Leonard E Parker Center for Gravitation, Cosmology and Astrophysics

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The Leonard E Parker Center for Gravitation, Cosmology and Astrophysics is supported by NASA, the National Science Foundation, UW-Milwaukee College of Letters and Science, and UW-Milwaukee Graduate School. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of these organizations.

Gravitational waves are produced by accelerating mass distributions with a quadrupole (or higher) moment. Once produced, gravitational waves travel through space-time at the speed of light and are essentially unaffected by the matter they encounter. As a result, gravitational waves emitted shortly after the Big Bang (and observed today) would carry unaltered information about the physical processes that generated them. These waves are expected to be generated by a large number of unresolved sources, forming a stochastic gravitational-wave background (SGWB). Many models exist for the generation of the SGWB; these include models of inflation, the pre-big-bang era, electroweak phase transitions, cosmic strings, magnetars and rotating neutron stars.

Gravitational waves stretch and compress the spatial dimensions perpendicular to the direction of wave propagation. In a Michelson interferometer with suspended mirrors, the gravitational wave would cause stretching and shrinking of orthogonal arms, which would result in corresponding fluctuations in the laser intensity at the output of the interferometer. A SGWB signal would cause random fluctuations in output laser power, which are indistinguishable from various instrumental noise sources.

The search for the SGWB using LIGO data is performed by cross-correlating data from pairs of interferometers. When similar waveforms occur across multiple detectors at the same time, a strong cross-correlation value is observed. The contributions to the cross-correlation in the frequency band 41.5 - 169.25 Hz, which contains 99% of the sensitivity, are summed to give an estimate of the gravitational-wave spectrum.

No evidence of a stochastic gravitational-wave background was identified, but the result constrains the energy density of the SGWB normalized by the critical energy density of the universe. The gravitational-wave spectrum is assumed to follow a power law with index, &alpha, such that &Omega_{GW}(f) = &Omega_{&alpha} &lowast (f/100Hz)^{&alpha}. For a frequency-independent spectrum, the gravitational-wave spectrum is constrained to be less than 6.9 x 10^{-6} at 95% confidence.

Prior to the result described here, the most constraining bounds on the SGWB in the frequency band around 100 Hz came from Big-Bang-Nucleosynthesis (BBN) and from cosmic microwave background (CMB) measurements. The BBN bound is derived from the fact that a large gravitational-wave energy density at the time of BBN would alter the abundances of the light nuclei produced in the process. A large gravitational-wave background at the time of decoupling of the CMB would alter the observed CMB and matter power spectra. This result has now surpassed these bounds, which is one of the major milestones that LIGO was designed to achieve.

The result also constrains models of cosmic (super)strings. Cosmic strings were originally proposed as topological defects formed during phase transitions in the early universe, but they can also be expanded to cosmological scales. Hence, searching for cosmic strings may provide a unique and powerful window into string theory and particle physics at the highest energy scales. Additionally, measurements of the SGWB offer the possibility of probing alternative models of the early universe cosmology, such as the pre-Big-Bang model.

Advanced LIGO and Advanced Virgo will provide 10 times greater sensitivity and cover a frequency band as low as 10 Hz, which will be useful to probe the gravitational-wave spectrum for information about the universe when it was less than one minute old.