Detecting relic gravitational waves in the CMB: Optimal parameters and their constraints

Abstract

The prospect of detecting relic gravitational waves (RGWs), through their imprint in the cosmic microwave background radiation, provides an excellent opportunity to study the very early Universe. In simplest viable theoretical models the RGW background is characterized by two parameters, the tensor-to-scalar ratio $r$ and the tensor spectral index $n_t$. In this paper, we analyze the potential joint constraints on these two parameters, $r$ and $n_t$, using the data from the upcoming cosmic microwave background radiation experiments. Introducing the notion of the best pivot multipole ${\ell }_t^{\ast }$, we find that at this pivot multipole the parameters $r$ and $n_t$ are uncorrelated, and have the smallest variances. We derive the analytical formulae for the best pivot multipole number ${\ell }_t^{\ast }$, and the variances of the parameters $r$ and $n_t$. We verify these analytical calculations using numerical simulation methods, and find agreement to within 20%. The analytical results provides a simple way to estimate the detection ability for the relic gravitational waves by the future observations of the cosmic microwave background radiation.

32 pages, 5 figures, Phys.Rev.D accepted

References in corpus (11)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectra
• Relic Gravitational Waves in the Accelerating Universe
• Cosmological footprints of loop quantum gravity
• Determining Cosmological Parameters with Latest Observational Data
• Tensor Microwave Background Fluctuations for Large Multipole Order
• The Polarization of the Cosmic Microwave Background Due to Primordial Gravitational Waves
• CMB Temperature Polarization Correlation and Primordial Gravitational Waves
• Detecting relic gravitational waves in the CMB: Comparison of different methods
• Relic Gravitational Waves And CMB Polarization In The Accelerating Universe
• Marginal distributions for cosmic variance limited CMB polarization data

Cited by in corpus (3)

• Relic Gravitational Waves with A Running Spectral Index and Its Constraints at High Frequencies
• Stable indications of relic gravitational waves in Wilkinson Microwave Anisotropy Probe data and forecasts for the Planck mission
• Detecting Relic Gravitational Waves in the CMB: Comparison of Planck and Ground-based Experiments