Simple Analytical Methods for Computing the Gravity-Wave Contribution to the Cosmic Background Radiation Anisotropy

Abstract

We present two simple analytical methods for computing the gravity wave contribution to the cosmic background radiation (CBR) anisotropy in inflationary models; one method uses a time-dependent transfer function, the other method uses an approximate gravity-wave mode function which is a simple combination of the lowest order spherical Bessel functions. We compare the CBR anisotropy tensor multipole spectrum computed using our methods with the previous result of the highly accurate numerical method, the ``Boltzmann'' method. Our time-dependent transfer function is more accurate than the time-independent transfer function found by Turner, White, and Lidsey; however, we find that the transfer function method is only good for $l \la 120$. Using our approximate gravity-wave mode function, we obtain much better accuracy; the tensor multipole spectrum we find differs by less than 2\% for $l \la 50$, less than 10\% for $l \la 120$, and less than 20\% for $l\le 300$ from the ``Boltzmann'' result. Our approximate graviton mode function should be quite useful in studying tensor perturbations from inflationary models.

The Boltzmann curve is updated, which leads to small corrections. LaTeX, 15 pages, 6 figures available via anonymous ftp at ftp://fnas08.fnal.gov/pub/Personal/ywang/

References in corpus (7)

• Tensor Perturbations in Inflationary Models as a Probe of Cosmology
• The Imprint of Gravitational Waves on the Cosmic Microwave Background
• Relic Gravitational Waves and Limits on Inflation
• Contribution of Long Wavelength Gravitational Waves to the CMB Anisotropy
• CBR anisotropy from primordial gravitational waves in inflationary cosmologies
• Testing Inflation with the Cosmic Microwave Background
• Cosmological Evolution of Scale-invariant Gravity Waves

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• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Reconstructing the Inflaton Potential --- an Overview
• Cosmological-Parameter Determination with Microwave Background Maps
• Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach
• Cosmology in the Next Millennium: Combining MAP and SDSS Data to Constrain Inflationary Models
• Numerical Relativity Investigation of the Effects of Gravitational Waves on the Inhomogeneity of the Universe
• A Fast and Accurate Algorithm for Computing Tensor CBR Anisotropy
• Applications of Cosmological Perturbation Theory in the Late Universe
• Origin & evolution of the Universe