Exact solutions of primordial gravitational waves

Abstract

The future detection projects of gravitational waves are expected to have the sensitivity of detecting the primordial gravitational waves, which may be useful to get new insight into the very early universe. It is essential to analyze the evolution equation of the gravitational waves to estimate the present field strength of the primordial gravitational waves. In this paper, we obtain analytic solutions of the gravitational wave equation in the presence of non-relativistic matters as well as the cosmological constant. Although it is difficult to obtain the solution directly, we find that the equation for the square of the amplitudes has a simple polynomial solution. This quantity, which is directly related to the energy density of the gravitational waves, turns out to be useful to construct analytic solutions for the amplitudes by using Weierstrass's elliptic functions.

arXiv comment18 pages, 3 figures

References in corpus (13)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Detector configuration of KAGRA - the Japanese cryogenic gravitational-wave detector
• Detecting the Cosmic Gravitational Wave Background with the Big Bang Observer
• Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model
• Primordial gravitational waves, precisely: The role of thermodynamics in the Standard Model
• Tensor Perturbations in Inflationary Models as a Probe of Cosmology
• Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach
• Gravitational waves as a probe of extended scalar sectors with the first order electroweak phase transition
• The Gravitational Universe
• The Heun equation and the Calogero-Moser-Sutherland system I: the Bethe Ansatz method
• Improved calculation of relic gravitational waves
• Multigravity and Space Time Foam
• The Hermite-Krichever ansatz for Fuchsian equations with applications to the sixth Painlevé equation and to finite-gap potentials

Cited by in corpus (2)

• Tracking Pre-inflation Era from density perturbation spectra
• Primordial gravitational waves spectrum in the interacting Bose-Einstein gas model