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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 

Inflation ends at ϵ$_{1}$ ( φ$_{end}$ ) = 1, which gives the value of the field at the end of inflation 

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 : 

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. 

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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]. 

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. 

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 

