Relic Gravitational Waves with A Running Spectral Index and Its Constraints at High Frequencies

Abstract

We study the impact of a running index ${\alpha }_t$ on the spectrum of relic gravitational waves (RGWs) over the whole range of frequency $(10^{-18}\sim 10^{10})$ Hz and reveal its implications in RGWs detections and in cosmology. Analytical calculations show that, although the spectrum of RGWs on low frequencies is less affected by ${\alpha }_t\ne 0$, but, on high frequencies, the spectrum is modified substantially. Investigations are made toward potential detections of the ${\alpha }_t$-modified RGWs for several kinds of current and planned detectors. The Advanced LIGO will likely be able to detect RGWs with ${\alpha }_t\ge 0$ for inflationary models with the inflation index $\beta =-1.956$ and the tensor-scalar ratio $r=0.55$. The future LISA can detect RGWs for a much broader range of (${\alpha }_t$, $\beta$, $r$), and will have a better chance to break a degeneracy between them. Constraints on ${\alpha }_t$ are estimated from several detections and cosmological observations. Among them, the most stringent one is from the bound of the Big Bang nucleosynthesis (BBN), and requires ${\alpha }_t<0.008$ rather conservatively for any reasonable ($\beta$, $r$), preferring a nearly power-law spectrum of RGWs. In light of this result, one would expect the scalar running index ${\alpha }_s$ to be of the same magnitude as ${\alpha }_t$, if both RGWs and scalar perturbations are generated by the same scalar inflation.

17 pages, 10 figures, Accepted by PRD

References in corpus (19)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects
• CMBPol Mission Concept Study: Probing Inflation with CMB Polarization
• Relic Gravitational Waves in the Accelerating Universe
• Perturbative Photon Fluxes Generated by High-Frequency Gravitational Waves and Their Physical Effects
• Is a step in the primordial spectral index favored by CMB data ?
• Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy
• The Parkes Pulsar Timing Array
• Using polarized maser to detect high-frequency relic gravitational waves
• Modifications by QCD transition and $e^{+}{e}^{-}$ annihilation on analytic spectrum of relic gravitational waves in accelerating universe
• Gravitational wave detection using high precision pulsar observations
• Detecting relic gravitational waves in the CMB: Comparison of different methods
• Microwave apparatus for gravitational waves observation
• Detecting Relic Gravitational Waves in the CMB: Comparison of Planck and Ground-based Experiments
• CMBPol Mission Concept Study: Reionization Science with the Cosmic Microwave Background
• All-sky search of NAUTILUS data
• All-sky incoherent search for periodic signals with Explorer 2005 data