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We study the impact of the use of the power series expression for theprimordial tensor spectrum on parameter estimation from future direct detectiongravitational wave experiments. The spectrum approximated by the power seriesexpansion may give large deviation from the true (fiducial) value when it isnormalized at CMB scale because of the large separation between CMB and directdetection scales. We derive the coefficients of the higher order terms of theexpansion up to the sixth order within the framework of the slow-rollapproximation and investigate how well the inclusion of higher order termsimproves the analytic prediction of the spectrum amplitude by comparing withnumerical results. Using the power series expression, we consider futureconstraints on inflationary parameters expected from direct detectionexperiments of the inflationary gravitational wave background and show that thetruncation of the higher order terms can lead to incorrect evaluation of theparameters. We present two example models; a quadratic chaotic inflation modeland mixed inflaton and curvaton model with a quartic inflaton potential.

Higher Order Corrections to the Primordial Gravitational Wave Spectrum and its Impact on Parameter Estimates for Inflation