The Dyer-Roeder distance-redshift relation in inhomogeneous universes

Using Monte-Carlo methods, we determine the best-fit value of the homogeneity parameter alpha in the Dyer-Roeder distance-redshift relation for a variety of redshifts, inhomogeneity models and cosmological parameter values. The relation between alpha and the fraction of compact objects, f_p, is found to be approximately linear. This relation can be parametrized with reasonable accuracy for all cases treated in this paper by alpha = a*f_p, where a = 0.6.Comment: 5 pages, 10 figures, submitted to Phys.Rev.

Type Ia supernova constraints on compact object dark matter

The nature of dark matter (DM) is an open question in cosmology, despite its abundance in the universe. While elementary particles have been posited to 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 $M \gtrsim 0.01 M_\odot$, using the Type Ia supernova Hubble diagram. Utilizing the Dyer-Roeder distance relation, where the homogeneous matter fraction is parameterized with $\eta$, we find a maximum fractional amount of DM in compact objects ($f_p$) of 0.50 at 95\% confidence level (C.L.), in the flat $\Lambda$CDM model and 0.49 when marginalising over a constant dark energy equation of state. These limits do not change when marginalising over cosmic curvature, demonstrating the robustness to the cosmological model. When allowing for the prior on $\eta$ to include $\eta > 1$, we derive $f_p < 0.32$ at 95$\%$ C.L., showing that the prior assumption of $\eta \leq 1$ gives a conservative upper limit on $f_p$. When including Cepheid calibrated supernovae, the 95\% C.L. constraints improve to $f_p < 0.25$. We find that the estimate for the Hubble constant in our inference is consistent with the homogeneous case, showing that inhomogeneities in the form of compact dark matter cannot account for the observed Hubble tension. In conclusion, we strongly exclude the possibility that PBHs with stellar masses and above form a dominant fraction of the dark matter.Comment: to be submitted to MNRAS Letter

Measuring the properties of extragalactic dust and implications for the Hubble diagram

Scattering and absorption of light by a homogeneous distribution of intergalactic large dust grains has been proposed as an alternative, non-cosmological explanation for the faintness of Type Ia supernovae at z\s im 0.5. We investigate the differential extinction for high-redshift sources caused by extragalactic dust along the line of sight. Future observations of Type Ia supernovae up to $z\sim 2$, e.g. by the proposed SNAP satellite, will allow the measurement of the properties of dust over cosmological distances. We show that 1% {\em relative} spectrophotometric accuracy (or broadband photometry) in the wavelength interval 0.7--1.5 $\mu$m is required to measure the extinction caused by ``grey'' dust down to $\delta m=0.02$ magnitudes. We also argue that the presence of grey dust is not necessarily inconsistent with the recent measurement of the brightness of a supernova at $z=1.7$ (SN 1997ff), in the absence of accurate spectrophotometric information of the supernova.Comment: Accepted by A&

Limiting the dimming of distant type Ia supernovae

Distant supernovae have been observed to be fainter than what is expected in a matter dominated universe. The most likely explanation is that the universe is dominated by an energy component with negative pressure -- dark energy. However, there are several astrophysical processes that could, in principle, affect the measurements and in order to be able to take advantage of the growing supernova statistics, the control of systematic effects is crucial. We discuss two of these; extinction due to intergalactic grey dust and dimming due to photon-axion oscillations and show how their effect on supernova observations can be constrained using observed quasar colours and spectra. For a wide range of intergalactic dust models, we are able to rule out any dimming larger than 0.2 magnitudes for a type Ia supernova at z=1. The corresponding limit for intergalactic Milky Way type dust is 0.03 mag. For the more speculative model of photons mixing with axions, we find that the effect is independent of photon energy for certain combinations of parameter values and a dimming as large as 0.6 magnitudes cannot be ruled out. These effects can have profound implications for the possibility of constraining dark energy properties using supernova observations.Comment: 19 pages, 11 figures Matches version accepted in JCAP. Some corrections due to minor bug in simulations, major conclusions unchange

Is Dark Energy Dynamical? Prospects for an Answer

Recent data advances offer the exciting prospect of a first look at whether dark energy has a dynamical equation of state or not. While formally theories exist with a constant equation of state, they are nongeneric -- Einstein's cosmological constant is a notable exception. So limits on the time variation, w', directly tell us crucial physics. Two recent improvements in supernova data from the Hubble Space Telescope allow important steps forward in constraining the dynamics of dark energy, possessing the ability to exclude models with w'\ga 1, if the universe truly has a cosmological constant. These data bring us much closer to the ``systematics'' era, where further improvements will come predominantly from more accurate, not merely more, observations. We examine the possible gains and point out the complementary roles of space and ground based observations in the near future. To achieve the leap to precision understanding of dark energy in the next generation will require specially designed space based measurements; we estimate the confidence level of detection of dynamics (e.g. distinguishing between $w'=0$ and $w'=1$) will be ~1.8\sigma after the ongoing generation, improving to more than 6.5\sigma in the dedicated space generation.Comment: 6 pages, 2 figures; version accepted to Phys. Rev.

SNOC: a Monte-Carlo simulation package for high-z supernova observations

We present a Monte-Carlo package for simulation of high-redshift supernova data, SNOC. Optical and near-infrared photons from supernovae are ray-traced over cosmological distances from the simulated host galaxy to the observer at Earth. The distances to the sources are calculated from user provided cosmological parameters in a Friedmann-Lemaitre universe, allowing for arbitrary forms of ``dark energy''. The code takes into account gravitational interactions (lensing) and extinction by dust, both in the host galaxy and in the line-of-sight. The user can also choose to include exotic effects like a hypothetical attenuation due to photon-axion oscillations. SNOC is primarily useful for estimations of cosmological parameter uncertainties from studies of apparent brightness of Type Ia supernovae vs redshift, with special emphasis on potential systematic effects. It can also be used to compute standard cosmological quantities like luminosity distance, lookback time and age of the universe in any Friedmann-Lemaitre model with or without quintessence.Comment: 16 pages, 3 figure

Cosmic distance-duality as probe of exotic physics and acceleration

In cosmology, distances based on standard candles (e.g. supernovae) and standard rulers (e.g. baryon oscillations) agree as long as three conditions are met: (1) photon number is conserved, (2) gravity is described by a metric theory with (3) photons travelling on unique null geodesics. This is the content of distance-duality (the reciprocity relation) which can be violated by exotic physics. Here we analyse the implications of the latest cosmological data sets for distance-duality. While broadly in agreement and confirming acceleration we find a 2-sigma violation caused by excess brightening of SN-Ia at z > 0.5, perhaps due to lensing magnification bias. This brightening has been interpreted as evidence for a late-time transition in the dark energy but because it is not seen in the d_A data we argue against such an interpretation. Our results do, however, rule out significant SN-Ia evolution and extinction: the "replenishing" grey-dust model with no cosmic acceleration is excluded at more than 4-sigma despite this being the best-fit to SN-Ia data alone, thereby illustrating the power of distance-duality even with current data sets.Comment: 6 pages, 4 colour figures. Version accepted as a Rapid Communication in PR

Near-IR search for lensed supernovae behind galaxy clusters: III. Implications for cluster modeling and cosmology

Massive galaxy clusters at intermediate redshifts act as gravitational lenses that can magnify supernovae (SNe) occurring in background galaxies. We assess the possibility to use lensed SNe to put constraints on the mass models of galaxy clusters and the Hubble parameter at high redshift. Due to the standard candle nature of Type Ia supernovae (SNe Ia), observational information on the lensing magnification from an intervening galaxy cluster can be used to constrain the model for the cluster mass distribution. A statistical analysis using parametric cluster models was performed to investigate the possible improvements from lensed SNe Ia for the accurately modeled galaxy cluster A1689 and the less well constrained cluster A2204. Time delay measurements obtained from SNe lensed by accurately modeled galaxy clusters can be used to measure the Hubble parameter. For a survey of A1689 we estimate the expected rate of detectable SNe Ia and of multiply imaged SNe. The velocity dispersion and core radius of the main cluster potential show strong correlations with the predicted magnifications and can therefore be constrained by observations of SNe Ia in background galaxies. This technique proves especially powerful for galaxy clusters with only few known multiple image systems. The main uncertainty for measurements of the Hubble parameter from the time delay of strongly lensed SNe is due to cluster model uncertainties. For the extremely well modeled cluster A1689, a single time delay measurement could be used to determine the Hubble parameter with a precision of ~ 10%. We conclude that observations of SNe Ia behind galaxy clusters can be used to improve the mass modeling of the large scale component of galaxy clusters and thus the distribution of dark matter. Time delays from SNe strongly lensed by accurately modeled galaxy clusters can be used to measure the Hubble constant at high redshifts.Comment: 10 pages, 8 figures, 3 tables. Accepted for publication in A&

Constraining dark energy fluctuations with supernova correlations

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.Comment: 18 pages, 6 figures, matches the published versio