[Paper Review] Cosmological Backgrounds of Gravitational Waves and eLISA

Jean-François Dufaux|arXiv (Cornell University)|Sep 18, 2012

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper evaluates the potential of the eLISA space-based gravitational wave observatory to detect cosmological stochastic backgrounds from first-order phase transitions and cosmic strings. It demonstrates that eLISA can distinguish these signals from instrumental noise due to their uniquely predicted frequency spectra, with cosmic strings potentially detectable across a broad frequency band, including by eLISA and other experiments like pulsar timing arrays and advanced ground-based detectors.

ABSTRACT

We review cosmological backgrounds of gravitational waves with a particular attention to the scientific potential of the eLISA/NGO mission. After an overview of cosmological backgrounds and detectors, we consider different cosmological sources that could lead to an observable signal. We then study the backgrounds produced by first-order phase transitions and networks of cosmic strings, assessing the prospects for their detection.

Motivation & Objective

• To assess the scientific potential of the eLISA mission for detecting cosmological gravitational wave (GW) backgrounds.
• To evaluate the detectability of stochastic GW backgrounds from first-order phase transitions and cosmic strings using eLISA’s sensitivity curve.
• To determine whether eLISA can distinguish cosmological GW signals from instrumental noise and astrophysical confusion noise.
• To identify the parameter space of cosmic strings and phase transitions that would yield observable GW signals with eLISA.
• To explore multi-messenger prospects by comparing eLISA sensitivity with that of pulsar timing arrays and ground-based detectors.

Proposed method

• Uses the normalized GW energy density spectrum $ h^2\Omega_{gw}(f) = \frac{h^2}{\rho_c} \frac{d\rho_{gw}}{d\log f} $ as the primary observable to characterize cosmological GW backgrounds.
• Applies theoretical models of GW emission from first-order phase transitions, including bubble wall dynamics and shock waves, to predict the resulting GW power spectrum.
• Models the GW background from cosmic strings using the loop production spectrum and the total radiated power $ P_{gw} \sim 50G\mu^2 $, with $ \mu $ as the string tension.
• Incorporates cosmological evolution effects, such as redshifting and changes in relativistic degrees of freedom, to compute the frequency dependence of the GW spectrum.
• Compares predicted GW backgrounds with eLISA’s sensitivity curve (after removing confusion noise from galactic binaries) and with observational bounds from LIGO, pulsar timing, and CMB measurements.
• Uses numerical simulations and analytical approximations to compute the frequency dependence of the signal, particularly the flat spectrum at high frequencies and $ \Omega_{gw} \propto f^{3/2} $ at low frequencies for long-lived loops.

Experimental results

Research questions

• RQ1 Can eLISA detect a stochastic gravitational wave background from first-order phase transitions, and under what conditions would the signal exceed the instrument’s noise threshold?
• RQ2 What is the frequency dependence of the gravitational wave background produced by cosmic strings, and how does it vary with loop lifetime and string tension?
• RQ3 Which regions of the cosmic string parameter space (characterized by $ G\mu $ and loop lifetime) are accessible to eLISA, and how do they compare with constraints from pulsar timing and ground-based detectors?
• RQ4 Can the distinct spectral shapes of phase transition and cosmic string backgrounds allow eLISA to distinguish them from instrumental noise and other astrophysical backgrounds?
• RQ5 To what extent can multi-instrument detection (e.g., eLISA + PTA + Advanced LIGO) improve the characterization of a cosmological GW signal?

Key findings

• The GW background from cosmic strings with long-lived loops exhibits a nearly flat spectrum at high frequencies (in the radiation era) and falls as $ \Omega_{gw} \propto f^{3/2} $ at low frequencies.
• For cosmic strings with $ G\mu \sim 10^{-12} $, the GW signal lies well above the eLISA sensitivity curve in the $ 10^{-4} \text{ to } 10^{-1} \text{ Hz} $ band, making detection feasible.
• eLISA can probe a large portion of the parameter space for cosmic strings arising in simple string theory models, particularly for $ G\mu \lesssim 10^{-12} $.
• A significant fraction of the cosmic string parameter space is accessible simultaneously to eLISA and other experiments like pulsar timing arrays, enabling cross-verification and improved signal characterization.
• The GW background from first-order phase transitions has a characteristic frequency dependence that allows it to be distinguished from noise and other backgrounds, especially if the transition is sufficiently strong.
• Current observational bounds (e.g., from LIGO S5 and pulsar timing) already constrain parts of the cosmic string parameter space, with the most stringent limits at $ f \sim 10^{-9} \text{ Hz} $, where $ h^2\Omega_{gw} \lesssim 6 \times 10^{-9} $.