The NANOGrav 15 yr data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15 yr observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach subparsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations.

Here we consider a flat FRW universe whose horizon entropy meets the Rényi entropy of nonextensive systems. In our model, the ordinary energy-momentum conservation law is not always valid. By applying the Clausius relation as well as the Cai-Kim temperature to the apparent horizon of a flat FRW universe, we obtain modified Friedmann equations. Fitting the model to the observational data on the current accelerated universe, some values for the model parameters are also addressed. Our study shows that the current accelerating phase of universe expansion may be described by a geometrical fluid, originated from the nonextensive aspects of geometry, which models a varying dark energy source interacting with the matter field in the Rastall way. Moreover, our results indicate that the probable nonextensive features of spacetime may also be used to model a varying dark energy source which does not interact with the matter field and is compatible with the current accelerated phase of the Universe.

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

Gaussian processes (GP) provide an elegant and model-independent method for extracting cosmological information from the observational data. In this work, we employ GP to perform a joint analysis by using the geometrical cosmological probes such as Supernova Type Ia (SN), Cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the H0LiCOW lenses sample to constrain the Hubble constant $$H_0$$H 0 , and reconstruct some properties of dark energy (DE), viz., the equation of state parameter w, the sound speed of DE perturbations $$c^2_s$$c s 2 , and the ratio of DE density evolution $$X = \rho _\mathrm{de}/\rho _\mathrm{de,0}$$X = ρ de / ρ de , 0 . From the joint analysis SN+CC+BAO+H0LiCOW, we find that $$H_0$$H 0 is constrained at 1.1% precision with $$H_0 = 73.78 \pm 0.84\ \hbox {km}\ \hbox {s}^{-1}\,\hbox {Mpc}^{-1}$$H 0 = 73.78 ± 0.84 km s - 1 Mpc - 1 , which is in agreement with SH0ES and H0LiCOW estimates, but in $$\sim 6.2 \sigma $$∼ 6.2 σ tension with the current CMB measurements of $$H_0$$H 0 . With regard to the DE parameters, we find $$c^2_s < 0$$c s 2 < 0 at $$\sim 2 \sigma $$∼ 2 σ at high z, and the possibility of X to become negative for $$z > 1.5$$z > 1.5 . We compare our results with the ones obtained in the literature, and discuss the consequences of our main results on the DE theoretical framework.

We use observations related to the variation of fundamental constants, in order to impose constraints on the viable and most used f(T) gravity models. In p