Computation of the Power Spectrum in Chaotic $1\mathrm{/}4\lambda {\varphi }^4$ Inflation

The phase-integral approximation devised by Fr"oman and Fr"oman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are explicitly obtained up to fifth order of the phase-integral approximation. As in previous reports [1-3], we point out that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.