The 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons.

Models of Dark Matter (DM) can leave unique imprints on the Universe’s small scale structure by boosting density perturbations on small scales. We study the capability of Pulsar Timing Arrays to search for, and constrain, subhalos from such models. The models of DM we consider are ordinary adiabatic perturbations in ΛCDM, QCD axion miniclusters, models with early matter domination, and vector DM produced during inflation. We show that ΛCDM, largely due to tidal stripping effects in the Milky Way, is out of reach for PTAs. Axion miniclusters may be within reach, although this depends crucially on whether the axion relic density is dominated by the misalignment or string contribution. Models where there is matter domination with a reheat temperature below 1 GeV may be observed with future PTAs. Lastly, vector DM produced during inflation can be detected if it is lighter than 10−16 GeV. We also make publicly available a Python Monte Carlo tool for generating the PTA time delay signal from any model of DM substructure.

We search for a first-order phase transition gravitational wave signal in 45 pulsars from the NANOGrav 12.5 year dataset. We find that the data can be explained in terms of a strong first order phase transition taking place at temperatures below the electroweak scale. In our search, we find that the signal from a first order phase transition is degenerate with that generated by Supermassive Black Hole Binary mergers. An interesting open question is how well gravitational wave observatories could separate such signals.

Dark matter substructure, such as primordial black holes (PBHs) and axion miniclusters, can induce phase shifts in pulsar timing arrays (PTAs) due to gravitational effects. In order to gain a more realistic forecast for the detectability of such models of dark matter with PTAs, we propose a Bayesian inference framework to search for phase shifts generated by PBHs and perform the analysis on mock PTA data with the software enterprise. For most PBH masses the constraints on the dark matter abundance agree with previous (frequentist) analyses (without mock data) to O(1) factors. This further motivates a dedicated search for PBHs (and dense small scale structures) in the mass range from 10 −8 M to well above 10 2 M with the Square Kilometer Array. Moreover, with a more optimistic set of timing parameters, future PTAs are predicted to constrain PBHs down to 10 −11 M . Lastly, we discuss the impact of backgrounds, such as Supermassive Black Hole Mergers, on detection prospects, suggesting a future program to separate a dark matter signal from other astrophysical sources.

We study quantum fluctuations in the lightcone metric of the 4-d Einstein-Hilbert action via dimensional reduction to Jackiw-Teitelboim (JT) gravity. In particular, we show that, in Einstein gravity, the causal development of a region in flat Minkowski spacetime, near a horizon defined by light sheets, can be described by an effective two-dimensional dilaton theory. This enables us to make use of known solutions of the JT action, where the spacetime position of a horizon has quantum uncertainty due to metric fluctuations. This quantum uncertainty can be then directly related to the original 4-d light cone coordinates, allowing us to compute the uncertainty in the time of a photon to travel from tip-to-tip of a causal diamond in flat 4-d Minkowski space. We find that both Planck and infrared scales (with the latter set by the size of the causal diamond) enter the uncertainty in photon travel time, such that the quantum fluctuation in the arrival time may be observably large.