6 field theory of phantom-type fields encounters the prob- lem of stability. In this case, the GB term with the pos- itive (or negative) coupling slows down (or speeds up) the evolution of the inflaton during inflation, which de- creases (or increases) the energy scale of the potential to be in agreement with the amplitude of scalar pertur- bations. However the amplitude of tensor perturbations only depends on the energy scale of the potential at the horizon-crossing time. Therefore, the tensor-to-scalar ra- tio is suppressed for α > 0 while it is enhanced for α < 0. As shown in Fig. 2, the model parameter α can shift the predicted r vertically for a fixed number of e-folds in the n$_{R}$ - r plane. For n = 2, the quadratic potential can be made a better fit to the data by the positive GB coupling. For n = 4, it is known that the model with α = 0 is excluded by the WMAP7+BAO+ H$_{0}$ analysis. However, in our scenario of inflation α > 0 . 7 is within the 2 σ contour for N > 50, and it is consistent with the data within the 95% confidence level. that the joint constraint on n$_{R}$ and r becomes a little tighter. The WMAP7+BAO+ H$_{0}$ data do not constrain n$_{T}$ . Basically all values allowed by the prior are also allowed by the potential and the coupling. In Fig. 2 we plot the values of n$_{R}$ and r in the models with n = 2 (top panel) and n = 4 (bottom panel) for different values of N and α . We can see that the model parameter α can shift the predicted r vertically for a fixed number of e-folds. For n = 2, the model with a positive α is more favored observationally. For n = 4, the model with α > 0 . 7 is consistent with the data within the 95% confidence level, in which the prediction for the tensor- to-scalar ratio is smaller than the α = 0 case while the prediction for n$_{R}$ is the same as the α = 0 case. Other ways to avoid the exclusion of the φ 4 potential have been studied in Ref. [18]. The results of this work are generic as soon as nonmin- imal couplings are considered. While it is always possible by means of a conformal transformation to work in the Einstein frame and to avoid the presence of a φ $^{2}$R term in the Lagrangian, the coupling of the scalar field to the GB term cannot be argued away by the same conformal transformation. While we studied perturbation spectra in the Einstein frame, similar properties hold in the Jor- dan frame. In this paper we have studied slow-roll inflation with a nonminimally coupled Gauss-Bonnet term. We have defined a combined hierarchy ( ϵ$_{i}$, δ$_{i}$ ) of Hubble and GB flow functions such that | ϵ$_{i}$ | ≪ 1 and | δ$_{i}$ | ≪ 1 is the analogue of the standard slow-roll approximation. It has been demonstrated that slow-roll solution is the attrac- tor solution under the slow-roll condition. We have an- alytically derived the power spectra of scalar and tensor perturbations. In general the spectral index of scalar per- turbations depends on the Hubble flow parameters and the GB flow parameters. However, the spectral index of tensor perturbations is independent of the GB flow pa- rameters to first order in the slow-roll approximation. In this scenario the standard consistency relation does not hold because of the GB correction. We thank H.-T. Ding and E. Komatsu for useful dis- cussions. Our numerical analysis was performed on the HPC cluster of the RWTH Aachen University. This work was supported by the Alexander von Humboldt Founda- tion. We apply our general formalism to large-field inflation with a monomial potential and the GB coupling (49). We focus on the case of ω = 1 and α < 1 since the Acknowledgments V. CONCLUSIONS AND DISCUSSIONS S. Tsujikawa, Phys. Lett. B 526 , 179 (2002) [arXiv:gr- qc/0110124]; A. Toporensky and S. Tsujikawa, Phys. Rev. D 65 , 123509 (2002) [arXiv:gr-qc/0202067]. [5] S. Tsujikawa, R. Brandenberger and F. Finelli, Phys. Rev. D 66 , 083513 (2002) [arXiv:hep-th/0207228]. [6] K. Bamba, Z. K. Guo and N. Ohta, Prog. Theor. Phys. 118 , 879 (2007) [arXiv:0707.4334]; K. Andrew, B. Bolen and C. A. Middleton, Gen. Rel. Grav. 39 , 2061 (2007) [arXiv:0708.0373]; R. Chingangbam, M. Sami, P. V. Tretyakov and A. V. Toporensky, Phys. Lett. B 661 , 162 (2008) [arXiv:0711.2122]; I. V. Kirnos and A. N. Makarenko, arXiv:0903.0083. [7] M. Satoh, S. Kanno and J. Soda, Phys. Rev. D 77 , 023526 (2008) [arXiv:0706.3585]; M. Satoh and J. Soda, JCAP 0809 , 019 (2008) [arXiv:0806.4594]. [8] S. Nojiri, S. D. Odintsov and M. Sasaki, Phys. Rev. D 71 , 123509 (2005) [arXiv:hep-th/0504052]; G. Cog- nola, E. Elizalde, S. Nojiri, S. D. Odintsov and [1] V. F. Mukhanov, H. A. Feldman and R. H. Bran- denberger, Phys. Rept. 215 , 203 (1992); D. H. Lyth and A. Riotto, Phys. Rept. 314 , 1 (1999) [arXiv:hep- ph/9807278]; K. A. Malik and D. Wands, Phys. Rept. 475 , 1 (2009) [arXiv:0809.4944]. [2] J. E. Lidsey, A. R. Liddle, E. W. Kolb, E. J. Copeland, T. Barreiro and M. Abney, Rev. Mod. Phys. 69 , 373 (1997) [arXiv:astro-ph/9508078]; B. A. Bassett, S. Tsu- jikawa and D. Wands, Rev. Mod. Phys. 78 , 537 (2006) [arXiv:astro-ph/0507632]. [3] D. J. Grossa and J. H. Sloana, Nucl. Phys. B 291 , 41 (1987); M. Gasperini, M. Maggiore and G. Veneziano, Nucl. Phys. B 494 , 315 (1997) [arXiv:hep-th/9611039]. [4] I. Antoniadis, J. Rizos and K. Tamvakis, Nucl. Phys. B 415 , 497 (1994) [arXiv:hep-th/9305025]; S. Kawai, M. a. Sakagami and J. Soda, Phys. Lett. B 437 , 284 (1998) [arXiv:gr-qc/9802033]; S. Kawai and J. Soda, Phys. Lett. B 460 , 41 (1999) [arXiv:gr-qc/9903017];