Abstract
In this chapter, we investigate the cosmic microwave background (CMB) bispectra of the intensity (temperature) and polarization modes induced by the graviton non-Gaussianities, which arise from the parity-conserving and parity-violating Weyl cubic terms with time-dependent coupling. By considering the time-dependent coupling, we find that even in the exact de Sitter space-time, the parity violation still appears in the three-point function of the primordial gravitational waves and could become large. Through the estimation of the CMB bispectra, we demonstrate that the signals generated from the parity-conserving and parity-violating terms appear in completely different configurations of multipoles. This signal is just good evidence of the parity violation in the non-Gaussianity of primordial gravitational waves. We find that the shape of this non-Gaussianity is similar to the so-called equilateral one. We naively estimate the observational bound on the model parameters.
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Notes
- 1.
\(\gamma _{ij}\) is identical to \(h_{ij}\) in Sect. 2.6.
- 2.
Here, we set that \(\tau _{*} < 0\).
- 3.
In Ref. [12], the authors have shown that for \(A=0\), the bispectrum from \(\widetilde{W}W^2\) has a nonzero value upward in the first order of the slow-roll parameter.
- 4.
The conventional expression of the CMB-reduced bispectrum as
$$\begin{aligned} b_{{X_1}{X_2}{X_3},{\ell _1}{\ell _2}{\ell _3}} \equiv (I_{{\ell _1}{\ell _2} {\ell _3}}^{0~0~0})^{-1} \sum _{{m_1}{m_2}{m_3}} \left( \begin{array}{ccc} \ell _1 &{} \ell _2 &{} \ell _3 \\ m_1 &{} m_2 &{} m_3 \end{array} \right) {\langle {\prod _{n=1}^3 a_{{X_n},{\ell _n}{m_n}}}\rangle } \end{aligned}$$(8.56)breaks down for \(\sum \nolimits _{n=1}^{3} \ell _n = \mathrm{odd }\) due to the divergence behavior of \((I_{\ell _1 \ell _2 \ell _3}^{0~0~0})^{-1}\). Here, replacing the \(I\) symbol with the \(G\) symbol, this problem is avoided. Of course, for \(\sum \nolimits _{n=1}^{3} \ell _n = \mathrm{even }\), \(G_{\ell _1 \ell _2 \ell _3}\) is identical to \(I_{\ell _1 \ell _2 \ell _3}^{0~0~0}\).
References
E. Komatsu, D.N. Spergel, Phys. Rev. D63, 063002 (2001). doi:10.1103/PhysRevD.63.063002
N. Bartolo, E. Komatsu, S. Matarrese, A. Riotto, Phys. Rep. 402, 103 (2004). doi:10.1016/j.physrep.2004.08.022
D. Babich, P. Creminelli, M. Zaldarriaga, JCAP 0408, 009 (2004). doi:10.1088/1475-7516/2004/08/009
E. Komatsu, et al., Astrophys. J. Suppl. 192, 18 (2011). doi:10.1088/0067-0049/192/2/18
J.M. Maldacena, JHEP 05, 013 (2003). doi:10.1088/1126-6708/2003/05/013
I. Brown, R. Crittenden, Phys. Rev. D72, 063002 (2005). doi:10.1103/PhysRevD.72.063002
P. Adshead, E.A. Lim, Phys. Rev. D82, 024023 (2010). doi:10.1103/PhysRevD.82.024023
M. Shiraishi, D. Nitta, S. Yokoyama, K. Ichiki, K. Takahashi, Prog. Theor. Phys. 125, 795 (2011). doi:10.1143/PTP.125.795
M. Shiraishi, D. Nitta, S. Yokoyama, K. Ichiki, K. Takahashi, Phys. Rev. D83, 123003 (2011). doi:10.1103/PhysRevD.83.123003
M. Shiraishi, S. Yokoyama, Prog. Theor. Phys. 126, 923 (2011). doi:10.1143/PTP.126.923
J.M. Maldacena, G.L. Pimentel, JHEP 1109, 045 (2011). doi:10.1007/JHEP09(2011)045
J. Soda, H. Kodama, M. Nozawa, JHEP 1108, 067 (2011). doi:10.1007/JHEP08(2011)067
S. Weinberg, Phys. Rev. D77, 123541 (2008). doi:10.1103/PhysRevD.77.123541
S. Alexander, J. Martin, Phys. Rev. D71, 063526 (2005). doi:10.1103/PhysRevD.71.063526
S. Saito, K. Ichiki, A. Taruya, JCAP 0709, 002 (2007). doi:10.1088/1475-7516/2007/09/002
V. Gluscevic, M. Kamionkowski, Phys. Rev. D81, 123529 (2010). doi:10.1103/PhysRevD.81.123529
L. Sorbo, JCAP 1106, 003 (2011). doi:10.1088/1475-7516/2011/06/003
T. Okamoto, W. Hu, Phys. Rev. D66, 063008 (2002). doi:10.1103/PhysRevD.66.063008
M. Kamionkowski, T. Souradeep, Phys. Rev. D83, 027301 (2011). doi:10.1103/PhysRevD.83.027301
M. Shiraishi, D. Nitta, S. Yokoyama, Prog. Theor. Phys. 126, 937 (2011). doi:10.1143/PTP.126.937
S. Weinberg, Phys. Rev. D72, 043514 (2005). doi:10.1103/PhysRevD.72.043514
L. Senatore, K.M. Smith, M. Zaldarriaga, JCAP 1001, 028 (2010). doi:10.1088/1475-7516/2010/01/028
A. Lewis, A. Challinor, A. Lasenby, Astrophys. J. 538, 473 (2000). doi:10.1086/309179.
A. Lewis, Phys. Rev. D70, 043011 (2004). doi:10.1103/PhysRevD.70.043011.
Slatec common mathematical library. http://www.netlib.org/slatec/
J.R. Pritchard, M. Kamionkowski, Annals Phys. 318, 2 (2005). doi:10.1016/j.aop.2005.03.005
D. Baskaran, L.P. Grishchuk, A.G. Polnarev, Phys. Rev. D74, 083008 (2006). doi:10.1103/PhysRevD.74.083008
P. Creminelli, A. Nicolis, L. Senatore, M. Tegmark, M. Zaldarriaga, JCAP 0605, 004 (2006). doi:10.1088/1475-7516/2006/05/004
P. Creminelli, L. Senatore, M. Zaldarriaga, M. Tegmark, JCAP 0703, 005 (2007). doi:10.1088/1475-7516/2007/03/005
K.M. Smith, M. Zaldarriaga, Mon. Not. Roy. Astron. Soc. 417, 2 (2011). doi:10.1111/j.1365-2966.2010.18175.x
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Shiraishi, M. (2013). Parity Violation of Gravitons in the CMB Bispectrum. In: Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54180-6_8
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