5 n$_{R}$ r 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 =0 =0.3 =−0.3 N=50 N=60 n$_{R}$ r 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 =0 =0.3 =0.7 N=50 N=60 n$_{R}$ r 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 4 2 N=50 N=60 FIG. 1: Two-dimensional joint marginalized constraint (68% and 95% confidence level) on the scalar spectral index n$_{R}$ and the tensor-to-scalar ratio r derived from the data combi- nation of WMAP7+BAO+ H 0 by imposing the standard con- sistency relation. The symbols show the predictions from the φ $^{4}$-potential (solid line) and φ $^{2}$-potential (dashed line) models with the number of e-folds equal to 50 (small) and 60 (large). FIG. 2: Tensor-to-scalar ratio r versus the spectral index n$_{R}$ for the inflation model (49) with n = 2 (top panel) and n = 4 (bottom panel). The contours show the 68% and 95% con- fidence level derived from WMAP7+BAO+ H 0 without the consistency relation. to roll down. Since the GB force dominates over the po- tential force, slow-roll inflation can be realized. In what follows we restrict our discussion to the case of α < 1. The flow parameters are From Eqs. (42) and (44) one gets The GB correction leads to a reduction of the tensor-to- scalar ratio if ξ$_{0}$ > 0 while an enhancement if ξ$_{0}$ < 0, which is still valid in the power-law inflation model with the exponential potential and GB coupling [11]. Inflation ends at ϵ$_{1}$ ( φ$_{end}$ ) = 1, which gives the value of the field at the end of inflation Figure 1 shows the two-dimensional joint marginalized constraint (68% and 95% confidence level) on n$_{R}$ and r from the 7-year WMAP+BAO+ H$_{0}$ by imposing the standard consistency relation [16]. The symbols show the predictions from the φ $^{4}$-potential (solid line) and φ $^{2}$- potential (dashed line) models with the number of e-folds equal to 50 (small) and 60 (large). We can see that the predicted points with N = 50 , 60 for the quartic poten- tial are far away from the 95% region. The quadratic potential is consistent with the data. Then from (8) we find the value of the field N e-folds before the end of inflation The spectral index n$_{R}$ and the tensor-to-scalar ratio r can be written in terms of the function of N : ϵ$_{1}$ ≃ 1 2 n $^{2}$(1 − α ) φ − $^{2}$, (50) ϵ$_{2}$ ≃ 2 n (1 − α ) φ − $^{2}$, (51) δ$_{1}$ n $^{2}$α (1 α ) φ − $^{2}$, (52) δ$_{2}$ ≃ 2 n (1 − α ) φ − $^{2}$. (53) n$_{R}$ − 1 = − n ( n + 2)(1 − α ) φ − $^{2}$, (54) r = 8 n $^{2}$(1 − α ) $^{2}$φ $^{2}$. (55) φ 2 end = 1 2 n $^{2}$(1 − α ) . (56) φ 2 = 2 n (1 − α )( N + n 4 ) . (57) n$_{R}$ − 1 = − 2( n + 2) 4 N + n , (58) r = 16 n (1 − α ) 4 N + n . (59) However, the consistency relation n$_{T}$ = − r/ 8 is bro- ken in the slow-roll inflation with the GB correction. Therefore, in our analysis, n$_{T}$ is varied independent of the tensor-to-scalar ratio. For the tensor perturbations we assume a power-law power spectrum, with a uniform prior on n$_{T}$ as − 0 . 5 < n$_{T}$ < 0. In Fig. 2 we show the 1 σ and 2 σ contours derived from the data combi- nation of WMAP7+BAO+ H$_{0}$ by using the CosmoMC package [17]. Compared to the contours of Fig. 1 we find Note that the spectral index is independent of V$_{0}$ and ξ$_{0}$ , but the tensor-to-scalar ratio depends on α = 4 V$_{0}$ξ$_{0}$/ 3.