Pulsar Timing Array Research Articles

Stochastic gravitational wave background: birth from string-wall death

We study a new source of stochastic gravitational wave background (SGWB) from the final collapse of a network of topological defects. Typically, the final collapse is considered negligible for generating gravitational waves (GWs) due to its subdominance compared with the network's long-term evolution in the scaling regime. However, in some cases, a network can be driven outside of horizon by inflation and later re-enter horizon. Then, the network's final collapse after re-entering horizon becomes the dominant GW source and therefore cannot be neglected. We demonstrate this phenomenon in the context of N DW = 1 string-wall networks which naturally arise in axion models, although the framework can be generalized to other types of topological networks. The final collapse of walls bounded by strings releases GWs. Our calculation of the corresponding GW spectrum suggests it could be related to the first few bins of the nano-Hertz SGWB signal possibly detected by various Pulsar Timing Array (PTA) collaborations. However, it is important to note that such GW spectrum falls within a relatively narrow frequency range, which may not completely account for the PTA signal that spans more than one order of magnitude in frequency. Furthermore, with different parameter choices, the resultant GWs generated in this mechanism could be probed by various GW interferometry experiments.

Connecting low-redshift LISA massive black hole mergers to the nHz stochastic gravitational wave background

Pulsar Timing Array (PTA) experiments worldwide recently reported evidence of a nHz stochastic gravitational wave background (sGWB) compatible with the existence of slowly inspiralling massive black hole (MBH) binaries (MBHBs). The shape of the signal contains valuable information about the evolution of z < 1 MBHs above 108 M⊙, suggesting a faster dynamical evolution of MBHBs towards the gravitational-wave-driven inspiral or a larger MBH growth than usually assumed. In this work, we investigate if the nHz sGWB could also provide constraints on the population of merging lower-mass MBHBs (< 107 M⊙) detectable by LISA. To this end, we use the L-Galaxies semi-analytical model applied to the Millennium suite of simulations. We generate a population of MBHs compatible simultaneously with current electromagnetic and nHz sGWB constraints by including the possibility that, in favourable environments, MBHs can accrete gas beyond the Eddington limit. The predictions of this new model for the sGWB show that the global (integrated up to high-z) LISA detection rate is not significantly affected when compared to a fiducial model whose nHz sGWB signal is ∼2 times smaller. In both cases, the global rate yields ∼12 yr−1 and is dominated by systems of 105 − 6 M⊙. The main differences are limited to low-z (z < 3), high-mass (> 106 M⊙) LISA MBHBs. The model compatible with the latest PTA results predicts up to ∼1.6 times more detections, with a rate of ∼1 yr−1. We find that these LISA MBHB systems have 50% probability of shining with bolometric luminosities > 1043 erg s−1. Hence, in case PTA results are confirmed and given the current MBH modelling, our findings suggest there will be higher chances to perform multimessenger studies with LISA MBHB than previously expected.

Constraints on inflation with null energy condition violation from advanced LIGO and advanced Virgo's first three observing runs

The null energy condition (NEC) is a cornerstone of general relativity, and its violation could leave observable imprints in the cosmic gravitational wave spectrum. Theoretical models suggest that NEC violations during inflation can amplify the primordial tensor power spectrum, leading to distinct features in the stochastic gravitational wave background (SGWB). In this work, we search for these NEC-violating signatures in the SGWB using data from Advanced LIGO and Advanced Virgo's first three observing runs. Our analysis reveals no statistically significant evidence of such signals, allowing us to place stringent upper limits on the tensor power spectrum amplitude, P T,2, during the second inflationary stage. Specifically, we find that P T,2 ≲ 0.15 at a 95% confidence level. Notably, this upper limit is consistent with constraints derived from pulsar timing array observations, reinforcing the hypothesis that NEC violations during inflation could explain the signal detected by pulsar timing arrays. Our findings contribute to a deeper understanding of the early Universe and highlight the potential of current and future gravitational wave experiments in probing the physics of inflation and NEC violations.

Pulsar Timing Noise from Brownian Motion of the Sun

Recently, pulsar timing arrays (PTAs) reported a signal at nanohertz frequencies consistent with a stochastic gravitational-wave background. Here, I show that the Brownian motion of the Sun as a result of its random gravitational interactions with the cluster of thousands of unmodeled main-belt asteroids of diameters ≲80 km, combined with small inaccuracies in the estimated masses of larger asteroids, introduces timing noise for pulsars, which is up to 20% of the reported signal at frequencies of ∼1 few years–1. The asteroid contribution needs to be modeled better in order to obtain accurate inferences from the PTA signal.

Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity f NL and g NL considered

Investigation of primordial non-Gaussianity holds immense importance in testing the inflation paradigm and shedding light on the physics of the early Universe. In this study, we conduct the complete analysis of scalar-induced gravitational waves (SIGWs) by incorporating the local-type non-Gaussianity f NL and g NL. We develop Feynman-like diagrammatic technique and derive semi-analytic formulas for both the energy-density fraction spectrum and the angular power spectrum. For the energy-density fraction spectrum, we analyze all the relevant Feynman-like diagrams, determining their contributions to the spectrum in an order-by-order fashion. As for the angular power spectrum, our focus lies on the initial inhomogeneities, giving rise to anisotropies in SIGWs, that arise from the coupling between short- and long-wavelength modes due to primordial non-Gaussianity. Our analysis reveals that this spectrum exhibits a typical multipole dependence, characterized by C̃ ℓ ∝ [ℓ(ℓ + 1)]-1, which plays a crucial role in distinguishing between different sources of gravitational waves. Depending on model parameters, significant anisotropies can be achieved. We also show that the degeneracies in model parameters can be broken. The findings of our study underscore the angular power spectrum as a robust probe for investigating primordial non-Gaussianity and the physics of the early Universe. Moreover, our theoretical predictions can be tested using space-borne gravitational-wave detectors and pulsar timing arrays.

Can Supercooled Phase Transitions Explain the Gravitational Wave Background Observed by Pulsar Timing Arrays?

Several pulsar timing array collaborations recently reported evidence of a stochastic gravitational wave background (SGWB) at nHz frequencies. While the SGWB could originate from the merger of supermassive black holes, it could be a signature of new physics near the 100MeV scale. Supercooled first-order phase transitions (FOPTs) that end at the 100MeV scale are intriguing explanations, because they could connect the nHz signal to new physics at the electroweak scale or beyond. Here, however, we provide a clear demonstration that it is not simple to create a nHz signal from a supercooled phase transition, due to two crucial issues that could rule out many proposed supercooled explanations and should be checked. As an example, we use a model based on nonlinearly realized electroweak symmetry that has been cited as evidence for a supercooled explanation. First, we show that a FOPT cannot complete for the required transition temperature of around 100MeV. Such supercooling implies a period of vacuum domination that hinders bubble percolation and transition completion. Second, we show that even if completion is not required or if this constraint is evaded, the Universe typically reheats to the scale of any physics driving the FOPT. The hierarchy between the transition and reheating temperature makes it challenging to compute the spectrum of the SGWB.

Ultrahigh frequency primordial gravitational waves beyond the kHz: The case of cosmic strings

We investigate gravitational-wave backgrounds (GWBs) of primordial origin that would manifest only at ultrahigh frequencies, from kilohertz to 100 gigahertz, and leave no signal at LIGO, the Einstein Telescope, the Cosmic Explorer, LISA, or pulsar-timing arrays. We focus on GWBs produced by cosmic strings and make predictions for the GW spectra scanning over high-energy scale (beyond 1010 GeV) particle physics parameters. Signals from local string networks can easily be as large as the big bang nucleosynthesis/cosmic microwave background bounds, with a characteristic strain as high as 10−26 in the 10 kHz band, offering prospects to probe grand unification physics in the 1014–1017 GeV energy range. In comparison, GWB from axionic strings is suppressed (with maximal characteristic strain ∼10−31) due to the early matter era induced by the associated heavy axions. We estimate the needed reach of hypothetical futuristic GW detectors to probe such GWB and, therefore, the corresponding high-energy physics processes. Beyond the information of the symmetry-breaking scale, the high-frequency spectrum encodes the microscopic structure of the strings through the position of the UV cutoffs associated with cusps and kinks, as well as potential information about friction forces on the string. The IR slope, on the other hand, reflects the physics responsible for the decay of the string network. We discuss possible strategies for reconstructing the scalar potential, particularly the scalar self-coupling, from the measurement of the UV cutoff of the GW spectrum. Published by the American Physical Society 2024

Testing gravity with cosmic variance-limited pulsar timing array correlations

Testing gravity with cosmic variance-limited pulsar timing array correlations

Probing the speed of scalar-induced gravitational waves with pulsar timing arrays

Probing the speed of scalar-induced gravitational waves with pulsar timing arrays

Gravitational wave sources for pulsar timing arrays

Gravitational wave sources for pulsar timing arrays

Mass-redshift dependency of supermassive black hole binaries for the gravitational wave background

ABSTRACT Studying how the black hole (BH)–(galaxy) bulge mass relation evolves with redshift provides valuable insights into the co-evolution of supermassive black holes and their host galaxies. However, obtaining accurate measurement of BH masses is challenging due to the bias towards the most massive and luminous galaxies. Instead, we focus on the BH and bulge masses as they vary with redshift using the EAGLE, Illustris, TNG100, TNG300, Horizon-AGN, and SIMBA large-scale cosmological simulations. We use an analytical astrophysical model with galaxy stellar mass function, pair fraction, merger time-scale and BH–bulge mass relation extended to include redshift evolution. The model can predict the intensity of the gravitational wave background (GWB) produced by a population of supermassive black hole binary (SMBHB) as a function of the frequency. This allows us to compare the predictions of this model with the constraints of pulsar timing array observations. Here, we employ Bayesian analysis for the parameter inference. We find that all six simulations are consistent $\le 3.5\sigma$ with a range of simulated GWB spectra. By fixing the BH–bulge mass parameters to the simulations we analyse the changes in the constraints on the other astrophysical parameters. Furthermore, we also examine the variation in SMBHB merger rate with mass and redshift between these large-scale simulations.

Asymptotic tails of massive gravitons in light of pulsar timing array observations

We demonstrate that the late time oscillatory tails of massive gravitons, present in both massive theories of gravity and effectively in extra-dimensional scenarios, could potentially contribute to gravitational waves with very long wavelengths. However, their impact on recent pulsar timing array observations might be relatively small, predominantly consisting of radiation emitted by black holes in our region of the Milky Way.

Broken blue-tilted inflationary gravitational waves: a joint analysis of NANOGrav 15-year and BICEP/Keck 2018 data

Recently, the pulsar timing array (PTA) collaborations havereported the evidence for a stochastic gravitational wavebackground (SGWB) at nano-Hertz band. The spectrum of inflationarygravitational wave (IGW) is unknown, which might exhibit differentpower law at different frequency-bands, thus if the PTA signal isprimordial, it will be significant to explore the underlyingimplications of current PTA and CMB data on IGW. In this Letter,we perform a joint Markov Chain Monte Carlo analysis for a brokenpower-law spectrum of IGW with the NANOGrav 15-year and BICEP/Keck2018 data. It is found that though the bestfit spectral tilt ofIGW at PTA band is n PTA T = 2.42+0.32 -0.91,at CMB band the bestfit is n CMB T = 0.55+0.37 -0.10 while a detectable amplitude of r with n CMB T ≃ 0 is still compatible. Theimplication of our results for inflation is also discussed.

Dissecting the stochastic gravitational wave background with astrometry

Astrometry, the precise measurement of star motions, offers an alternative avenue to investigate low-frequency gravitational waves through the spatial deflection of photons, complementing pulsar timing arrays reliant on timing residuals. Upcoming data from Gaia, Theia, and Roman can not only cross-check pulsar timing array findings but also explore the uncharted frequency range bridging pulsar timing arrays and LISA. We present an analytical framework to evaluate the feasibility of detecting a gravitational wave background, considering measurement noise and the intrinsic variability of the stochastic background. Furthermore, we highlight astrometry's crucial role in uncovering key properties of the gravitational wave background, such as spectral index and chirality, employing information-matrix analysis. Finally, we simulate the emergence of quadrupolar correlations, commonly referred to as the generalized Hellings-Downs curves.

Observing gravitational waves with solar system astrometry

The subtle influence of gravitational waves on the apparent positioning of celestial bodies offers novel observational windows [1,2,3,4]. We calculate the expected astrometric signal induced by an isotropic Stochastic Gravitational Wave Background (SGWB) in the short distance limit. Our focus is on the resultant proper motion of Solar System objects, a signal on the same time scales addressed by Pulsar Timing Arrays (PTA). We derive the corresponding astrometric deflection patterns, finding that they manifest as distinctive dipole and quadrupole correlations or, in some cases, may not be present. Our analysis encompasses both Einsteinian and non-Einsteinian polarisations. We estimate the upper limits for the amplitude of SGWBs that could be obtained by tracking the proper motions of large numbers of solar system objects such as asteroids. We find that for SGWBs with negative spectral indices, such as that generated by Super Massive Black Hole Binaries (SMBHB), the constraints from these observations could rival those from PTAs. With the Gaia satellite and the Vera C. Rubin Observatory poised to track an extensive sample of asteroids — ranging from 𝒪(105) to 𝒪(106), we highlight the significant future potential for similar surveys to contribute to our understanding of the SGWB.

Did we hear the sound of the Universe boiling? Analysis using the full fluid velocity profiles and NANOGrav 15-year data

In this paper, we analyse sound waves arising from a cosmic phase transition where the full velocity profile is taken into account as an explanation for the gravitational wave spectrum observed by multiple pulsar timing array groups. Unlike the broken power law used in the literature, in this scenario the power law after the peak depends on the macroscopic properties of the phase transition, allowing for a better fit with pulsar timing array (PTA) data. We compare the best fit with that obtained using the usual broken power law and, unsurprisingly, find a better fit with the gravitational wave (GW) spectrum that utilizes the full velocity profile. Even more importantly, the thermal parameters that produce the best fit are quite different. We then discuss models that can produce the best-fit point and complementary probes using CMB experiments and searches for light particles in DUNE, IceCUBE-Gen2, neutrinoless double β-decay, and forward physics facilities (FPF) at the LHC like FASERν, etc.

Quantum gravity effects on fermionic dark matter and gravitational waves

We explore the phenomenological consequences of breaking discrete global symmetries in quantum gravity (QG). We extend a previous scenario where discrete global symmetries are responsible for scalar dark matter (DM) and domain walls (DWs), to the case of fermionic DM, considered as a feebly interacting massive particle, which achieves the correct DM relic density via the freeze-in mechanism. Due to the mixing between DM and the standard model neutrinos, various indirect DM detection methods can be employed to constrain the QG scale, the scale of freeze-in, and the reheating temperature simultaneously. Since such QG symmetry breaking leads to DW annihilation, this may generate the characteristic gravitational wave background, and hence explain the recent observations of the gravitational wave spectrum by pulsar timing arrays. This work therefore highlights a tantalizing possibility of probing the effective scale of QG from observations.

The second data release from the European Pulsar Timing Array

The European Pulsar Timing Array (EPTA) and Indian Pulsar Timing Array (InPTA) collaborations have measured a low-frequency common signal in the combination of their second and first data releases, respectively, with the correlation properties of a gravitational wave background (GWB). Such a signal may have its origin in a number of physical processes including a cosmic population of inspiralling supermassive black hole binaries (SMBHBs); inflation, phase transitions, cosmic strings, and tensor mode generation by the non-linear evolution of scalar perturbations in the early Universe; and oscillations of the Galactic potential in the presence of ultra-light dark matter (ULDM). At the current stage of emerging evidence, it is impossible to discriminate among the different origins. Therefore, for this paper, we consider each process separately, and investigated the implications of the signal under the hypothesis that it is generated by that specific process. We find that the signal is consistent with a cosmic population of inspiralling SMBHBs, and its relatively high amplitude can be used to place constraints on binary merger timescales and the SMBH-host galaxy scaling relations. If this origin is confirmed, this would be the first direct evidence that SMBHBs merge in nature, adding an important observational piece to the puzzle of structure formation and galaxy evolution. As for early Universe processes, the measurement would place tight constraints on the cosmic string tension and on the level of turbulence developed by first-order phase transitions. Other processes would require non-standard scenarios, such as a blue-tilted inflationary spectrum or an excess in the primordial spectrum of scalar perturbations at large wavenumbers. Finally, a ULDM origin of the detected signal is disfavoured, which leads to direct constraints on the abundance of ULDM in our Galaxy.

Pulsar timing array source ensembles

The stochastic gravitational wave background for pulsar timing arrays is often modeled by a Gaussian ensemble which is isotropic and unpolarized. However, the Universe has a discrete set of polarized gravitational wave sources at specific sky locations. Can we trust that the Gaussian ensemble is an accurate description? To investigate this, we explicitly construct an ensemble containing N individual binary sources with circular orbits. The orbital inclination angles are randomly distributed, hence the individual sources are elliptically polarized. We then compute the first two moments of the Hellings and Downs correlation, as well as the pulsar-averaged correlation mean and (cosmic) variance. The first moments are the same as for a previously studied ensemble of circularly polarized sources. However, the second moments, and hence the variances, are different for the two ensembles. While neither discrete source model is exactly described by a Gaussian ensemble, we show that in the limit of large N, the differences are small. Published by the American Physical Society 2024

Comparing Recent Pulsar Timing Array Results on the Nanohertz Stochastic Gravitational-wave Background

The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational-wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within 1σ. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we “extended” each PTA’s data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings–Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA’s Data Release 3, which will involve not just adding in additional pulsars but also including data from all three PTAs where any given pulsar is timed by more than a single PTA.