldarriaga M., JCAP, 1408 (2014) 016.
Binetruy P., Bohe A., Caprini C. and Dufaux J.-F., JCAP, 1206 (2012) 027.
Biagetti M., Fasiello M. and Riotto A., Phys. Rev. D, 88 (2013) 103518.
Khlebnikov S. Yu. and Tkachev I. I., Phys. Rev. Lett., 77 (1996) 219.
Calabrese E. et al., JCAP, 1408 (2014) 010.
Ade P. A. R. et al., Astrophys. J., 794 (2014) 171.
Eimer J. R., Bennett C. L., Chuss D. T., Marriage T. A., Wollack E. J. and Zeng L., Proc. SPIE Int. Soc. Opt. Eng., 8452 (2012) 845220.
Gandilo Natalie N. et al., The Primordial Inflation Polarization Explorer (PIPER), arXiv:1607.06172 (2016).
Crill B. P. et al., Proc. SPIE Int. Soc. Opt. Eng., 7010 (2008) 2P.
Bouchet F. R. et al., 1102.2181 [astro-ph.CO] preprint (2011).
André P. et al., JCAP, 1402 (2014) 006.
Matsumura T. et al., Mission design of LiteBIRD, 1311.2847 [astro-ph.IM] (J. Low. Temp. Phys., 176 (2014) 733).
Kogut A. et al., JCAP, 1107 (2011) 025.
Dodelson S., Rozo E. and Stebbins A., Phys. Rev. Lett., 91 (2003) 021301.
Masui K. W. and Pen U.-L., Phys. Rev. Lett., 105 (2010) 161302.
Jeong D. and Schmidt F., Phys. Rev. D, 86 (2012) 083512.
Smith T. L., Pierpaoli E. and Kamionkowski M., Phys. Rev. Lett., 97 (2006) 021301.
Aasi J. et al., Class. Quantum Grav., 32 (2015) 074001.
Klein A. et al., Phys. Rev. D, 93 (2016) 024003.
Bird S., Cholis I., Muñoz J. B., Ali-Haïmoud Y., Kamionkowski M., Kovetz E. D., Raccanelli A. and Riess A. G., 1603.00464 [astro-ph.CO] preprint (2016).
Sasaki M., Suyama T., Tanaka T. and Yokoyama S., 1603.08338 [astro-ph.CO] preprint (2016).
Clesse S. and García-Bellido J., 1603.05234 [astro-ph.CO] preprint (2016).
Abbott B. P. et al., Phys. Rev. Lett., 116 (2016) 061102.
Blair D. et al., Sci. China Phys. Mech. Astron., 58 (2015) 120402.
Brout R., Englert F. and Gunzig E., Ann. Phys., 115 (1978) 78.
Starobinsky A. A., Phys. Lett. B, 91 (1980) 99.
Kazanas D., Astrophys. J., 241 (1980) L59.
Sato K., Mon. Not. R. Astron. Soc., 195 (1981) 467.
Guth A. H., Phys. Rev. D, 23 (1981) 347.
Linde A. D., Phys. Lett. B, 108 (1982) 389.
Albrecht A., Steinhardt P. J., Turner M. S. and Wilczek F., Phys. Rev. Lett., 48 (1982) 1437.
Abbott L. F., Farhi E. and Wise M. B., Phys. Lett. B, 117 (1982) 29.
Mukhanov V. F. and Chibisov G. V., JETP Lett., 33 (1981) 532 (Pisma Zh. Eksp. Teor. Fiz., 33 (1981) 549).
Hawking S. W., Phys. Lett. B, 115 (1982) 295.
Guth A. H. and Pi S. Y., Phys. Rev. Lett., 49 (1982) 1110.
Starobinsky A. A., Phys. Lett. B, 117 (1982) 175.
Abbott L. F. and Wise M. B., Nucl. Phys. B, 244 (1984) 541.
Mukhanov V. F., JETP Lett., 41 (1985) 493 (Pisma Zh. Eksp. Teor. Fiz., 41 (1985) 402).
Ade P. A. R. et al., 1502.01589 [astro-ph.CO] preprint (2015).
Lidsey J. E., Liddle A. R., Kolb E. W., Copeland E. J., Barreiro T. and Abney M., Rev. Mod. Phys., 69 (1997) 373.
Liddle A. R., Parsons P. and Barrow J. D., Phys. Rev. D, 50 (1994) 7222.
Lyth D. H. and Riotto A., Phys. Rep., 314 (1999) 1.
Ade P. A. R. et al., 1502.02114 [astro-ph.CO] preprint (2015).
Lucchin F. and Matarrese S., Phys. Lett. B, 164 (1985) 282.
Dolgov A. D. and Linde A. D., Phys. Lett. B, 116 (1982) 329.
Kofman L., Linde A. D. and Starobinsky A. A., Phys. Rev. Lett., 73 (1994) 3195.
Linde A. D., Phys. Lett. B, 116 (1982) 335.
Ashoorioon A., Bhupal Dev P. S. and Mazumdar A., Mod. Phys. Lett. A, 29 (2014) 1450163.
Krauss L. M. and Wilczek F., Phys. Rev. D, 89 (2014) 047501.
Bruni M., Matarrese S., Mollerach S. and Sonego S., Class. Quantum Grav., 14 (1997) 2585.
Matarrese S., Mollerach S. and Bruni M., Phys. Rev. D, 58 (1998) 043504.
Acquaviva V., Bartolo N., Matarrese S. and Riotto A., Nucl. Phys. B, 667 (2003) 119.
Bardeen J. M., Phys. Rev. D, 22 (1980) 1882.
Kodama H. and Sasaki M., Prog. Theor. Phys. Suppl., 78 (1984) 1.
Mukhanov V. F., Feldman H. A. and Brandenberger R. H., Phys. Rep., 215 (1992) 203.
Liddle A. R. and Lyth D. H., Cosmological inflation and large scale structure (Cambridge University Press, Cambridge, UK) 2000.
Sasaki M., Prog. Theor. Phys., 76 (1986) 1036.
Taruya A. and Nambu Y., Phys. Lett. B, 428 (1998) 37.
Lukash V. N., Sov. Phys. JETP, 52 (1980) 807 (Zh. Eksp. Teor. Fiz., 79 (1980) 1601).
Lyth D. H., Phys. Rev. D, 31 (1985) 1792.
Liddle A. R. and Turner M. S., Phys. Rev. D, 50 (1994) 758 (Erratum: Phys. Rev. D, 54 (1996) 2980).
Ade P. A. R. et al., 1502.01592 [astro-ph.CO] preprint (2015).
Grishchuk L. P., Sov. Phys. JETP, 40 (1975) 409 (Zh. Eksp. Teor. Fiz., 67 (1974) 825).
Starobinsky A. A., JETP Lett., 30 (1979) 682 (Pisma Zh. Eksp. Teor. Fiz., 30 (1979) 719).
Rubakov V. A., Sazhin M. V. and Veryaskin A. V., Phys. Lett. B, 115 (1982) 189.
Fabbri R. and Pollock M. D., Phys. Lett. B, 125 (1983) 445.
Grishchuk L. P., Zh. Eksp. Teor. Fiz., 66 (1974) 833.
Grishchuk L. P., Annals N. Y. Acad. Sci., 302 (1977) 439.
Misner C. W., Thorne K. S. and Wheeler J. A., Gravitation (W. H. Freeman, San Francisco) 1973.
Bunch T. S. and Davies P. C. W., Proc. R. Soc. London A, 360 (1978) 117.
Mollerach S., Matarrese S. and Lucchin F., Phys. Rev. D, 50 (1994) 4835.
Alba V. and Maldacena J., JHEP, 03 (2016) 115.
Adamek J., Durrer R. and Tansella V., JCAP, 1601 (2016) 024.
Maggiore M., Gravitational Waves. Vol. 1: Theory and Experiments, Oxford Master Series in Physics (Oxford University Press) 2007 http://www.oup.com/uk/catalogue/?ci=9780198570745.
Watanabe Y. and Komatsu E., Phys. Rev. D, 73 (2006) 123515.
Lyth D. H., Phys. Lett. B, 147 (1984) 403 (Erratum: Phys. Lett. B, 150 (1985) 465).
Lyth D. H., Phys. Rev. Lett., 78 (1997) 1861.
Boubekeur L. and Lyth D., JCAP, 0507 (2005) 010.
Baumann D. and McAllister L., Phys. Rev. D, 75 (2007) 123508.
Boubekeur L., Phys. Rev. D, 87 (2013) 061301.
Efstathiou G. and Mack K. J., JCAP, 0505 (2005) 008.
Garcia-Bellido J., Roest D., Scalisi M. and Zavala I., JCAP, 1409 (2014) 006.
Garcia-Bellido J., Roest D., Scalisi M. and Zavala I., Phys. Rev. D, 90 (2014) 123539.
Easther R., Kinney W. H. and Powell B. A., JCAP, 0608 (2006) 004.
Endlich S., Nicolis A. and Wang J., JCAP, 1310 (2013) 011.
Gruzinov A., Phys. Rev. D, 70 (2004) 063518.
Bartrum S., Bastero-Gil M., Berera A., Cerezo R., Ramos R. O. and Rosa J. G., Phys. Lett. B, 732 (2014) 116.
Bastero-Gil M., Berera A., Moss I. G. and Ramos R. O., JCAP, 1405 (2014) 004.
Bastero-Gil M., Berera A., Ramos R. O. and Rosa J. G., hep-ph/1604.08838 preprint (2016).
Cheung C., Creminelli P., Fitzpatrick A. L., Kaplan J. and Senatore L., JHEP, 03 (2008) 014.
Tsujikawa S., Lect. Notes Phys., 892 (2015) 97.
Cannone D., Tasinato G. and Wands D., JCAP, 1501 (2015) 029.
Cannone D., Gong J.-O. and Tasinato G., JCAP, 1508 (2015) 003.
Graef L. and Brandenberger R., JCAP, 1510 (2015) 009.
Lin C. and Labun L. Z., JHEP, 03 (2016) 128.
Abolhasani A. A., Akhshik M., Emami R. and Firouzjahi H., JCAP, 1603 (2016) 020.
Bartolo N., Cannone D., Ricciardone A. and Tasinato G., JCAP, 1603 (2016) 044.
Cai Y., Wang Y.-T. and Piao Y.-S., 1602.05431 [astro-ph.CO] preprint (2016).
Brandenberger R. H., Nayeri A., Patil S. P. and Vafa C., Phys. Rev. Lett., 98 (2007) 231302.
Gasperini M. and Veneziano G., Phys. Rep., 373 (2003) 1.
Khoury J., Ovrut B. A., Steinhardt P. J. and Turok N., Phys. Rev. D, 64 (2001) 123522.
Tomita K., Prog. Theor. Phys., 37 (1967) 831.
Carrilho P. and Malik K. A., JCAP, 1602 (2016) 021.
Matarrese S., Pantano O. and Saez D., Phys. Rev. D, 47 (1993) 1311.
Matarrese S., Pantano O. and Saez D., Phys. Rev. Lett., 72 (1994) 320.
Nakamura K., Prog. Theor. Phys., 110 (2003) 723.
Nakamura K., Prog. Theor. Phys., 117 (2007) 17.
Carbone C. and Matarrese S., Phys. Rev. D, 71 (2005) 043508.
Noh H. and Hwang J.-c., astro-ph/0305123 preprint (2003).
Carbone C., Baccigalupi C. and Matarrese S., Phys. Rev. D, 73 (2006) 063503.
Baumann D., Steinhardt P. J., Takahashi K. and Ichiki K., Phys. Rev. D, 76 (2007) 084019.
Ananda K. N., Clarkson C. and Wands D., Phys. Rev. D, 75 (2007) 123518.
Mollerach S., Harari D. and Matarrese S., Phys. Rev. D, 69 (2004) 063002.
Fidler C, Pettinari G. W., Beneke M., Crittenden R., Koyama K. and Wands D., JCAP, 1407 (2014) 011.
Assadullahi H. and Wands D., Phys. Rev. D, 79 (2009) 083511.
Cook J. L. and Sorbo L., Phys. Rev. D, 85 (2012) 023534 (Erratum: Phys. Rev. D, 86 (2012) 069901).
Enqvist K. and Sloth M. S., Nucl. Phys. B, 626 (2002) 395.
Bartolo N., Matarrese S., Riotto A. and Vaihkonen A., Phys. Rev. D, 76 (2007) 061302.
Enqvist K., Nurmi S. and Rigopoulos G. I., JCAP, 0810 (2008) 013.
Suyama T. and Yokoyama J., Phys. Rev. D, 84 (2011) 083511.
Kawasaki M., Kitajima N. and Yokoyama S., JCAP, 1308 (2013) 042.
Biagetti M., Dimastrogiovanni E., Fasiello M. and Peloso M., JCAP, 1504 (2015) 011.
Fujita T., Yokoyama J. and Yokoyama S., PTEP, 2015 (2015) 043E01.
Chung D. J. H., Kolb E. W., Riotto A. and Tkachev I. I., Phys. Rev. D, 62 (2000) 043508.
Barnaby N. and Peloso M., Phys. Rev. Lett., 106 (2011) 181301.
Barnaby N., Namba R. and Peloso M., JCAP, 1104 (2011) 009.
Barnaby N., Pajer E. and Peloso M., Phys. Rev. D, 85 (2012) 023525.
Anber M. M. and Sorbo L., Phys. Rev. D, 85 (2012) 123537.
Namba R., Peloso M., Shiraishi M., Sorbo L. and Unal C., JCAP, 1601 (2016) 041.
Ben-Dayan I., 1604.07899 [astro-ph.CO] preprint (2016).
Garretson W. D., Field G. B. and Carroll S. M., Phys. Rev. D, 46 (1992) 5346.
Cook J. L. and Sorbo L., JCAP, 1311 (2013) 047.
Kofman L., Linde A. D. and Starobinsky A. A., Phys. Rev. D, 56 (1997) 3258.
Pearce L., Peloso M. and Sorbo L., 1603.08021 [astro-ph.CO] preprint (2016).
Anber M. M. and Sorbo L., Phys. Rev. D, 81 (2010) 043534.
Meerburg P. D. and Pajer E., JCAP, 1302 (2013) 017.
Domcke V., Pieroni M. and Binétruy P., 1603.01287 [astro-ph.CO] preprint (2016).
Anber M. M. and Sorbo L., JCAP, 0610 (2006) 018.
Lue A., Wang L.-M. and Kamionkowski M., Phys. Rev. Lett., 83 (1999) 1506.
Vachaspati T., Phys. Rev. Lett., 87 (2001) 251302.
Shiraishi M., Ricciardone A. and Saga S., JCAP, 1311 (2013) 051.
Bartolo N., Matarrese S., Peloso M. and Shiraishi M., JCAP, 1501 (2015) 027.
Acernese F. et al., Class. Quantum Grav., 22 (2005) S869.
Gluscevic V. and Kamionkowski M., Phys. Rev. D, 81 (2010) 123529.
Mirbabayi M., Senatore L., Silverstein E. and Zaldarriaga M., Phys. Rev. D, 91 (2015) 063518.
Ferreira R. Z. and Sloth M. S., JHEP, 12 (2014) 139.
Mukohyama S., Namba R., Peloso M. and Shiu G., JCAP, 1408 (2014) 036.
Shiraishi M., Hikage C., Namba R., Namikawa T. and Hazumi M., 1606.06082 [astro-ph.CO] preprint (2016).
Baumann D. et al., AIP Conf. Proc., 1141 (2009) 10.
Seto N. and Taruya A., Phys. Rev. Lett., 99 (2007) 121101.
Seto N. and Taruya A., Phys. Rev. D, 77 (2008) 103001.
Crowder S. G., Namba R., Mandic V., Mukohyama S. and Peloso M., Phys. Lett. B, 726 (2013) 66.
Hyde J. M., Phys. Rev. D, 92 (2015) 044026.
Lyth D. H. and Liddle A. R., The primordial density perturbation: Cosmology, inflation and the origin of structure (Cambridge University Press, Cambridge, UK) 2009.
Traschen J. H. and Brandenberger R. H., Phys. Rev. D, 42 (1990) 2491.
Albrecht A. and Steinhardt P. J., Phys. Rev. Lett., 48 (1982) 1220.
Linde A. D., Phys. Lett. B, 129 (1983) 177.
Linde A. D., Phys. Rev. D, 49 (1994) 748.
Garcia-Bellido J. and Linde A. D., Phys. Rev. D, 57 (1998) 6075.
Felder G. N., Garcia-Bellido J., Greene P. B., Kofman L., Linde A. D. and Tkachev I., Phys. Rev. Lett., 87 (2001) 011601.
Garcia-Bellido J., Garcia Perez M. and Gonzalez-Arroyo A., Phys. Rev. D, 67 (2003) 103501.
Easther R. and Lim E. A., JCAP, 0604 (2006) 010.
Easther R., Giblin J. T. and Lim E. A., Phys. Rev. D, 77 (2008) 103519.
Greene P. B., Kofman L., Linde A. D. and Starobinsky A. A., Phys. Rev. D, 56 (1997) 6175.
Felder G. N. and Kofman L., Phys. Rev. D, 75 (2007) 043518.
Dufaux J. F., Bergman A., Felder G. N., Kofman L. and Uzan J.-P., Phys. Rev. D, 76 (2007) 123517.
Dufaux J.-F., Felder G., Kofman L. and Navros O., JCAP, 0903 (2009) 001.
Felder G. N., Kofman L. and Linde A. D., Phys. Rev. D, 64 (2001) 123517.
Garcia-Bellido J. and Figueroa D. G., Phys. Rev. Lett., 98 (2007) 061302.
Price L. R. and Siemens X., Phys. Rev. D, 78 (2008) 063541.
Garcia-Bellido J., Figueroa D. G. and Sastre A., Phys. Rev. D, 77 (2008) 043517.
Garcia-Bellido J., Preheating the universe in hybrid inflation, in Proceedings of the 33rd Recontres de Moriond fundamental parameters in cosmology 1998, pp. 29–34.
Easther R., Giblin, Jr. J. T. and Lim E. A., Phys. Rev. Lett., 99 (2007) 221301.
Figueroa D. G., García-Bellido J. and Torrentí F., 1602.03085 [astro-ph.CO] preprint (2016).
Figueroa D. G., Aspects of reheating, Ph.D. thesis (Madrid) 2010.
Podolsky D. I., Felder G. N., Kofman L. and Peloso M., Phys. Rev. D, 73 (2006) 023501.
Dufaux J. F., Felder G. N., Kofman L., Peloso M. and Podolsky D., JCAP, 0607 (2006) 006.
Greene B. R., Prokopec T. and Roos T. G., Phys. Rev. D, 56 (1997) 6484.
Bethke L., Figueroa D. G. and Rajantie A., JCAP, 1406 (2014) 047.
Maggiore M., Stochastic backgrounds of gravitational waves, in Proceedings of the Gravitational waves: A challenge to theoretical astrophysics. Trieste, Italy, June 6–9, 2000 2000, pp. 397–414.
Felder G. N. and Tkachev I., Comput. Phys. Commun., 178 (2008) 929.
Figueroa D. G., Garcia-Bellido J. and Rajantie A., JCAP, 1111 (2011) 015.
Huang Z., Phys. Rev. D, 83 (2011) 123509.
Crowder J. and Cornish N. J., Phys. Rev. D, 72 (2005) 083005.
Giblin, Jr. J. T., Price L. R. and Siemens X., JCAP, 1008 (2010) 012.
Enqvist K., Figueroa D. G. and Meriniemi T., Phys. Rev. D, 86 (2012) 061301.
Figueroa D. G. and Meriniemi T., JHEP, 10 (2013) 101.
Figueroa D. G., JHEP, 11 (2014) 145.
Fenu E., Figueroa D. G., Durrer R. and Garcia-Bellido J., JCAP, 0910 (2009) 005.
Bethke L., Figueroa D. G. and Rajantie A., Phys. Rev. Lett., 111 (2013) 011301.
Lozanov K. D. and Amin M. A., hep-ph/1603.05663 preprint (2016).
Weinberg S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York) 1972.
Clifton T., Ferreira P. G., Padilla A. and Skordis C., Phys. Rep., 513 (2012) 1.
Amendola L., Ballesteros G. and Pettorino V., Phys. Rev. D, 90 (2014) 043009.
Pettorino V. and Amendola L., Phys. Lett. B, 742 (2015) 353.
Raveri M., Baccigalupi C., Silvestri A. and Zhou S.-Y., Phys. Rev. D, 91 (2015) 061501.
Xu L., Phys. Rev. D, 91 (2015) 103520.
Saltas I. D., Sawicki I., Amendola L. and Kunz M., Phys. Rev. Lett., 113 (2014) 191101.
Cai Y., Wang Y.-T. and Piao Y.-S., Phys. Rev. D, 91 (2015) 103001.
Dubovsky S., Flauger R., Starobinsky A. and Tkachev I., Phys. Rev. D, 81 (2010) 023523.
Fasiello M. and Ribeiro R. H., JCAP, 1507 (2015) 027.
Malsawmtluangi N. and Suresh P. K., gr-qc/1603.05836 preprint (2016).
Noumi T. and Yamaguchi M., hep-th/1403.6065 preprint (2014).
Creminelli P., Gleyzes J., Noreña J. and Vernizzi F., Phys. Rev. Lett., 113 (2014) 231301.
Burrage C, Cespedes S. and Davis A.-C., gr-qc/1604.08038 preprint (2016).
Blas D., Ivanov M. M., Sawicki I. and Sibiryakov S., gr-qc/1602.04188 preprint (2016).
Ellis J., Mavromatos N. E. and Nanopoulos D. V., gr-qc/1602.04764 (2016).
Collett T. E. and Bacon D., 1602.05882 [astro-ph.HE] preprint (2016).
Bicudo P., gr-qc/1602.04337 preprint (2016).
Abbott B. P. et al., gr-qc/1602.03841 preprint (2016).
Copeland E. J., Sami M. and Tsujikawa S., Int. J. Mod. Phys. D, 15 (2006) 1753.
Amendola L. and Tsujikawa S., Dark energy: theory and observations (Cambridge University Press, New York) 2010.
Sotiriou T. P. and Faraoni V., Rev. Mod. Phys., 82 (2010) 451.
De Felice A. and Tsujikawa S., Phys. Rev. D, 91 (2015) 103506.
Cai Y., Wang Y.-T. and Piao Y.-S., JHEP, 02 (2016) 059.
Bergmann P. G., Int. J. Theor. Phys., 1 (1968) 25.
Nordtvedt, Jr. K., Astrophys. J., 161 (1970) 1059.
Wagoner R. V., Phys. Rev. D, 1 (1970) 3209.
Brans C. and Dicke R. H., Phys. Rev., 124 (1961) 925.
Nicolis A., Rattazzi R. and Trincherini E., Phys. Rev. D, 79 (2009) 064036.
Deffayet C., Deser S. and Esposito-Farese G., Phys. Rev. D, 80 (2009) 064015.
Deffayet C., Esposito-Farese G. and Vikman A., Phys. Rev. D, 79 (2009) 084003.
Deffayet C., Gao X., Steer D. A. and Zahariade G., Phys. Rev. D, 84 (2011) 064039.
de Rham C. and Tolley A. J., JCAP, 1005 (2010) 015.
Kobayashi T., Yamaguchi M. and Yokoyama J., Prog. Theor. Phys., 126 (2011) 511.
Horndeski G. W., Int. J. Theor. Phys., 10 (1974) 363.
Burrage C., de Rham C., Seery D. and Tolley A. J., JCAP, 1101 (2011) 014.
Mizuno S. and Koyama K., Phys. Rev. D, 82 (2010) 103518.
Kobayashi T., Yamaguchi M. and Yokoyama J., Phys. Rev. Lett., 105 (2010) 231302.
Kobayashi T., Yamaguchi M. and Yokoyama J., Phys. Rev. D, 83 (2011) 103524.
Deffayet C., Pujolas O., Sawicki I. and Vikman A., JCAP, 1010 (2010) 026.
Armendariz-Picon C., Damour T. and Mukhanov V. F., Phys. Lett. B, 458 (1999) 209.
Kamada K., Kobayashi T., Yamaguchi M. and Yokoyama J., Phys. Rev. D, 83 (2011) 083515.
Kunimitsu T., Suyama T., Watanabe Y. and Yokoyama J., JCAP, 1508 (2015) 044.
Grishchuk L. P. and Sidorov Yu. V., Phys. Rev. D, 42 (1990) 3413.
Pearle P. M., Phys. Rev. A, 39 (1989) 2277.
Bassi A., Lochan K., Satin S., Singh T. P. and Ulbricht H., Rev. Mod. Phys., 85 (2013) 471.
Perez A., Sahlmann H. and Sudarsky D., Class. Quantum Grav., 23 (2006) 2317.
De Unanue A. and Sudarsky D., Phys. Rev. D, 78 (2008) 043510.
Diez-Tejedor A., Leon G. and Sudarsky D., Gen. Relativ. Gravit., 44 (2012) 2965.
Martin J., Vennin V. and Peter P., Phys. Rev. D, 86 (2012) 103524.
Das S., Lochan K., Sahu S. and Singh T. P., Phys. Rev. D, 88 (2013) 085020 (Erratum: Phys. Rev. D, 89 (2014) 109902).
León G. and Bengochea G. R., Eur. Phys. J. C, 76 (2016) 29.
Polarski D. and Starobinsky A. A., Class. Quantum Grav., 13 (1996) 377.
Martin J. and Vennin V., Phys. Rev. D, 93 (2016) 023505.
Leon G., Bengochea G. R. and Landau S. J., gr-qc/1605.03632 preprint (2016).
Camerini R., Durrer R., Melchiorri A. and Riotto A., Phys. Rev. D, 77 (2008) 101301.
Dodelson S., Phys. Rev. Lett., 112 (2014) 191301.
Caligiuri J. and Kosowsky A., Phys. Rev. Lett., 112 (2014) 191302.
Cai Y.-F., Gong J.-O., Pi S., Saridakis E. N. and Wu S.-Y., Nucl. Phys. B, 900 (2015) 517.
Biagetti M., Kehagias A. and Riotto A., Phys. Rev. D, 91 (2015) 103527.
Ashoorioon A., Phys. Lett. B, 747 (2015) 446.
Cai Y.-F., Easson D. A. and Brandenberger R., JCAP, 1208 (2012) 020.
Cai Y.-F., McDonough E., Duplessis F. and Brandenberger R. H., JCAP, 1310 (2013) 024.
Gong J.-O., JCAP, 1407 (2014) 022.
Wands D., Bartolo N., Matarrese S. and Riotto A., Phys. Rev. D, 66 (2002) 043520.
Price L. C., Peiris H. V., Frazer J. and Easther R., Phys. Rev. Lett., 114 (2015) 031301.
Chen X., Huang M.-x., Kachru S. and Shiu G., JCAP, 0701 (2007) 002.
Matarrese S. and Riotto A., JCAP, 0308 (2003) 007.
Das S., Sahu S., Banerjee S. and Singh T. P., Phys. Rev. D, 90 (2014) 043503.
Wang Y. and Xue W., JCAP, 1410 (2014) 075.
Ashoorioon A., Dimopoulos K., Sheikh-Jabbari M. M. and Shiu G., Phys. Lett. B, 737 (2014) 98.
Cai Y.-F. and Wang Y., Phys. Lett. B, 735 (2014) 108.
Unnikrishnan S. and Shankaranarayanan S., JCAP, 1407 (2014) 003.
Meerburg P. D., Hlozek R., Hadzhiyska B. and Meyers J., Phys. Rev. D, 91 (2015) 103505.
Cabass G., Pagano L., Salvati L., Gerbino M., Giusarma E. and Melchiorri A., Phys. Rev. D, 93 (2016) 063508.
Lasky P. D. et al., Phys. Rev. X, 6 (2016) 011035.
Boyle L., Smith K. M., Dvorkin C. and Turok N., Phys. Rev. D, 92 (2015) 043504.
Errard J., Feeney S. M., Peiris H. V. and Jaffe A. H., JCAP, 1603 (2016) 052.
Huang Q.-G., Wang S. and Zhao W., JCAP, 1510 (2015) 035.
Kuroyanagi S., Nakayama K. and Yokoyama J., PTEP, 2015 (2015) 013E02.
Kuroyanagi S., Nakayama K. and Saito S., Phys. Rev. D, 84 (2011) 123513.
Kuroyanagi S., Chiba T. and Sugiyama N., Phys. Rev. D, 83 (2011) 043514.
Boyle L. A. and Steinhardt P. J., Phys. Rev. D, 77 (2008) 063504.
Seto N. and Yokoyama J., J. Phys. Soc. Jap., 72 (2003) 3082.
Kuroyanagi S., Tsujikawa S., Chiba T. and Sugiyama N., Phys. Rev. D, 90 (2014) 063513.
Nakayama K., Saito S., Suwa Y. and Yokoyama J., JCAP, 0806 (2008) 020.
Kuroyanagi S., Takahashi T. and Yokoyama S., JCAP, 1502 (2015) 003.
Nakayama K., Saito S., Suwa Y. and Yokoyama J., Phys. Rev. D, 77 (2008) 124001.
Dai L., Kamionkowski M. and Wang J., Phys. Rev. Lett., 113 (2014) 041302.
Zhao W. and Zhang Y., Phys. Rev. D, 74 (2006) 043503.
Turner M. S., White M. J. and Lidsey J. E., Phys. Rev. D, 48 (1993) 4613.
Jinno R., Moroi T. and Takahashi T., JCAP, 1412 (2014) 006.
Jinno R., Moroi T. and Nakayama K., JCAP, 1401 (2014) 040.
Smith T. L., Kamionkowski M. and Cooray A., Phys. Rev. D, 73 (2006) 023504.
Smith T. L., Kamionkowski M. and Cooray A., Phys. Rev. D, 78 (2008) 083525.
Gong J.-O., Pi S. and Leung G., JCAP, 1505 (2015) 027.
Martin J., Ringeval C. and Vennin V., Phys. Rev. Lett., 114 (2015) 081303.
Martin J. and Ringeval C., Phys. Rev. D, 82 (2010) 023511.
Creminelli P., Nacir D. L., Simonovi M., Trevisan G. and Zaldarriaga M., Phys. Rev. D, 90 (2014) 083513.
Munoz J. B. and Kamionkowski M., Phys. Rev. D, 91 (2015) 043521.
Cook J. L., Dimastrogiovanni E., Easson D. A. and Krauss L. M., JCAP, 1504 (2015) 047.
Cai R.-G., Guo Z.-K. and Wang S.-J., Phys. Rev. D, 92 (2015) 063506.
Ade P. A. R. et al., Astron. Astrophys., 571 (2014) A22.
Kinney W. H. and Riotto A., JCAP, 0603 (2006) 011.
Liddle A. R. and Leach S. M., Phys. Rev. D, 68 (2003) 103503.
Domcke V. and Heisig J., Phys. Rev. D, 92 (2015) 103515.
Weinberg S., Phys. Rev. D, 69 (2004) 023503.
Bashinsky S., submitted to Phys. Rev. D, eprint: astro-ph/0505502.
Dicus D. A. and Repko W. W., Phys. Rev. D, 72 (2005) 088302.
Zhao W., Zhang Y. and Xia T., Phys. Lett. B, 677 (2009) 235.
Jinno R., Moroi T. and Nakayama K., Phys. Rev. D, 86 (2012) 123502.
Shchedrin G., gr-qc/1204.1384 preprint (2012).
Stefanek B. A. and Repko W. W., Phys. Rev. D, 88 (2013) 083536.
Dent J. B., Krauss L. M., Sabharwal S. and Vachaspati T., Phys. Rev. D, 88 (2013) 084008.
Mangilli A., Bartolo N., Matarrese S. and Riotto A., Phys. Rev. D, 78 (2008) 083517.
Saga S., Ichiki K. and Sugiyama N., Phys. Rev. D, 91 (2015) 024030.
Lattanzi M., Benini R. and Montani G., Class. Quantum Grav., 27 (2010) 194008.
Kamionkowski M. and Kosowsky A., Annu. Rev. Nucl. Part. Sci., 49 (1999) 77.
Hu W. and Dodelson S., Annu. Rev. Astron. Astrophys., 40 (2002) 171.
Dodelson S., Modern Cosmology (Academic Press, Amsterdam) 2003.
Hu W. and White M. J., New Astron., 2 (1997) 323.
Rees M. J., Astronphys. J., 153 (1968) 1.
Kosowsky A., Ann. Phys., 246 (1996) 49.
Cabella P. and Kamionkowski M., Theory of cosmic microwave background polarization, presented at International School of Gravitation and Cosmology: The Polarization of the Cosmic Microwave Background Rome, Italy, September 6–11, 2003 2004.
Kamionkowski M. and Kovetz E. D., 1510.06042 [astro-ph.CO] preprint (2015).
Kamionkowski M., Kosowsky A. and Stebbins A., Phys. Rev. D, 55 (1997) 7368.
Zaldarriaga M. and Seljak U., Phys. Rev. D, 55 (1997) 1830.
Newman E. and Penrose R., J. Math. Phys., 3 (1962) 566.
Adam R. et al., 1502.01588 [astro-ph.CO] preprint (2015).
Lewis A., Challinor A. and Turok N., Phys. Rev. D, 65 (2002) 023505.
Knox L. and Song Y.-S., Phys. Rev. Lett., 89 (2002) 011303.
Kesden M., Cooray A. and Kamionkowski M., Phys. Rev. Lett., 89 (2002) 011304.
Hu W. and Okamoto T., Astrophys. J., 574 (2002) 566.
Peiris H. V. et al., Astrophys. J. Suppl., 148 (2003) 213.
Galli S., Benabed K., Bouchet F., Cardoso J.-F., Elsner F., Hivon E., Mangilli A., Prunet S. and Wandelt B., Phys. Rev. D, 90 (2014) 063504.
Polnarev A. G., Miller N. J. and Keating B. G., Mon. Not. R. Astron. Soc., 386 (2008) 1053.
Ade P. A. R. et al., 1502.01594 [astro-ph.CO] preprint (2015).
Feng B., Li H., Li M.-z. and Zhang X.-m., Phys. Lett. B, 620 (2005) 27.
Li M. and Zhang X., Phys. Rev. D, 78 (2008) 103516.
Ade P. A. R. et al., Phys. Rev. Lett., 112 (2014) 241101.
Ade P. et al., Phys. Rev. Lett., 114 (2015) 101301.
Kamionkowski M. and Souradeep T., Phys. Rev. D, 83 (2011) 027301.
Shiraishi M., Nitta D., Yokoyama S., Ichiki K. and Takahashi K., Prog. Theor. Phys., 125 (2011) 795.
Shiraishi M., Yokoyama S., Ichiki K. and Takahashi K., Phys. Rev. D, 82 (2010) 103505.
Shiraishi M., Nitta D. and Yokoyama S., Prog. Theor. Phys., 126 (2011) 937.
Meerburg P. D., Meyers J., van Engelen A. and Ali-Haïmoud Y., Phys. Rev. D, 93 (2016) 123511.
Jeong D. and Kamionkowski M., Phys. Rev. Lett., 108 (2012) 251301.
Schmidt F., Pajer E. and Zaldarriaga M., Phys. Rev. D, 89 (2014) 083507.
Dai L., Jeong D. and Kamionkowski M., Phys. Rev. D, 88 (2013) 043507.
Schmidt F. and Jeong D., Phys. Rev. D, 86 (2012) 083513.
Schmidt F. and Jeong D., Phys. Rev. D, 86 (2012) 083527.
Dai L., Kamionkowski M. and Jeong D., Phys. Rev. D, 86 (2012) 125013.
Cooray A., Kamionkowski M. and Caldwell R. R., Phys. Rev. D, 71 (2005) 123527.
Li C. and Cooray A., Phys. Rev. D, 74 (2006) 023521.
Book L. G., Kamionkowski M. and Souradeep T., Phys. Rev. D, 85 (2012) 023010.
Book L., Kamionkowski M. and Schmidt F., Phys. Rev. Lett., 108 (2012) 211301.
Lu T. and Pen U.-L., Mon. Not. R. Astron. Soc., 388 (2008) 1819.
Pen U.-L., New Astron., 9 (2004) 417.
Pajer E., Schmidt F. and Zaldarriaga M., Phys. Rev. D, 88 (2013) 083502.
Ando S. and Kamionkowski M., Phys. Rev. Lett., 100 (2008) 071301.
Pullen A. R. and Kamionkowski M., Phys. Rev. D, 76 (2007) 103529.
Maldacena J. M., JHEP, 05 (2003) 013.
Maldacena J. M. and Pimentel G. L., JHEP, 09 (2011) 045.
Seery D., Sloth M. S. and Vernizzi F., JCAP, 0903 (2009) 018.
Giddings S. B. and Sloth M. S., JCAP, 1101 (2011) 023.
Giddings S. B. and Sloth M. S., Phys. Rev. D, 84 (2011) 063528.
Creminelli P. and Zaldarriaga M., JCAP, 0410 (2004) 006.
Dimastrogiovanni E., Fasiello M., Jeong D. and Kamionkowski M., JCAP, 1412 (2014) 050.
Hanson D. and Lewis A., Phys. Rev. D, 80 (2009) 063004.
Dai L., Jeong D. and Kamionkowski M., Phys. Rev. D, 87 (2013) 103006.
Akhshik M., JCAP, 1505 (2015) 043.
Endlich S., Horn B., Nicolis A. and Wang J., Phys. Rev. D, 90 (2014) 063506.
Dimastrogiovanni E., Fasiello M. and Kamionkowski M., (2015).
Brahma S., Nelson E. and Shandera S., Phys. Rev. D, 89 (2014) 023507.
Mangano G., Miele G., Pastor S. and Peloso M., Phys. Lett. B, 534 (2002) 8.
Weinberg S., Cosmology (Oxford University Press, Oxford, UK) 2008.
Hou Z., Keisler R., Knox L., Millea M. and Reichardt C., Phys. Rev. D, 87 (2013) 083008.
Pagano L., Salvati L. and Melchiorri A., 1508.02393 [astro-ph.CO] preprint (2015).
Boyle L. A. and Buonanno A., Phys. Rev. D, 78 (2008) 043531.
Nakama T. and Suyama T., Phys. Rev. D, 92 (2015) 121304.
Nakama T. and Suyama T., gr-qc/1605.04482 preprint (2016).
Polnarev A. G., Sov. Astron., 29 (1985) 607.
Ota A., Takahashi T., Tashiro H. and Yamaguchi M., JCAP, 1410 (2014) 029.
Chluba J., Dai L., Grin D., Amin M. and Kamionkowski M., Mon. Not. R. Astron. Soc., 446 (2015) 2871.
Bashinsky S. and Seljak U., Phys. Rev. D, 69 (2004) 083002.
Dodelson S., Phys. Rev. D, 82 (2010) 023522.
Joshi B. C., Int. J. Mod. Phys. D, 22 (2013) 1341008.
Moore C. J., Cole R. H. and Berry C. P. L., Class. Quantum Grav., 32 (2015) 015014.
Huang Q.-G. and Wang S., JCAP, 1506 (2015) 021.
Abbott B. P. et al., Rep. Prog. Phys., 72 (2009) 076901.
Manchester R. N. et al., Publ. Astron. Soc. Austral., 30 (2013) 17.
Ade P. A. R. et al., Astron. Astrophys., 571 (2014) A16.
Page L. et al., Astrophys. J. Suppl., 170 (2007) 335.
Scoville N. et al., Astrophys. J. Suppl., 172 (2007) 38.
York D. G. et al., Astron. J., 120 (2000) 1579.
Verde L., Peiris H. and Jimenez R., JCAP, 0601 (2006) 019.
Adam R. et al., 1502.01582 [astro-ph.CO] preprint (2015).
Lentati L. et al., Mon. Not. R. Astron. Soc., 453 (2015) 2576.
McLaughlin M. A., Class. Quantum Grav., 30 (2013) 224008.
Janssen G. et al., PoS A, ASKA14 (2015) 037.
Abadie J. et al., Phys. Rev. D, 81 (2010) 102001.
Aasi J. et al., Phys. Rev. Lett., 113 (2014) 231101.
Abbott B. P. et al., Phys. Rev. Lett., 116 (2016) 131102.
Unnikrishnan C. S., Int. J. Mod. Phys. D, 22 (2013) 1341010.
Aso Y., Michimura Y., Somiya K., Ando M., Miyakawa O., Sekiguchi T., Tatsumi D. and Yamamoto H., Phys. Rev. D, 88 (2013) 043007.
Punturo M. et al., Class. Quantum Grav., 27 (2010) 194002.
Kawamura S. et al., Class. Quantum Grav., 28 (2011) 094011.
Kuroda K., Ni W.-T. and Pan W.-P., Int. J. Mod. Phys. D, 24 (2015) 1530031.
Thrane E. and Romano J. D., Phys. Rev. D, 88 (2013) 124032.
Petiteau A., to appear.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guzzetti, M.C., Bartolo, N., Liguori, M. et al. Gravitational waves from inflation. Riv. Nuovo Cim. 39, 399–495 (2016). https://doi.org/10.1393/ncr/i2016-10127-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1393/ncr/i2016-10127-1