Abstract:Quantum fluctuations of the gravitational field in the early Universe, amplified by inflation, produce a primordial gravitational-wave background across a broad frequency band. We derive constraints on the spectrum of this gravitational radiation, and hence on theories of the early Universe, by combining experiments that cover 29 orders of magnitude in frequency. These include Planck observations of cosmic microwave background temperature and polarization power spectra and lensing, together with baryon acousti… Show more
“…Interestingly, the peak frequency with T ann ∼ 1 GeV is within the target range of pulsar timing observations [50][51][52][53]. The current 95% confidence upper limit reads Ω gw h 2 < 2.3 × 10 −10 at ν 1yr 3 × 10 −8 Hz [52].…”
Section: Jhep08(2016)044supporting
confidence: 61%
“…The current 95% confidence upper limit reads Ω gw h 2 < 2.3 × 10 −10 at ν 1yr 3 × 10 −8 Hz [52]. The gravitational waves from the domain wall annihilation have a frequency dependence, Ω gw ∝ ν 3 , at ν < ν peak .…”
Section: Jhep08(2016)044mentioning
confidence: 92%
“…Instead, we expect that the string-wall network survives until a later time, and collapses during the QCD phase transition, emitting gravitational waves. We derive an upper bound on the PQ breaking scale by the pulsar timing experiments [50][51][52][53].…”
We study the formation and evolution of topological defects in an aligned axion model with multiple Peccei-Quinn scalars, where the QCD axion is realized by a certain combination of the axions with decay constants much smaller than the conventional PecceiQuinn breaking scale. When the underlying U(1) symmetries are spontaneously broken, the aligned structure in the axion field space exhibits itself as a complicated string-wall network in the real space. We find that the string-wall network likely survives until the QCD phase transition if the number of the Peccei-Quinn scalars is greater than two. The stringwall system collapses during the QCD phase transition, producing a significant amount of gravitational waves in the nano-Hz range at present. The typical decay constant is constrained to be below O(100) TeV by the pulsar timing observations, and the constraint will be improved by a factor of 2 in the future SKA observations.
“…Interestingly, the peak frequency with T ann ∼ 1 GeV is within the target range of pulsar timing observations [50][51][52][53]. The current 95% confidence upper limit reads Ω gw h 2 < 2.3 × 10 −10 at ν 1yr 3 × 10 −8 Hz [52].…”
Section: Jhep08(2016)044supporting
confidence: 61%
“…The current 95% confidence upper limit reads Ω gw h 2 < 2.3 × 10 −10 at ν 1yr 3 × 10 −8 Hz [52]. The gravitational waves from the domain wall annihilation have a frequency dependence, Ω gw ∝ ν 3 , at ν < ν peak .…”
Section: Jhep08(2016)044mentioning
confidence: 92%
“…Instead, we expect that the string-wall network survives until a later time, and collapses during the QCD phase transition, emitting gravitational waves. We derive an upper bound on the PQ breaking scale by the pulsar timing experiments [50][51][52][53].…”
We study the formation and evolution of topological defects in an aligned axion model with multiple Peccei-Quinn scalars, where the QCD axion is realized by a certain combination of the axions with decay constants much smaller than the conventional PecceiQuinn breaking scale. When the underlying U(1) symmetries are spontaneously broken, the aligned structure in the axion field space exhibits itself as a complicated string-wall network in the real space. We find that the string-wall network likely survives until the QCD phase transition if the number of the Peccei-Quinn scalars is greater than two. The stringwall system collapses during the QCD phase transition, producing a significant amount of gravitational waves in the nano-Hz range at present. The typical decay constant is constrained to be below O(100) TeV by the pulsar timing observations, and the constraint will be improved by a factor of 2 in the future SKA observations.
“…There, Ω GW (f ) exhibits a long plateau (∝ f 0 ) over a frequency range which covers the bands of most GW experiments at the present, e.g., aLIGO/Virgo and the LISA mission. The amplitude of this plateau depends on the value of r alone, independent of f (see, e.g., [102]). For r = 0.01 shown here, this amplitude is ∼ 10 −16 , more than six orders of magnitude below the sensitivities of current GW detectors, which is the main reason why the SGWB from inflation (in ΛCDM) was not expected to be detectable by current major GW detection experiments listed in §I D.…”
Section: Results: Present-day Sgwb Energy Density Spectrum and Itsmentioning
We consider an alternative to WIMP cold dark matter (CDM), ultralight bosonic dark matter (m 10 −22 eV/c 2 ) described by a complex scalar field (SFDM) with a global U (1) symmetry, for which the comoving particle number density, or charge density, is conserved after particle production during standard reheating. We allow for a repulsive self-interaction. In a ΛSFDM universe, SFDM starts relativistic, evolving from stiff (w = 1) to radiation-like (w = 1/3), before becoming nonrelativistic at late times (w = 0). Thus, before the familiar radiation-dominated era, there is an earlier era of stiff-SFDM-domination. During both the stiff-SFDM-dominated and radiation-dominated eras, the expansion rate is higher than in ΛCDM. SFDM particle mass m and quartic self-interaction coupling strength λ, are therefore constrained by cosmological observables, particularly N eff , the effective number of neutrino species during BBN, and zeq, the redshift of matter-radiation equality. Furthermore, since the stochastic gravitational wave background (SGWB) from inflation is amplified during the stiff-SFDM-dominated era, it can contribute a radiationlike component large enough to affect these observables, by further boosting the expansion rate after the stiff era ends. Remarkably, this same amplification makes detection of the SGWB possible at high frequencies by current laser interferometer experiments, e.g., aLIGO/Virgo and LISA. For SFDM particle parameters that satisfy these cosmological constraints, the amplified SGWB is detectable by LIGO for a broad range of reheat temperatures T reheat , for values of the tensor-to-scalar ratio r currently allowed by CMB polarization measurements. For a given r and λ/(mc 2 ) 2 , the marginally-allowed ΛSFDM model for each T reheat has the smallest m that satisfies the cosmological constraints, and maximizes the present SGWB energy density for that T reheat . This SGWB is then maximally detectable for values of T reheat for which modes that reenter the horizon when reheating ended have frequencies today that lie within the LIGO sensitive band. For example, for the family of marginally-allowed models with r = 0.01 and λ/(mc 2 ) 2 = 10 −18 eV −1 cm 3 , the maximally detectable ΛSFDM model has T reheat ≃ 2 × 10 4 GeV and m ≃ 1.6 × 10 −19 eV/c 2 , for which we predict an aLIGO O1 run detection with signal-to-noise ratio of ∼ 10. We show that the null detection of the SGWB recently reported by the aLIGO O1 run excludes the parameter range 8.75 × 10 3 T reheat (GeV) 1.7 × 10 5 for this illustrative family at 95% confidence, thereby demonstrating that GW detection experiments can already place a new kind of cosmological constraint on SFDM. A wider range of SFDM parameters and reheat temperatures should be accessible to aLIGO/Virgo O5, with the potential to detect this unique signature of the ΛSFDM model. For this same illustrative family, for example, a 3σ detection is predicted for 600 T reheat (GeV) 10 7 .
“…84, which is taken from Lasky et al. (2016). Also shown are curves for theoretical models with a large tensor-to-scalar ratio () and a range of spectral tilts .Fig.…”
We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.Electronic supplementary materialThe online version of this article (doi:10.1007/s41114-017-0004-1) contains supplementary material, which is available to authorized users.
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