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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 62 , Issue 12 : 120412(2019) https://doi.org/10.1007/s11433-019-9446-1

Inflation model selection revisited

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  • ReceivedJun 6, 2019
  • AcceptedJul 1, 2019
  • PublishedJul 30, 2019
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Abstract

We update the constraints on the power spectra of primordial curvature perturbation and tensor perturbation including Planck data 2015 (P15) and recently released BICEP2/Keck data (BK15), Baryon Acoustic Oscillation data and the Type Ia supernovae data. We find that the upper limits of tensor-to-scalar ratio are $0.061$, $0.064$ and $0.072$ at 95% confidence level (CL) in the $\Lambda$CDM+$r$, $\Lambda$CDM+$r$+$\alpha_{\rm~s}$ and $\Lambda$CDM+$r$+$\alpha_{\rm~s}$+$\beta_{\rm~s}$ models respectively, where $\alpha_{\rm~s}$ and $\beta_{\rm~s}$ are the running of scalar spectral index and running of running. The inflation model with a concave potential is favored at more than 95% CL. In addition, parametrizing the slow-roll parameter $\epsilon\sim~1/N^p$, where $N$ is the e-folding number before the end of inflation and taken in the range of $[50,60]$ and $[14,75]$ respectively, we conclude that the inflation model with a monomial potential $V(\phi)\sim~\phi^n$ is disfavored at more than 95% CL, and both the Starobinsky inflation model and brane inflation model are still consistent with the data.


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11690021, 11575271, and 11747601), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDB23000000, and XDA15020701), and Top-Notch Young Talents Program of China.


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  • Figure 1

    (Color online) The marginalized contour plots and likelihood distributions for parameters $r$ and $n_{\rm~s}$ at 68%$~\mathrm{CL}$ and 95% $\mathrm{CL}$ from Planck15+BK15+BAO+JLA datasets.

  • Figure 2

    (Color online) The marginalized contour plots and likelihood distributions for parameters $r$, $n_{\rm~s}$ and $\alpha_{\rm~s}$ at 68% CL and 95% CL from Planck15+BK15+BAO+JLA datasets.

  • Figure 3

    (Color online) The marginalized contour plots and likelihood distributions for parameters $r$, $n_{\rm~s}$, $\alpha_{\rm~s}$ and $\beta_{\rm~s}$ at 68%$~\mathrm{CL}$ and 95%$~\mathrm{CL}$ from Planck15+BK15+BAO+JLA datasets.

  • Figure 4

    (Color online) The marginalized contour plot for parameters $n_{\rm~s}$ and $r$ at 68%$~\mathrm{CL}$ and 95%$~\mathrm{CL}$ from Planck15+BK15+BAO+JLA datasets. The red region represents natural inflation; the cyan line represents SBS inflation; the yellow line represents Starobinsky inflation; the green line, the orange line and the magenta line represents $\phi^2$, $\phi$ and $\phi^{2/3}$ inflation model.

  • Figure 5

    (Color online) The marginalized contour plots for parameter $p$ and $c$ at 68% CL and 95% CL from Planck15+BK15+BAO+JLA datasets. The blue and red regions correspond to $N\in[50,60]$ and $N\in[14,75]$ condition, respectively.

  • Table 1   The 68% limits on the cosmological parameters in the $\Lambda$CDM+$r$ model, the $\Lambda$CDM+$r+\alpha_{\rm~s}$model and the $\Lambda$CDM+$r+\alpha_{\rm~s}+\beta_{\rm~s}$ model from the data combinations of Planck15+BK15+BAO+JLA
    Parameters $\Lambda$CDM+r$\Lambda$CDM+r+$\alpha_{\rm~s}$ $\Lambda$CDM+r+$\alpha_{\rm~s}$+$\beta_{\rm~s}$
    $\Omega_{\rm~b}h^2$ $0.02233\pm0.00013$ $0.02234\pm0.00014$ $0.02229\pm0.00014$
    $\Omega_{\rm~c}h^2$ $0.1182\pm0.0007$ $0.1182\pm0.0007$ $0.1183\pm0.0007$
    $100\theta_{\mathrm{MC}}$ $1.0410\pm0.0003$ $1.0410\pm0.0003$ $1.0410\pm0.0003$
    $\tau$ $0.062\pm0.008$ $0.062\pm0.008$ $0.063\pm0.007$
    $\ln\left(10^{10}A_{\rm~s}\right)$ $3.159\pm0.017$ $3.149\pm0.034$ $3.123\pm0.040$
    $n_{\rm~s}$ $0.9680\pm0.0034$ $0.9748^{+0.0211}_{-0.0214}$ $1.0193^{+0.0442}_{-0.0440}$
    $r_{0.002}$ (95% CL) $<0.061~$ $<0.064$ $<0.072$
    $\alpha_{\rm~s}$ $-0.0022^{+0.0069}_{-0.0068}$ $-0.0401^{+0.0343}_{-0.0338}$
    $\beta_{\rm~s}$ $0.0145^{+0.0127}_{-0.0131}$

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