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The calculation of the averaged Hubble expansion rate in an averaged perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small corrections to the background value of the expansion rate, which could be important for measuring the Hubble constant from local observations. It also predicts an intrinsic variance associated with the finite scale of any measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its variance depend on both the definition of the Hubble rate and the spatial surface on which the average is performed. We quantitatively study different definitions of the averaged Hubble rate encountered in the literature by consistently calculating the backreaction effect at second order in perturbation theory, and compare the results. We employ for the first time a recently developed gauge-invariant definition of an averaged scalar. We also discuss the variance of the Hubble rate for the different definitions.
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In relativistic inhomogeneous cosmology, structure formation couples to average cosmological expansion. A conservative approach to modelling this assumes an Einstein--de Sitter model (EdS) at early times and extrapolates this forward in cosmological time as a background model against which average properties of todays Universe can be measured. This requires adopting an early-epoch--normalised background Hubble constant $H_1^{bg}$. Here, we show that the $Lambda$CDM model can be used as an observational proxy to estimate $H_1^{bg}$ rather than choose it arbitrarily. We assume (i) an EdS model at early times; (ii) a zero dark energy parameter; (iii) bi-domain scalar averaging---division of the spatial sections into over- and underdense regions; and (iv) virialisation (stable clustering) of collapsed regions. We find $H_1^{bg}= 37.7 pm 0.4$ km/s/Mpc (random error only) based on a Planck $Lambda$CDM observational proxy. Moreover, since the scalar-averaged expansion rate is expected to exceed the (extrapolated) background expansion rate, the expected age of the Universe should be much less than $2/(3 H_1^{bg}) = 17.3$ Gyr. The maximum stellar age of Galactic Bulge microlensed low-mass stars (most likely: 14.7 Gyr; 68% confidence: 14.0--15.0 Gyr) suggests an age about a Gyr older than the (no-backreaction) $Lambda$CDM estimate.
We present a detailed study of the methodology for correlating `dark sirens (compact binaries coalescences without electromagnetic counterpart) with galaxy catalogs. We propose several improvements on the current state of the art, and we apply them to the GWTC-2 catalog of LIGO/Virgo gravitational wave (GW) detections, and the GLADE galaxy catalog, performing a detailed study of several sources of systematic errors that, with the expected increase in statistics, will eventually become the dominant limitation. We provide a measurement of $H_0$ from dark sirens alone, finding as the best result $H_0=67.3^{+27.6}_{-17.9},,{rm km}, {rm s}^{-1}, {rm Mpc}^{-1}$ ($68%$ c.l.) which is, currently, the most stringent constraint obtained using only dark sirens. Combining dark sirens with the counterpart for GW170817 we find $H_0= 72.2^{+13.9}_{-7.5} ,{rm km}, {rm s}^{-1}, {rm Mpc}^{-1}$. We also study modified GW propagation, which is a smoking gun of dark energy and modifications of gravity at cosmological scales, and we show that current observations of dark sirens already start to provide interesting limits. From dark sirens alone, our best result for the parameter $Xi_0$ that measures deviations from GR (with $Xi_0=1$ in GR) is $Xi_0=2.1^{+3.2}_{-1.2}$. We finally discuss limits on modified GW propagation under the tentative identification of the flare ZTF19abanrhr as the electromagnetic counterpart of the binary black hole coalescence GW190521, in which case our most stringent result is $Xi_0=1.8^{+0.9}_{-0.6}$. We release the publicly available code $tt{DarkSirensStat}$, which is available under open source license at url{https://github.com/CosmoStatGW/DarkSirensStat}.
It is shown, from the two independent approaches of McCrea-Milne and of Zeldovich, that one can fully recover the set equations corresponding to the relativistic equations of the expanding universe of Friedmann-Lemaitre-Robertson-Walker geometry. Although similar, the Newtonian and relativistic set of equations have a principal difference in the content and hence define two flows, local and global ones, thus naturally exposing the Hubble tension at the presence of the cosmological constant Lambda. From this, we obtain absolute constraints on the lower and upper values for the local Hubble parameter, sqrt{Lambda c^2/3} simeq 56.2$ and sqrt{Lambda c^2} simeq 97.3 (km/sec Mpc^{-1}), respectively. The link to the so-called maximum force--tension issue in cosmological models is revealed.
In this paper, we constrain the dimensionless Compton wavelength parameter $B_0$ of $f(R)$ gravity as well as the mass of sterile neutrino by using the cosmic microwave background observations, the baryon acoustic oscillation surveys, and the linear growth rate measurements. Since both the $f(R)$ model and the sterile neutrino generally predict scale-dependent growth rates, we utilize the growth rate data measured in different wavenumber bins with the theoretical growth rate approximatively scale-independent in each bin. The employed growth rate data come from the peculiar velocity measurements at $z=0$ in five wavenumber bins, and the redshift space distortions measurements at $z=0.25$ and $z=0.37$ in one wavenumber bin. By constraining the $f(R)$ model alone, we get a tight 95% upper limit of $log_{10}B_0<-4.1$. This result is slightly weakened to $log_{10}B_0<-3.8$ (at 2$sigma$ level) once we simultaneously constrain the $f(R)$ model and the sterile neutrino mass, due to the degeneracy between the parameters of the two. For the massive sterile neutrino parameters, we get the effective sterile neutrino mass $m_{ u,{rm{sterile}}}^{rm{eff}}<0.62$ eV (2$sigma$) and the effective number of relativistic species $N_{rm eff}<3.90$ (2$sigma$) in the $f(R)$ model. As a comparison, we also obtain $m_{ u,{rm{sterile}}}^{rm{eff}}<0.56$ eV (2$sigma$) and $N_{rm eff}<3.92$ (2$sigma$) in the standard $Lambda$CDM model.
Galileon gravity offers a robust gravitational theory for explaining cosmic acceleration, having a rich phenomenology of testable behaviors. We explore three classes of Galileon models -- standard uncoupled, and linearly or derivatively coupled to matter -- investigating the expansion history with particular attention to early time and late time attractors, as well as the linear perturbations. From the relativistic and nonrelativistic Poisson equations we calculate the generalizations of the gravitational strength (Newtons constant), deriving its early and late time behavior. By scanning through the parameters we derive distributions of the gravitational strength at various epochs and trace the paths of gravity in its evolution. Using ghost-free and stability criteria we restrict the allowed parameter space, finding in particular that the linear and derivative coupled models are severely constrained by classical instabilities in the early universe.
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