Note on gauge invariance of second order cosmological perturbations

[1]
J. M. Bardeen, Phys. Rev. D 22, 1882 (1980)
[2]
G. F. R. Ellis and M. Bruni, Phys. Rev. D 40, 1804 (1989)
[3]
M. Bruni, P. K. S. Dunsby, and G. F. R. Ellis, Astrophys. J. 395, 34 (1992)
[4]
C. F. Sopuerta, M. Bruni, and L. Gualtieri, Phys. Rev. D 70, 064002 (2004), arXiv:gr-qc/0306027
[5]
M. Bruni, S. Matarrese, S. Mollerach et al., Class. Quant. Grav. 14, 2585 (1997), arXiv:gr-qc/9609040[gr-qc
[6]
S. Sonego and M. Bruni, Commun. Math. Phys. 193, 209 (1998), arXiv:gr-qc/9708068
[7]
K. Nakamura, Phys. Rev. D 74, 101301 (2006), arXiv:grqc/0605107[gr-qc
[8]
V. F. Mukhanov, H. Feldman, and R. H. Brandenberger, Phys. Rept. 215, 203 (1992)
[9]
P. A. Zyla et al. (Particle Data Group), PTEP 2020, 083C01 (2020)
[10]
S. Matarrese, S. Mollerach, and M. Bruni, Phys. Rev. D 58, 043504 (1998), arXiv:astro-ph/9707278
[11]
K. A. Malik and D. Wands, Phys. Rept. 475, 1 (2009), arXiv:0809.4944[astro-ph
[12]
G. Domènech and M. Sasaki, Phys. Rev. D 97, 023521 (2018), arXiv:1709.09804[gr-qc
[13]
J.-O. Gong, (2019), arXiv: 1909.12708[gr-qc]
[14]
D. H. Lyth and Y. Rodriguez, Phys. Rev. D 71, 123508 (2005), arXiv:astro-ph/0502578
[15]
M. Bruni, R. Crittenden, K. Koyama et al., Phys. Rev. D 85, 041301 (2012), arXiv:1106.3999[astro-ph.CO
[16]
M. Bruni and S. Sonego, Class. Quant. Grav. 16, L29 (1999), arXiv:gr-qc/9906017
[17]
J. Yoo and R. Durrer, JCAP 09, 016 (2017), arXiv:1705.05839 [astro-ph.CO
[18]
K. Nakamura, Class. Quant. Grav. 31, 135013 (2014), arXiv:1403.1004[gr-qc
[19]
S. Mollerach, D. Harari, and S. Matarrese, Phys. Rev. D 69, 063002 (2004), arXiv:astro-ph/0310711
[20]
K. N. Ananda, C. Clarkson, and D. Wands, Phys. Rev. D 75, 123518 (2007), arXiv:gr-qc/0612013
[21]
D. Baumann, P. J. Steinhardt, K. Takahashi et al., Phys. Rev. D 76, 084019 (2007), arXiv:hep-th/0703290
[22]
H. Assadullahi and D. Wands, Phys. Rev. D 81, 023527 (2010), arXiv:0907.4073[astro-ph.CO
[23]
S. Saga, K. Ichiki, and N. Sugiyama, Phys. Rev. D 91, 024030 (2015), arXiv:1412.1081[astro-ph.CO
[24]
L. Alabidi, K. Kohri, M. Sasaki et al., JCAP 09, 017 (2012), arXiv:1203.4663[astro-ph.CO
[25]
L. Alabidi, K. Kohri, M. Sasaki et al., JCAP 05, 033 (2013), arXiv:1303.4519[astro-ph.CO
[26]
K. Inomata and T. Nakama, Phys. Rev. D 99, 043511 (2019), arXiv:1812.00674[astro-ph.CO
[27]
N. Orlofsky, A. Pierce, and J. D. Wells, Phys. Rev. D 95, 063518 (2017), arXiv:1612.05279[astro-ph.CO
[28]
I. Ben-Dayan, B. Keating, D. Leon et al., JCAP 06, 007 (2019), arXiv:1903.11843[astro-ph.CO
[29]
K. Kohri and T. Terada, Phys. Rev. D 97, 123532 (2018), arXiv:1804.08577[gr-qc
[30]
J. R. Espinosa, D. Racco, and A. Riotto, JCAP 09, 012 (2018), arXiv:1804.07732[hep-ph
[31]
S. Wang, T. Terada, and K. Kohri, Phys. Rev. D 99, 103531 (2019), arXiv:1903.05924[astro-ph.CO
[32]
S. J. Kapadia, K. L. Pandey, T. Suyama et al., Phys. Rev. D 101, 123535 (2020), arXiv:2005.05693[astro-ph.CO
[33]
S. J. Kapadia, K. L. Pandey, T. Suyama et al., (2020), arXiv: 2009.05514[gr-qc]
[34]
R.-g. Cai, S. Pi, and M. Sasaki, Phys. Rev. Lett. 122, 201101 (2019), arXiv:1810.11000[astro-ph.CO
[35]
C. Yuan, Z.-C. Chen, and Q.-G. Huang, Phys. Rev. D 101, 043019 (2020), arXiv:1910.09099[astro-ph.CO
[36]
C. Yuan and Q.-G. Huang, (2020), arXiv: 2007.10686[astroph.CO]
[37]
E. Bugaev and P. Klimai, Phys. Rev. D 81, 023517 (2010)
[38]
E. Bugaev and P. Klimai, Phys. Rev. D 83, 083521 (2011), arXiv:1012.4697[astro-ph.CO
[39]
R. Saito and J. Yokoyama, Phys. Rev. Lett. 102, 161101 (2009), [Erratum: Phys. Rev. Lett.107, 069901(2011)], arXiv: 0812.4339[astro-ph]
[40]
R. Saito and J. Yokoyama, Prog. Theor. Phys. 123, 867 (2010), [Erratum: Prog. Theor. Phys.126, 351(2011)], arXiv: 0912.5317[astro-ph.CO]
[41]
T. Nakama and T. Suyama, Phys. Rev. D 94, 043507 (2016), arXiv:1605.04482[gr-qc
[42]
Y.-F. Cai, C. Chen, X. Tong et al., Phys. Rev. D 100, 043518 (2019), arXiv:1902.08187[astro-ph.CO
[43]
K. Inomata and T. Terada, Phys. Rev. D 101, 023523 (2020), arXiv:1912.00785[gr-qc
[44]
C. Yuan, Z.-C. Chen, and Q.-G. Huang, Phys. Rev. D 101, 063018 (2020), arXiv:1912.00885[astro-ph.CO
[45]
M. Giovannini, (2020), arXiv: 2005.04962[hep-th]
[46]
J.-C. Hwang, D. Jeong, and H. Noh, Astrophys. J. 842, 46 (2017), arXiv:1704.03500[astro-ph.CO
[47]
Y. Lu, A. Ali, Y. Gong et al., (2020), arXiv: 2006.03450[gr-qc]
[48]
V. De Luca, G. Franciolini, A. Kehagias et al., JCAP 2003, 014 (2020), arXiv:1911.09689[gr-qc
[49]
K. Tomikawa and T. Kobayashi, Phys. Rev. D 101, 083529 (2020), arXiv:1910.01880[gr-qc
[50]
E. Bertschinger, in Les Houches Summer School on Cosmology and Large Scale Structure (Session 60) (1993) pp. 273–348, arXiv: astro-ph/9503125
[51]
E. Lifshitz, J. Phys. (USSR) 10, 116 (1946)
[52]
K. Nakamura, PTEP 043, (2013), arXiv:1105.4007[gr-qc
[53]
K. Nakamura, Prog. Theor. Phys. 117, 17 (2007), arXiv:grqc/0605108
[54]
K. Nakamura, (2020), 10.9734/bpi/taps/v3, arXiv: 1912.12805 [gr-qc]
[55]
M. Hohmann, Phys. Rev. D 101, 024061 (2020), arXiv:1910.09245[gr-qc
[56]
C. Uggla and J. Wainwright, Class. Quant. Grav. 29, 105002 (2012), arXiv:1112.0880[gr-qc
[57]
K. A. Malik and D. Wands, (1998), arXiv: gr-qc/9804046
[58]
K. Inomata, (2020), arXiv: 2008.12300[gr-qc]
[59]
C. Pitrou, X. Roy, and O. Umeh, Class. Quant. Grav. 30, 165002 (2013), arXiv:1302.6174[astro-ph.CO
[60]
S. Weinberg, Cosmology (2008)
[61]
M. Maggiore, Gravitational Waves. Vol. 2: Astrophysics and Cosmology (Oxford University Press, 2018)
[62]
J. W. York, Jr., Annales de L’Institut Henri Poincare Section (A) Physique Theorique 21, 319 (1974)