We investigate the case of a homogeneous tachyon field coupled to gravity in a spatially flat Friedman-Robertson-Walker spacetime. Assuming the field evolution to be exponentially decaying with time we solve the field equations and show that, under certain conditions, the scale factor represents an accelerating universe, following a phase of decelerated expansion. We make use of a model of dark energy (with p = −ρ) and dark matter (p = 0) where a single scalar field (tachyon) governs the dynamics of both the dark components. We show that this model fits the current supernova data as well as the canonical ΛCDM model. We give the bounds on the parameters allowed by the current data.

The most detailed constraints on the accelerating expansion of the universe and the nature of dark energy are derived from the high-redshift supernova data, assuming that the luminosity distance versus redshift relation is isotropic and the errors in the measurements are Gaussian. There is a possibility that there is a systematic direction dependence in the data, either due to uncorrected, known physical processes or because there are tiny departures from the cosmological principle, making the universe slightly anisotropic. To investigate this possibility, we introduce a statistic based on extreme value theory and apply it to the gold data sets from Riess et al. Our analysis indicate a systematic, directional dependence in the supernova data in both sets, which using the bootstrap distribution comes to about 80 per cent level of confidence for Riess et al. and 90 per cent for Riess et al. Equally importantly, we show that while the 2007 data fit cold dark matter ( CDM) model better than the 2004 data, the level of non-Gaussianity, quantified by departures of our statistic from the Gaussian predictions has become worse. In fact, we find that Riess et al. data lie totally outside the distribution obtained by assuming the noise to be Gaussian.

We revise and extend the extreme value statistic, introduced in Gupta et al., to study direction dependence in the high‐redshift supernova data, arising either from departures, from the cosmological principle or due to direction‐dependent statistical systematics in the data. We introduce a likelihood function that analytically marginalizes over the Hubble constant and use it to extend our previous statistic. We also introduce a new statistic that is sensitive to direction dependence arising from living off‐centre inside a large void as well as from previously mentioned reasons for anisotropy. We show that for large data sets, this statistic has a limiting form that can be computed analytically. We apply our statistics to the gold data sets from Riess et al., as in our previous work. Our revision and extension of the previous statistic show that the effect of marginalizing over the Hubble constant instead of using its best‐fitting value on our results is only marginal. However, correction of errors in our previous work reduces the level of non‐Gaussianity in the 2004 gold data that were found in our earlier work. The revised results for the 2007 gold data show that the data are consistent with isotropy and Gaussianity. Our second statistic confirms these results.

We use 47 gravitational wave sources from the Third LIGO–Virgo–Kamioka Gravitational Wave Detector Gravitational Wave Transient Catalog (GWTC–3) to estimate the Hubble parameter H(z), including its current value, the Hubble constant H 0. Each gravitational wave (GW) signal provides the luminosity distance to the source, and we estimate the corresponding redshift using two methods: the redshifted masses and a galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the source mass distribution and H(z). The source mass distribution displays a peak around 34 M ⊙, followed by a drop-off. Assuming this mass scale does not evolve with the redshift results in a H(z) measurement, yielding H 0 = 68 − 8 + 12 km s − 1 Mpc − 1 (68% credible interval) when combined with the H 0 measurement from GW170817 and its electromagnetic counterpart. This represents an improvement of 17% with respect to the H 0 estimate from GWTC–1. The second method associates each GW event with its probable host galaxy in the catalog GLADE+, statistically marginalizing over the redshifts of each event’s potential hosts. Assuming a fixed BBH population, we estimate a value of H 0 = 68 − 6 + 8 km s − 1 Mpc − 1 with the galaxy catalog method, an improvement of 42% with respect to our GWTC–1 result and 20% with respect to recent H 0 studies using GWTC–2 events. However, we show that this result is strongly impacted by assumptions about the BBH source mass distribution; the only event which is not strongly impacted by such assumptions (and is thus informative about H 0) is the well-localized event GW190814.