We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Einstein gravity.

We investigate constraints on dark energy fluctuations using type Ia supernovae. If dark energy is not in the form of a cosmological constant, that is if the equation of state is not equal to -1, we expect not only temporal, but also spatial variations in the energy density. Such fluctuations would cause local variations in the universal expansion rate and directional dependences in the redshift-distance relation. We present a scheme for relating a power spectrum of dark energy fluctuations to an angular covariance function of standard candle magnitude fluctuations. The predictions for a phenomenological model of dark energy fluctuations are compared to observational data in the form of the measured angular covariance of Hubble diagram magnitude residuals for type Ia supernovae in the Union2 compilation. The observational result is consistent with zero dark energy fluctuations. However, due to the limitations in statistics, current data still allow for quite general dark energy fluctuations as long as they are in the linear regime.

Inhomogeneous universe models have been proposed as an alternative explanation for the apparent acceleration of the cosmic expansion that does not require dark energy. In the simplest class of inhomogeneous models, we live within a large, spherically symmetric void. Several studies have shown that such a model can be made consistent with many observations, in particular the redshift-luminosity distance relation for type Ia supernovae, provided that the void is of Gpc size and that we live close to the center. Such a scenario challenges the Copernican principle that we do not occupy a special place in the universe. We use the first-year Sloan Digital Sky Survey-II supernova search data set as well as the Constitution supernova data set to put constraints on the observer position in void models, using the fact that off-center observers will observe an anisotropic universe. We first show that a spherically symmetric void can give good fits to the supernova data for an on-center observer, but that the two data sets prefer very different voids. We then continue to show that the observer can be displaced at least fifteen percent of the void scale radius from the center and still give an acceptable fit to the supernova data. When combined with the observed dipole anisotropy of the cosmic microwave background however, we find that the data compells the observer to be located within about one percent of the void scale radius. Based on these results, we conclude that considerable fine-tuning of our position within the void is needed tofit the supernova data, strongly disfavouring the model from a Copernican principle point of view.

We discuss the possibility of identifying anisotropic and/or inhomogeneous cosmological models using type Ia supernova data. A search for correlations in current type Ia peak magnitudes over a large range of angular scales yields a null result. However, the same analysis limited to supernovae at low redshift shows a feeble anticorrelation at the 2σ level at angular scales θ≈40°. Upcoming data from, e.g., the SNLS (Supernova Legacy Survey) and the SDSS-II (SDSS: Sloan Digital Sky Survey) supernova searches will improve our limits on the size of—or possibly detect—possible correlations also at high redshift at the per cent level in the near future. With data from the proposed SNAP (SuperNova Acceleration Probe) satellite, we will be able to detect the induced correlations from gravitational lensing on type Ia peak magnitudes on scales less than a degree.

Despite its continued observational successes, there is a persistent (and growing) interest in extending cosmology beyond the standard model, Lambda CDM. This is motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm. In this paper, we summarize the current status of Lambda CDM as a physical theory, and review investigations into possible alternatives along a number of different lines, with a particular focus on highlighting the most promising directions. While the fundamental problems are proving reluctant to yield, the study of alternative cosmologies has led to considerable progress, with much more to come if hopes about forthcoming high-precision observations and new theoretical ideas are fulfilled.

A potential solution to the Hubble tension is the hypothesis that the Milky Way is located near the center of a matter underdensity. We model this scenario through the Lemaître-Tolman-Bondi formalism with the inclusion of a cosmological constant (ΛLTB) and consider a generalized Gaussian parametrization for the matter density profile. We constrain the underdensity and the background cosmology with a combination of data sets: the Pantheon Sample of type Ia supernovae (both the full catalogue and a redshift-binned version of it), a collection of baryon acoustic oscillations data points and the distance priors extracted from the latest Planck data release. The analysis with the binned supernovae suggests a preference for a -13 % density drop with a size of approximately 300 Mpc, interestingly matching the prediction for the so-called KBC void already identified on the basis of independent analyses using galaxy distributions. The constraints obtained with the full Pantheon Sample are instead compatible with a homogeneous cosmology and we interpret this radically different result as a cautionary tale about the potential bias introduced by employing a binned supernova data set. We quantify the level of improvement on the Hubble tension by analyzing the constraints on the B-band absolute magnitude of the supernovae, which provides the calibration for the local measurements of H₀. Since no significant difference is observed with respect to an analogous fit performed with a standard ΛCDM cosmology, we conclude that the potential presence of a local underdensity does not resolve the tension and does not significantly degrade current supernova constraints on H₀.

We analyze the effect that peculiar velocities have on the cosmological inferences we make using luminosity distance indicators, such as Type Ia supernovae. In particular we study the corrections required to account for (1) our own motion, (2) correlations in galaxy motions, and (3) a possible local under- or overdensity. For all of these effects we present a case study showing the impact on the cosmology derived by the Sloan Digital Sky Survey-II Supernova Survey (SDSS-II SN Survey). Correcting supernova (SN) redshifts for the cosmic microwave background (CMB) dipole slightly overcorrects nearby SNe that share some of our local motion. We show that while neglecting the CMB dipole would cause a shift in the derived equation of state of Δw ~ 0.04 (at fixed Ω m ), the additional local-motion correction is currently negligible (Δw <~ 0.01). We then demonstrate a covariance-matrix approach to statistically account for correlated peculiar velocities. This down-weights nearby SNe and effectively acts as a graduated version of the usual sharp low-redshift cut. Neglecting coherent velocities in the current sample causes a systematic shift of Δw ~ 0.02. This will therefore have to be considered carefully when future surveys aim for percent-level accuracy and we recommend our statistical approach to down-weighting peculiar velocities as a more robust option than a sharp low-redshift cut.

The first cosmological results from the ESSENCE supernova survey (Wood-Vasey and coworkers) are extended to a wider range of cosmological models including dynamical dark energy and nonstandard cosmological models. We fold in a greater number of external data sets such as the recent Higher-z release of high-redshift supernovae (Riess and coworkers), as well as several complementary cosmological probes. Model comparison statistics such as the Bayesian and Akaike information criteria are applied to gauge the worth of models. These statistics favor models that give a good fit with fewer parameters. Based on this analysis, the preferred cosmological model is the flat cosmological constant model, where the expansion history of the universe can be adequately described with only one free parameter describing the energy content of the universe. Among the more exotic models that provide good fits to the data, we note a preference for models whose best-fit parameters reduce them to the cosmological constant model.

The nature of dark matter (DM) is a central question in cosmology today. While elementary particles could explain DM, compact astrophysical objects such as black holes formed in the early Universe offer a theoretically appealing alternate route. Here, we constrain the fraction of DM that can be made up of primordial black holes (PBHs) with masses M≳0.01M_⊙⁠, with Type Ia supernovae. Utilizing the Dyer–Roeder distance relation, we find a maximum fractional amount of DM in compact objects (f_p) of 0.50 at 95 per cent confidence level (C.L.), in the flat Lambda cold dark matter model and 0.49 when marginalizing over a constant dark energy equation of state or spatial curvature, demonstrating robustness to the cosmological model. With a prior on the homogeneity parameter, η, including values >1, we derive η = 1.08 ± 0.17, hence, f_p < 0.32 at 95 per cent C.L., showing that the prior assumption of η ≤ 1 gives a conservative upper limit on f_p. The Hubble constant we infer is consistent with the homogeneous case, showing that inhomogeneities like compact DM cannot account for the observed Hubble tension. In conclusion, we can exclude stellar masses PBHs as comprising all of the observed DM.

Constraints on models of the late time acceleration of the universe assume the cosmological principle of homogeneity and isotropy on large scales. However, small scale inhomogeneities can alter observational and dynamical relations, affecting the inferred cosmological parameters. For precision constraints on the properties of dark energy, it is important to assess the potential systematic effects arising from these inhomogeneities. In this study, we use the Type Ia supernova magnitude-redshift relation to constrain the inhomogeneities as described by the Dyer-Roeder distance relation and the effect they have on the dark energy equation of state (w), together with priors derived from the most recent results of the measurements of the power spectrum of the Cosmic Microwave Background and Baryon Acoustic Oscillations. We find that the parameter describing the inhomogeneities (eta) is weakly correlated with w. The best fit values w = -0.933 +/- 0.065 and eta = 0.61 +/- 0.37 are consistent with homogeneity at < 2 sigma level. Assuming homogeneity (eta = 1), we find w = -0.961 +/- 0.055, indicating only a small change in w. For a time-dependent dark energy equation of state, w(0) = -0.951 +/- 0.112 and w(a) = 0.059 +/- 0.418, to be compared with w(0) = -0.983 +/- 0.127 and w(a) = 0.07 +/- 0.432 in the homogeneous case, which is also a very small change. We do not obtain constraints on the fraction of dark matter in compact objects, f(p), at the 95% C.L. with conservative corrections to the distance formalism. Future supernova surveys will improve the constraints on eta, and hence, f(p), by a factor of similar to 10.

Recent re-calibration of the Type Ia supernova (SNe Ia) magnitude-redshift relation combined with cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data have provided excellent constraints on the standard cosmological model. Here, we examine particular classes of alternative cosmologies, motivated by various physical mechanisms, e.g. scalar fields, modified gravity and phase transitions to test their consistency with observations of SNe Ia and the ratio of the angular diameter distances from the CMB and BAO. Using a model selection criterion for a relative comparison of the models (the Bayes Factor), we find moderate to strong evidence that the data prefer flat Lambda CDM over models invoking a thawing behaviour of the quintessence scalar field. However, some exotic models like the growing neutrino mass cosmology and vacuum metamorphosis still present acceptable evidence values. The bimetric gravity model with only the linear interaction term as well as a simplified Galileon model can be ruled out by the combination of SNe Ia and CMB/BAO datasets whereas the model with linear and quadratic interaction terms has a comparable evidence value to standard Lambda CDM. Thawing models are found to have significantly poorer evidence compared to flat Lambda CDM cosmology under the assumption that the CMB compressed likelihood provides an adequate description for these non-standard cosmologies. We also present estimates for constraints from future data and find that geometric probes from oncoming surveys can put severe limits on non-standard cosmological models.

We report lensing magnifications, extinction, and time-delay estimates for the first resolved, multiply imaged Type Ia supernova iPTF16geu, at z = 0.409, using Hubble Space Telescope (HST) observations in combination with supporting ground-based data. Multiband photometry of the resolved images provides unique information about the differential dimming due to dust in the lensing galaxy. Using HST and Keck AO reference images taken after the SN faded, we obtain a total lensing magnification for iPTF16geu of mu = 67.8(-2.9)(+2.6), accounting for extinction in the host and lensing galaxy. As expected from the symmetry of the system, we measure very short time-delays for the three fainter images with respect to the brightest one: -0.23 +/- 0.99,-1.43 +/- 0.74, and 1.36 +/- 1.07 d. Interestingly, we find large differences between the magnifications of the four supernova images, even after accounting for uncertainties in the extinction corrections: Delta m(1) = -3.88(-0.06)(+0.07), Delta m(2) = -2.99(-0.08)(+0.09), Delta m(3) = -2.19(-0.15)(+0.14), and Delta m(4) = -2.40(-0.12)(+0.14) mag, discrepant with model predictions suggesting similar image brightnesses. A possible explanation for the large differences is gravitational lensing by substructures, micro- or millilensing, in addition to the large-scale lens causing the image separations. We find that the inferred magnification is insensitive to the assumptions about the dust properties in the host and lens galaxy.

The observed magnifications and light curves of the quadruply imaged iPTF16geu supernova (SN) offers a unique opportunity to study a lens system with a variety of independent constraints. The four observed positions can be used to constrain the macrolens model. The magnifications and light curves at the four SN positions are more useful to constrain microlensing models. We define the macrolens model as a combination of a baryonic component that traces the observed light distribution, and a dark matter halo component. We constrained the macrolens model using the positional constraints given by the four observed images, and compared it with the best model obtained when magnification constraints were included. We found that the magnification cannot be explained by a macrolens model alone, and that contributions from substructures such as microlenses are needed to explain the observed magnifications. We considered microlens models based on the inferred stellar mass from the baryonic component of the macrolens model, and used the observed magnification and light curves to constrain the contribution from microlenses. We computed the likelihood of a variety of macro and micro lens models where we varied the dark matter halo, baryonic component, and microlens configurations. We used information about the position, magnification, and, for the first time, the light curves of the four observed SN images. We combined macrolens and microlens models in order to reproduce the observations; the four SN positions, magnifications, and lack of fluctuations in the light curves. After marginalizing over the model parameters, we found that larger stellar surface mass densities are preferred. This result suggests that the mass of the baryonic component is dominated by its stellar component. We conclude that microlensing from the baryonic component suffices to explain the observed flux ratios and light curves.

We study the cosmic expansion history of massive bigravity with a viable matter coupling which treats both metrics on equal footing. We derive the Friedmann equation for the effective metric through which matter couples to the two metrics, and study its solutions. For certain parameter choices, the background cosmology is identical to that of LCDM. More general parameters yield dynamical dark energy, which can still be in agreement with observations of the expansion history. We study specific parameter choices of interest, including minimal models, maximally-symmetric models, and a candidate partially-massless theory.

We study the Integrated Sachs-Wolfe (ISW) effect in ghost-free, massive bigravity, where only one metric couples to matter. We focus on the infinite-branch bigravity (IBB) model which exhibits viable cosmic expansion histories and stable linear perturbations, while the cosmological constant is set to zero and the late-time accelerated expansion of the Universe is due solely to the gravitational interaction terms. The ISW contribution to the CMB auto-correlation power spectrum is predicted, as well as the cross-correlation between the CMB temperature anisotropies and the large-scale structure. We use ISW amplitudes as observed in the WMAP 9-year temperature data together with galaxy and AGN data provided by the WISE mission, in order to compare the theoretical predictions to the observations. The ISW amplitudes in IBB are found to be larger than the corresponding ones in the standard LCDM model by roughly a factor of 1.5, but are still consistent with the observations.

We study the integrated Sachs-Wolfe (ISW) effect in ghost-free, massive bigravity. We focus on the infinite-branch bigravity (IBB) model which exhibits viable cosmic expansion histories and stable linear perturbations, while the cosmological constant is set to zero and the late-time accelerated expansion of the Universe is due solely to the gravitational interaction terms. The ISW contribution to the CMB auto-correlation power spectrum is predicted, as well as the cross-correlation between the CMB temperature anisotropies and large-scale structure. We use ISW amplitudes as inferred from the WMAP 9-year temperature data together with galaxy and AGN data provided by the WISE mission in order to compare the theoretical predictions to the observations. The ISW amplitudes in IBB are found to be larger than the corresponding ones in the standard Lambda CDM model by roughly a factor of 1.5, but are still consistent with the observations.

In this paper we study the phenomenology of stars and galaxies in massive bigravity. We give parameter conditions for the existence of viable star solutions when the radius of the star is much smaller than the Compton wavelength of the graviton. If these parameter conditions are not met, we constrain the ratio between the coupling constants of the two metrics, in order to give viable conditions for e. g. neutron stars. For galaxies, we put constraints on both the Compton wavelength of the graviton and the conformal factor and coupling constants of the two metrics. The relationship between black holes and stars, and whether the former can be formed from the latter, is discussed. We argue that the different asymptotic structure of stars and black holes makes it unlikely that black holes form from the gravitational collapse of stars in massive bigravity.

Accretion of dark energy onto black holes will take place when dark energy is not a cosmological constant. It has been proposed that the time evolution of the mass of the black holes in binary systems due to dark energy accretion could be detectable by gravitational radiation. This would make it possible to use observations of black hole binaries to measure local dark energy properties, e.g., to determine the sign of 1+w where w is the dark energy equation of state. In this Letter we show that such measurements are unfeasible due to the low accretion rates.

We derive dynamical and gravitational lensing properties of local sources in the Hassan-Rosen bimetric gravity theory. Observations of elliptical galaxies rule out values of the effective length-scale of the theory, in units of the Hubble radius, in the interval 10(-6). lambda(g) = rH less than or similar to 10(-3), unless the proportionality constant between the metrics at the background level is far from unity, in which case general relativity is effectively restored for local sources. In order to have background solutions resembling the concordance cosmological model, without fine-tuning of the parameters of the model, we are restricted to the upper interval, or lambda(g) /gamma H similar to 1, for which the Vainshtein mechanism is expected to restore general relativity for local sources. Except for a limited range of parameter values, the Hassan-Rosen theory is thus consistent with the observed lensing and dynamical properties of elliptical galaxies.

We report the discovery of a multiply imaged, gravitationally lensed type Ia supernova, iPTF16geu (SN 2016geu), at redshift z = 0.409. This phenomenon was identified because the light from the stellar explosion was magnified more than 50 times by the curvature of space around matter in an intervening galaxy. We used high-spatial-resolution observations to resolve four images of the lensed supernova, approximately 0.3 arc seconds from the center of the foreground galaxy. The observations probe a physical scale of ~1 kiloparsec, smaller than is typical in other studies of extragalactic gravitational lensing. The large magnification and symmetric image configuration imply close alignment between the lines of sight to the supernova and to the lens. The relative magnifications of the four images provide evidence for substructures in the lensing galaxy.

Aims: Powerful gravitational telescopes in the form of massive galaxy clusters can be used to enhance the light collecting power over a limited field of view by about an order of magnitude in flux. This effect is exploited here to increase the depth of a survey for lensed supernovae at near-IR wavelengths.

Methods: We present a pilot supernova search programme conducted with the ISAAC camera at VLT. Lensed galaxies behind the massive clusters A1689, A1835, and AC114 were observed for a total of 20 h divided into 2, 3, and 4 epochs respectively, separated by approximately one month to a limiting magnitude J ≲ 24 (Vega). Image subtractions including another 20 h worth of archival ISAAC/VLT data were used to search for transients with lightcurve properties consistent with redshifted supernovae, both in the new and reference data.

Results: The feasibility of finding lensed supernovae in our survey was investigated using synthetic lightcurves of supernovae and several models of the volumetric type Ia and core-collapse supernova rates as a function of redshift. We also estimate the number of supernova discoveries expected from the inferred star-formation rate in the observed galaxies. The methods consistently predict a Poisson mean value for the expected number of supernovae in the survey of between N_SN = 0.8 and 1.6 for all supernova types, evenly distributed between core collapse and type Ia supernovae. One transient object was found behind A1689, 0.5 arcsec from a galaxy with photometric redshift z_gal = 0.6 ± 0.15. The lightcurve and colors of the transient are consistent with being a reddened type IIP supernova at z_SN = 0.59. The lensing model predicts 1.4 mag of magnification at the location of the transient, without which this object would not have been detected in the near-IR ground-based search described in this paper (unlensed magnitude J ~ 25). We perform a feasibility study of the potential for lensed supernovae discoveries with larger and deeper surveys and conclude that the use of gravitational telescopes is a very exciting path for new discoveries. For example, a monthly rolling supernova search of a single very massive cluster with the HAWK-I camera at VLT would yield ≳ 10 lensed supernova lightcurves per year, where type Ia supernovae would constitute about half of the expected sample. Based on observations made with ESO telescopes at the La Silla Paranal Observatory under programme ID 079.A-0192 and ID 081.A-0734.

Detecting gravitationally lensed supernovae is among the biggest challenges in astronomy. It involves a combination of two very rare phenomena: catching the transient signal of a stellar explosion in a distant galaxy and observing it through a nearly perfectly aligned foreground galaxy that deflects light towards the observer. Here we describe how high-cadence optical observations with the Zwicky Transient Facility, with its unparalleled large field of view, led to the detection of a multiply imaged type Ia supernova, SN Zwicky, also known as SN 2022qmx. Magnified nearly 25-fold, the system was found thanks to the standard candle nature of type Ia supernovae. High-spatial-resolution imaging with the Keck telescope resolved four images of the supernova with very small angular separation, corresponding to an Einstein radius of only θ_E = 0.167″ and almost identical arrival times. The small θ_E and faintness of the lensing galaxy are very unusual, highlighting the importance of supernovae to fully characterize the properties of galaxy-scale gravitational lenses, including the impact of galaxy substructures.

Observations of galaxy-scale strong gravitational lensing systems enable unique tests of departures from general relativity at the kilo- to megaparsec scale. In this work, the gravitational slip parameter γ_PN, measuring the amplitude of a hypothetical fifth force, is constrained using 130 elliptical galaxy lens systems. We implement a lens model with a power-law total mass density and a deprojected De Vaucouleurs luminosity density, favored over a power-law luminosity density. To break the degeneracy between the lens velocity anisotropy β and the gravitational slip, we introduce a new prior on the velocity anisotropy based on recent dynamical data. For a constant gravitational slip, we find γ_PN= in agreement with general relativity at the 68% confidence level. Introducing a Compton wavelength λ_g, effectively screening the fifth force at small and large scales, the best fit is obtained for λ_g∼0.2  Mpc and γ_PN=. A local minimum is found at λ_g∼100  Mpc and γ_PN=. We conclude that there is no evidence in the data for a significant departure from general relativity and that using accurate assumptions and having good constraints on the lens galaxy model is key to ensure reliable constraints on the gravitational slip.

We investigate the possibility of correcting for magnification due to gravitational lensing of standard candlesources, such as Type Ia supernovae. Our method uses the observed properties of the foreground galaxies along thelines of sight to each source, and the accuracy of the lensing correction depends on the quality and depth of theseobservations as well as the uncertainties in translating the observed luminosities to the matter distribution in thelensing galaxies. The current work is limited to cases in which the matter density is dominated by the individualgalaxy halos. However, it is straightforward to generalize the method to also include gravitational lensing fromcluster scale halos.We show that the dispersion due to lensing for a standard candle source at z ¼1:5 can be reducedfrom about 7% toP3%; i.e., the magnification correction is useful in reducing the scatter in the Type Ia Hubble diagram,especially at high redshifts where the required long exposure times make it hard to reach large statistics andthe dispersion due to lensing becomes comparable to the intrinsic Type Ia scatter.

In general relativity, the endpoint of spherically symmetric gravitational collapse is a Schwarzschild-[(A)dS] black hole. In bimetric gravity, it has been speculated that a static end state must also be Schwarzschild-[(A)dS]. To this end, we present a set of exact solutions, including collapsing massless dust particles. For these, the speculation is confirmed.

Bimetric gravity is a ghost-free and observationally viable extension of general relativity, exhibiting both a massless and a massive graviton. The observed abundances of light elements can be used to constrain the expansion history of the Universe at the period of Big Bang nucleosynthesis. Applied to bimetric gravity, we readily obtain constraints on the theory parameters which are complementary to other observational probes. For example, the mixing angle between the two gravitons must satisfy θ≲ 18^∘ in the graviton mass range ≳ 10-16 eV/c2, representing a factor of two improvement compared with other cosmological probes.

Ghost-free bimetric gravity is an extension of general relativity, featuring a massive spin-2 field coupled to gravity. We parameterize the theory with a set of observables having specific physical interpretations. For the background cosmology and the static, spherically symmetric solutions (for example approximating the gravitational potential of the solar system), there are four directions in the parameter space in which general relativity is approached. Requiring that there is a working screening mechanism and a nonsingular evolution of the Universe, we place analytical constraints on the parameter space which rule out many of the models studied in the literature. Cosmological solutions where the accelerated expansion of the Universe is explained by the dynamical interaction of the massive spin-2 field rather than by a cosmological constant, are still viable.

Ghost-free bimetric gravity is a theory of two interacting spin-2 fields, one massless and one massive, in addition to the standard matter particles and fields, thereby generalizing Einstein's theory of general relativity. To parameterize the theory, we use five observables with specific physical interpretations. We present, for the first time, observational constraints on these parameters that: (i) apply to the full theory, (ii) are consistent with a working screening mechanism (i.e., restoring general relativity locally), (iii) exhibit a continuous, real-valued background cosmology (without the Higuchi ghost). For the cosmological constraints, we use data sets from the cosmic microwave background, baryon acoustic oscillations, and type Ia supernovae. Bimetric cosmology provides a good fit to data even for large values of the mixing angle between the massless and massive gravitons. Interestingly, the best-fit model is a self-accelerating solution where the accelerated expansion is due to the dynamical massive spin-2 field, without a cosmological constant. Due to the screening mechanism, the models are consistent with local tests of gravity such as solar system tests and gravitational lensing by galaxies. We also comment on the possibility of alleviating the Hubble tension with this theory.

Fifth forces are ubiquitous in modified theories of gravity. In this paper, we analyze their effect on the Cepheid-calibrated cosmic distance ladder, specifically with respect to the inferred value of the Hubble constant (H₀). We consider a variety of effective models where the strength, or amount of screening, of the fifth force is estimated using proxy fields related to the large-scale structure of the Universe. To quantify the level of tension between the local distance ladder and the Planck value for H₀, we calculate the probability of obtaining a test result at least as extreme as the observed one, assuming that the model is correct (the p-value). For all models considered, the level of agreement is ≳20%, relieving the tension compared to the concordance model, exhibiting an agreement of only 1%. The alleviated discrepancy comes partially at the cost of an increased tension between distance estimates from Cepheids and the tip of the red-giant branch (TRGB). Demanding also that the consistency between Cepheid and TRGB distance estimates is not impaired, some fifth force models can still accommodate the data with a probability ≳20%. This provides incentive for more detailed investigations of fundamental theories on which the effective models are based and their effect on the Hubble tension.

Fifth forces are ubiquitous in modified theories of gravity. To be compatible with observations, such a force must be screened on Solar System scales but may still give a significant contribution on galactic scales. If this is the case, the fifth force can influence the calibration of the cosmic distance ladder, hence changing the inferred value of the Hubble constant H₀. In this paper, we analyze symmetron screening and show that it generally increases the Hubble tension. On the other hand, by doing a full statistical analysis, we show that cosmic distance ladder data are able to constrain the theory to a level competitive with Solar System tests—currently the most constraining tests of the theory. For the standard coupling case, the constraint on the symmetron Compton wavelength is λ_C≲2.5  Mpc. Thus, distance ladder data constitutes a novel and powerful way of testing this, and similar, types of theories.

Bimetric gravity can reproduce the accelerated expansion of the Universe, without a cosmological constant. However, the stability of these solutions to linear perturbations has been questioned, suggesting exponential growth of structure in this approximation. We present a simple model of structure formation, for which an analytical solution is derived. The solution is well-behaved, showing that there is no physical instability with respect to these perturbations. The model can yield a growth of structure exhibiting measurable differences from ACDM.

We report the results from spectroscopic observations of the multiple images of the strongly lensed Type Ia supernova (SN Ia), iPTF16geu, obtained with ground-based telescopes and the Hubble Space Telescope (HST). From a single epoch of slitless spectroscopy with HST, we resolve spectra of individual lensed supernova images for the first time. This allows us to perform an independent measurement of the time-delay between the two brightest images, Delta t = 1.4 +/- 5.0 d, which is consistent with the time-delay measured from the light curves. We also present measurements of narrow emission and absorption lines characterizing the interstellar medium in the SN Ia host galaxy at z = 0.4087, as well as in the foreground lensing galaxy at z = 0.2163. We detect strong Naid absorption in the host galaxy, indicating that iPTF16geu belongs to a subclass of SNe Ia displaying 'anomalously' large Naid column densities compared to dust extinction derived from light curves. For the lens galaxy, we refine the measurement of the velocity dispersion, sigma = 129 +/- 4 kms(-1), which significantly constrains the lens model. We use ground-based spectroscopy, boosted by a factor similar to 70 from lensing magnification, to study the properties of a high-z SN Ia with unprecedented signal-to-noise ratio. The spectral properties of the supernova, such as pseudo-Equivalent widths of several absorption features and velocities of the Si II-line, indicate that iPTF16geu is a normal SN Ia. We do not detect any significant deviations of the SN spectral energy distribution from microlensing of the SN photosphere by stars and compact objects in the lensing galaxy.

High-redshift Type Ia supernovae (SNe Ia) are likely to be gravitationally lensed by dark matter haloes of galaxies in the foreground. Since SNe Ia have very small dispersion after light-curve shape and colour corrections, their brightness can be used to measure properties of the dark matter haloes via gravitational magnification. We use observations of galaxies and SNe Ia within the Great Observatories Origins Deep Survey (GOODS) to measure the relation between galaxy luminosity and dark matter halo mass. The relation we investigate is a scaling law between velocity dispersion and galaxy luminosity in the B band: σ = σ*(L/L*)η, where L* = 1010h-2Lsolar. The best-fitting values to this relation are σ* = 136 kms-1 and η = 0.27. We find σ* <~ 190 kms-1 at the 95 per cent confidence level. This method provides an independent cross-check of measurements of dark matter halo properties from galaxy-galaxy lensing studies. Our results agree with the galaxy-galaxy lensing results, but have much larger uncertainties. The GOODS sample of SNe Ia is relatively small (we include 24 SNe) and the results therefore depend on individual SNe Ia. We have investigated a number of potential systematic effects. Light-curve fitting, which affects the inferred brightness of the SNe Ia, appears to be the most important one. Results obtained using different light-curve fitting procedures differ at the 68.3 per cent confidence level.

Aims: Magnification and de-magnification due to gravitational lensing will contribute to the brightness scatter of type Ia supernovae (SNe Ia). The purpose of this paper is to investigate the possibility of decreasing this scatter by correcting individual SNe Ia using observations of galaxies in the foreground, without introducing any extra bias. Methods: We simulate a large number of SN Ia lines of sight populated by galaxies. For each line of sight the true magnification factor and an estimate thereof are calculated. The estimated magnification factor corresponds to what an observer would infer from a survey like the SNLS. Using the simulated data we investigate the possibility of estimating the magnification of individual supernovae with enough precision to be able to correct their brightness for gravitational lensing with negligible bias. Results: Our simulations show that the bias arising from gravitational lensing corrections of individual SNe Ia is negligible for current and next generation surveys and that the scatter from lensing can be reduced by approximately a factor of 2. The total scatter in the SN Ia magnitudes could be reduced by 4% for an intrinsic dispersion of 0.13 mag. For an intrinsic dispersion of 0.09 mag, which may be feasible for future surveys, the total scatter could be reduced by 6%. This will reduce the errors on cosmological parameters derived from supernova data by 4-8%. The prospect of correcting for lensing is thus very good.

Gravitational lensing of high-redshift supernovae is potentially an important source of uncertainty when cosmological parameters are being derived from the measured brightness of Type Ia supernovae, especially in deep surveys with scarce statistics. Photometric and spectroscopic measurements of foreground galaxies along the lines of sight of 33 supernovae discovered with the Hubble Space Telescope, both core-collapse and Type Ia, are used to model the magnification probability distributions of the sources. Modelling galaxy halos with SIS or NFW profiles and using M/L scaling laws provided by the Faber-Jackson and Tully-Fisher relations, we find clear evidence for supernovae with lensing (de)magnification. However, the magnification distribution of the Type Ia supernovae used to determine cosmological distances matches very well the expectations for an unbiased sample; i.e., their mean magnification factor is consistent with unity. Our results show that the lensing distortions of the supernova brightness can be well understood for the GOODS sample and that correcting for this effect has a negligible impact on the derived cosmological parameters.

The flux from distant Type Ia supernovae (SNe) is likely to be amplified or de-amplified by gravitational lensing due to matter distributions along the line of sight. A gravitationally lensed supernova would appear brighter or fainter than the average SN at a particular redshift. We estimate the magnification of 26 SNe in the GOODS fields and search for a correlation with the residual magnitudes of the SNe. The residual magnitude, i.e. the difference between observed and average magnitude predicted by the 'concordance model' of the Universe, indicates the deviation in flux from the average SN. The linear correlation coefficient for this sample is r = 0.29. For a similar, but uncorrelated sample, the probability of obtaining a correlation coefficient equal to or higher than this value is ~10%, i.e. a tentative detection of lensing at ~90% confidence level. Although the evidence for a correlation is weak, our result is in accordance with what could be expected given the small size of the sample.

Gravitational waves emitted by chirping supermassive black hole binaries could in principle be used to obtain very accurate distance determinations. Provided they have an electromagnetic counterpart from which the redshift can be determined, these standard sirens could be used to build a high-redshift Hubble diagram. Errors in the distance measurements will most likely be dominated by gravitational lensing. We show that the (de)magnification due to inhomogeneous foreground matter will increase the scatter in the measured distances by a factor of ~10. We propose to use optical and IR data of the foreground galaxies to minimize the degradation from weak lensing. We find that the net effect of correcting the estimated distances for lensing is comparable to increasing the sample size by a factor of 3 when using the data to constrain cosmological parameters.

We present measurements of the Hubble diagram for 103 Type Ia supernovae (SNe) with redshifts 0.04 < z < 0.42, discovered during the first season (Fall 2005) of the Sloan Digital Sky Survey-II (SDSS-II) Supernova Survey. These data fill in the redshift "desert" between low- and high-redshift SN Ia surveys. Within the framework of the MLCS2K2 light-curve fitting method, we use the SDSS-II SN sample to infer the mean reddening parameter for host galaxies, RV = 2.18 ± 0.14stat ± 0.48syst, and find that the intrinsic distribution of host-galaxy extinction is well fitted by an exponential function, P(AV ) = exp(-AV /τV), with τV = 0.334 ± 0.088 mag. We combine the SDSS-II measurements with new distance estimates for published SN data from the ESSENCE survey, the Supernova Legacy Survey (SNLS), the Hubble Space Telescope (HST), and a compilation of Nearby SN Ia measurements. A new feature in our analysis is the use of detailed Monte Carlo simulations of all surveys to account for selection biases, including those from spectroscopic targeting. Combining the SN Hubble diagram with measurements of baryon acoustic oscillations from the SDSS Luminous Red Galaxy sample and with cosmic microwave background temperature anisotropy measurements from the Wilkinson Microwave Anisotropy Probe, we estimate the cosmological parameters w and ΩM, assuming a spatially flat cosmological model (FwCDM) with constant dark energy equation of state parameter, w. We also consider constraints upon ΩM and ΩΛ for a cosmological constant model (ΛCDM) with w = -1 and non-zero spatial curvature. For the FwCDM model and the combined sample of 288 SNe Ia, we find w = -0.76 ± 0.07(stat) ± 0.11(syst), ΩM = 0.307 ± 0.019(stat) ± 0.023(syst) using MLCS2K2 and w = -0.96 ± 0.06(stat) ± 0.12(syst), ΩM = 0.265 ± 0.016(stat) ± 0.025(syst) using the SALT-II fitter. We trace the discrepancy between these results to a difference in the rest-frame UV model combined with a different luminosity correction from color variations; these differences mostly affect the distance estimates for the SNLS and HST SNe. We present detailed discussions of systematic errors for both light-curve methods and find that they both show data-model discrepancies in rest-frame U band. For the SALT-II approach, we also see strong evidence for redshift-dependence of the color-luminosity parameter (β). Restricting the analysis to the 136 SNe Ia in the Nearby+SDSS-II samples, we find much better agreement between the two analysis methods but with larger uncertainties: w = -0.92 ± 0.13(stat)+0.10 -0.33(syst) for MLCS2K2 and w = -0.92 ± 0.11(stat)+0.07 -0.15 (syst) for SALT-II.

We set out to rederive the 8 Hubble parameter values obtained from estimated relative galaxy ages by Simon et al. We find that to obtain the level of precision claimed in H(⁠z⁠), unrealistically small galaxy age uncertainties have to be assumed. Also, some parameter values will be correlated. In our analysis we find that the uncertainties in the Hubble parameter values are significantly larger when 8 independent H(⁠z⁠) are obtained using Monte Carlo sampling. Smaller uncertainties can be obtained using Gaussian processes, but at the cost of strongly correlated results. We do not obtain any useful constraints on the Hubble parameter from the galaxy data employed.

A fact is that an Einstein solution in one sector in ghost-free bimetric theory implies an Einstein solution in the other sector. Earlier studies have also shown that some classes of bimetric models necessitate proportional solutions between the sectors. Here, we consider a general setup of the parameters in the theory as well as the general algebraic form of the potential. We show that, if one sector has an Einstein solution, the solutions are either proportional or block proportional with at most two different eigenvalues in the square root governing metric interactions.

We consider the Hassan-Rosen bimetric field equations in vacuum when the two metrics share a single common null direction in a spherically symmetric configuration. By solving these equations, we obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. Besides not being asymptotically flat, the found solutions are nonstationary admitting only three global spacelike Killing vector fields which are the generators of spatial rotations. Hence, these are spherically symmetric bimetric vacuum solutions with the minimal number of isometries. The absence of staticity formally disproves an analogue statement to Birkhoff's theorem in the ghost-free bimetric theory which would state that a spherically symmetric solution is necessarily static in empty space.

We present a method for solving the constraint equations in the Hassan-Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a polytropic fluid in general relativity, here called Lane-Emden-like equations. Using a numerical code which solves the evolution equations in the standard 3 + 1 form, we also obtain a short-term development of the initial data for these bimetric spherical clouds. The evolution highlights some important features of the bimetric theory such as the interwoven and oscillating null cones representing the essential nonbidiagonality in the dynamics of the two metrics. The simulations are in the strong-field regime and show that, at least at an early stage, if the bimetric initial data are close to those for general relativity, the bimetric evolution stays close to the evolution in general relativity as well, and with no instabilities, albeit with small oscillations in the metric fields. In addition, we determine initial data and first evolution for vacuum bimetric spherically symmetric nonstationary solutions, providing generic counterexamples to a statement analog to Jebsen-Birkhoff theorem in bimetric relativity.

Recently, Kenna-Allison et al claimed that bimetric gravity cannot give rise to a viable cosmological expansion history while at the same time being compatible with local gravity tests. In this note we review that claim and combine various results from the literature to provide several simple counter examples. We conclude that the results of Kenna-Allison et al cannot hold in general.

We constrain the light extinction properties of Milky Way dust. We investigated the correlations between dust column density as inferred from infrared data and the observed colours of celestial objects at cosmological distances with low levels of colour dispersion. Results derived using colours of quasars, brightest central galaxies, and luminous red galaxies are broadly consistent, indicating a proportionality constant between the reddening E(B - V) = A(B) - A(V) and the dust column density D-T (given in units of MJy/sr) of p = E(B - V)/D-T similar to 0.02 and a reddening parameter R-V = Lambda(V)/E(B - V) similar to 3 with fractional uncertainties of approximately 10%. The data do not provide any evidence for spatial variations in the dust properties, except for a possible hint of scatter in the dust extinction properties at the longest optical wavelengths.

In this note, we discuss how possible expansion histories of the Universe can be inferred in a simple way, for arbitrary energy contents. No new physical results are obtained, but the goal is rather to discuss an alternative way of writing the Friedmann equation in order to facilitate an intuitive understanding of the possible solutions; for students and researchers alike. As has been noted in passing by others, this specific form of the Friedmann equation allows us to view the universal expansion as a particle rolling along a frictionless track. Specific examples depicted include the current concordance cosmological model as well as a stable static universal model.

The bimetric generalization of general relativity has been proven to be able to give an accelerated background expansion consistent with observations. Apart from the energy densities coupling to one or both of the metrics, the expansion will depend on the cosmological constant contribution to each of them, as well as the three parameters describing the interaction between the two metrics. Even for fixed values of these parameters can several possible solutions, so called branches, exist. Different branches can give similar background expansion histories for the observable metric, but may have different properties regarding, for example, the existence of ghosts and the rate of structure growth. In this paper, we outline a method to find viable solution branches for arbitrary parameter values. We show how possible expansion histories in bimetric gravity can be inferred qualitatively, by picturing the ratio of the scale factors of the two metrics as the spatial coordinate of a particle rolling along a frictionless track. A particularly interesting example discussed is a specific set of parameter values, where a cosmological dark matter background is mimicked without introducing ghost modes into the theory.

We investigate what current cosmological data tells us about the cosmological expansion rate in a model independent way. Specifically, we study if the expansion was decelerating at high redshifts and is accelerating now, without referring to any model for the energy content of the universe, nor to any specific theory of gravity. This differs from most studies of the expansion rate which, e.g., assumes some underlying parameterised model for the dark energy component of the universe. To accomplish this, we have devised a new method to probe the expansion rate without relying on such assumptions. Using only supernova data, we conclude that there is little doubt that the universe has been accelerating at late times. However, contrary to some previous claims, we can not determine if the universe was previously decelerating. For a variety of methods used for constraining the expansion history of the universe, acceleration is detected from supernovae alone at >5σ, regardless of the curvature of the universe. Specifically, using a Taylor expansion of the scale factor, acceleration today is detected at >12σ. If we also include the ratio of the scale of the baryon acoustic oscillations as imprinted in the cosmic microwave background and in the large scale distribution of galaxies, it is evident from the data that the expansion decelerated at high redshifts, but only with the assumption of a flat or negatively curved universe.

The Lambda Cold Dark Matter model (Lambda CDM) represents the current standard model in cosmology. Within this, there is a tension between the value of the Hubble constant, H-0, inferred from local distance indicators and the angular scale of fluctuations in the Cosmic Microwave Background (CMB). In terms of Bayseian evidence, we investigate whether the tension is significant enough to warrant new physics in the form of modifying or adding energy components to the standard cosmological model. We find that late time dark energy explanations are not favoured by data whereas a pre-CMB decoupling extra dark energy component has a positive, although not substantial, Bayesian evidence. A constant equation of state of the additional early energy density is constrained to 0.086(-0.03)(+0:04). Although this value deviates significantly from 1/3, valid for dark radiation, the latter is favoured based on the Bayesian evidence. If the tension persists, future estimates of H-0 at the 1% level will be able to decisively determine which of the proposed explanations is favoured.