On model selection forecasting, dark energy and modified gravity

The Fisher matrix approach allows one to calculate in advance how well a given experiment will be able to estimate model parameters, and has been an invaluable tool in experimental design. In the same spirit, we present here a method to predict how well a given experiment can distinguish between different models, regardless of their parameters. From a Bayesian viewpoint, this involves computation of the Bayesian evidence. In this paper, we generalize the Fisher matrix approach from the context of parameter fitting to that of model testing, and show how the expected evidence can be computed under the same simplifying assumption of a Gaussian likelihood as the Fisher matrix approach for parameter estimation. With this 'Laplace approximation' all that is needed to compute the expected evidence is the Fisher matrix itself. We illustrate the method with a study of how well upcoming and planned experiments should perform at distinguishing between dark energy models and modified gravity theories. In particular, we consider the combination of 3D weak lensing, for which planned and proposed wide-field multiband imaging surveys will provide suitable data, and probes of the expansion history of the Universe, such as proposed supernova and baryonic acoustic oscillations surveys. We find that proposed large-scale weak-lensing surveys from space should be able readily to distinguish General Relativity from modified gravity models.     

Cosmic microwave background anisotropy in the decaying neutrino cosmology

It is attractive to suppose for several astrophysical reasons that the Universe has close to the critical density in light (∼30 eV) neutrinos which decay radiatively with a lifetime of ∼10²³ s. In such a cosmology the Universe is re-ionized early and the last scattering surface of the cosmic microwave background significantly broadened. We calculate the resulting angular power spectrum of temperature fluctuations in the cosmic microwave background. As expected, the acoustic peaks are significantly damped relative to the standard case. This would allow a definitive test of the decaying neutrino cosmology with the forthcoming MAP Planck surveyor missions.     

Dark matter annihilation at cosmological redshifts: possible relic signal from annihilation of weakly interacting massive particles

We discuss the possibility of observing the products of the dark matter annihilation that was going on in the early Universe. Of all the particles that could be generated by this process, we consider only photons, as they are both uncharged and easily detectable. The younger the Universe was, the higher the dark matter concentration n and the annihilation rate (proportional to n ²) were. However, the emission from the very early Universe cannot reach us because of the opacity. The main part of the signal was generated at the moment the Universe had just become transparent for the photons produced by the annihilation. Thus, the dark matter annihilation in the early Universe should have created a sort of relic emission. We obtain its flux and the spectrum.
If weakly interacting massive particles (WIMPs) constitute dark matter, it is shown that we may expect an extragalactic gamma-ray signal in the energy range 0.5–20 MeV with a maximum near 8 MeV. We show that an experimentally observed excess in the gamma-ray background at 0.5–20 MeV could be created by the relic signal from the annihilation of WIMPs only if the dark matter structures in the Universe had appeared before the Universe became transparent for the annihilation products  ( z ≃ 300)  . We discuss in more detail physical conditions whereby this interpretation could be possible.     

Theory and statistics of weak lensing from large-scale mass inhomogeneities

Weak lensing by large-scale mass inhomogeneities in the Universe induces correlations in the observed ellipticities of distant sources. We first review the harmonic analysis and statistics required of these correlations and discuss calculations for the predicted signal. We consider the ellipticity correlation function, the mean-square ellipticity, the ellipticity power spectrum and a global maximum-likelihood analysis to isolate a weak-lensing signal from the data. Estimates for the sensitivity of a survey of a given area, surface density, and mean intrinsic source ellipticity are presented. We then apply our results to the FIRST radio-source survey. We predict an rms ellipticity of roughly 0.011 in 1 × 1 deg² pixels and 0.018 in 20 × 20 arcmin² pixels if the power spectrum is normalized to σ₈ Ω^0.53 = 0.6, as indicated by the cluster abundance. The signal is significantly larger in some models if the power spectrum is normalized instead to the COBE anisotropy. The uncertainty in the predictions from imprecise knowledge of the FIRST redshift distribution is about 25 per cent in the rms ellipticity. We show that FIRST should be able to make a statistically significant detection of a weak-lensing signal for cluster-abundance-normalized power spectra.     

Decelerating universes older than their Hubble times

Recent observations suggest that Hubble's constant is large, and hence that the Universe appears to be younger than some of its constituents. The traditional escape route, which assumes that the expansion is accelerating, appears to be blocked by observations of Type Ia supernovae, which suggest that the Universe is decelerating. These observations are reconciled in a model in which the Universe has experienced an inflationary phase in the recent past, driven by an ultralight inflaton, the Compton wavelength of which is of the same order as the Hubble radius.     

Primordial black holes

Primordial black holes (PBHs) are a profound signature of primordial cos-mological structures and provide a theoretical tool to study nontrivial physics of the early Universe. The mechanisms of PBH formation are discussed and observational constraints on the PBH spectrum, or effects of PBH evaporation, are shown to re-strict a wide range of particle physics models, predicting an enhancement of the ul-traviolet part of the spectrum of density perturbations, early dust-like stages, first or-der phase transitions and stages of superheavy metastable particle dominance in the early Universe. The mechanism of closed wall contraction can lead, in the inflation-ary Universe, to a new approach to galaxy formation, involving primordial clouds of massive BHs created around the intermediate mass or supermassive BH and playing the role of galactic seeds.     

Quark-Novae Ia in the Hubble diagram: implications for dark energy

The accelerated expansion of the Universe was proposed through the use of Type-Ia supernovae （SNe） as standard candles. The standardization depends on an empirical correlation between the stretch/color and peak luminosity of the light curves. The use of Type-Ia SNe as standard candles rests on the assumption that their properties （and this correlation） do not vary with redshift. We consider the possibility that the majority of Type-Ia SNe are in fact caused by a Quark-Nova detonation in a tight neutron-star-CO-white-dwarf binary system, which forms a Quark-Nova Ia （QN-Ia）. The spin-down energy injected by the Quark-Nova remnant （the quark star） contributes to the post-peak light curve and neatly explains the observed correlation between peak luminosity and light curve shape. We demonstrate that the parameters describing QN-Ia are NOT constant in redshift. Simulated QN-Ia light curves provide a test of the stretch/color correlation by comparing the true distance modulus with that determined using SN light curve fitters. We determine a correction between the true and fitted distance moduli, which when applied to Type-Ia SNe in the Hubble diagram recovers the ΩM = 1 cosmology. We conclude that Type-Ia SNe observations do not necessitate the need for an accelerating expansion of the Universe （if the observed SNe Ia are dominated by QNe Ia） and by association the need for dark energy.     

Non-parametric inversion of gravitational lensing systems with few images using a multi-objective genetic algorithm

Galaxies acting as gravitational lenses are surrounded by, at most, a handful of images. This apparent paucity of information forces one to make the best possible use of what information is available to invert the lens system. In this paper, we explore the use of a genetic algorithm to invert in a non-parametric way strong lensing systems containing only a small number of images. Perhaps the most important conclusion of this paper is that it is possible to infer the mass distribution of such gravitational lens systems using a non-parametric technique. We show that including information about the null space (i.e. the region where no images are found) is prerequisite to avoid the prediction of a large number of spurious images, and to reliably reconstruct the lens mass density. While the total mass of the lens is usually constrained within a few per cent, the fidelity of the reconstruction of the lens mass distribution depends on the number and position of the images. The technique employed to include null space information can be extended in a straightforward way to add additional constraints, such as weak-lensing data or time-delay information.     

Cosmic equation of state and advanced LIGO-type gravitational wave experiments

It is hoped that the future generation of interferometric gravitational wave detectors will provide accurate measurements of the final stages of binary in-spirals. The sources probed by such experiments are of extragalactic origin and the observed chirp mass is the intrinsic chirp mass multiplied by (1+ z ) where z is the redshift of the source. Moreover the luminosity distance is a direct observable in such experiments. This creates the possibility to establish a new kind of cosmological test, supplementary to more standard ones.
Recent observations of distant type Ia supernovae light curves suggest that the expansion of the Universe has recently begun to accelerate. A popular explanation of the present accelerating expansion of the Universe is to assume that some part Ω_Q of the matter–energy density is in the form of a dark component called 'the quintessence' with the equation of state p _Q= wρ _Q with w ≥−1 . In this paper we consider the predictions concerning observations of binary in-spirals in future LIGO-type interferometric experiments assuming a 'quintessence cosmology'. In particular we compute the expected redshift distributions of observed events in the a priori admissible range of parameters describing the equation of state for the quintessence. We find that this distribution has a robust dependence on the cosmic equation of state.     

Weak lensing in the second post-Newtonian approximation: gravitomagnetic potentials and the integrated Sachs–Wolfe effect

Dark matter currents in the large-scale structure give rise to gravitomagnetic terms in the metric, which affect the light propagation. Corrections to the weak-lensing power spectrum due to these gravitomagnetic potentials are evaluated by perturbation theory. A connection between gravitomagnetic lensing and the integrated Sachs–Wolfe (iSW) effect is drawn, which can be described by a line-of-sight integration over the divergence of the gravitomagnetic vector potential. This allows the power spectrum of the iSW-effect to be derived within the framework of the same formalism as derived for gravitomagnetic lensing and reduces the iSW-effect to a second-order lensing phenomenon. The three-dimensional power spectra are projected by means of a generalized Limber-equation to yield the angular power spectra. Gravitomagnetic corrections to the weak-lensing spectrum are negligible at currently accessible scales, and cosmic-variance considerations suggest that the detection of the iSW-effect's contribution to the cosmic microwave background angular power spectrum is too small to be detectable at multipoles probed by the Planck satellite.     

Analytic solutions for coupled linear perturbations

Analytic solutions for the evolution of cosmological linear density perturbations in the baryonic gas and collisionless dark matter are derived. The solutions are expressed in a closed form in terms of elementary functions, for arbitrary baryonic mass fraction. They are obtained assuming =1 and a time-independent comoving Jeans wavenumber, k _J. By working with a time variable ln( t ^2/3), the evolution of the perturbations is described by linear differential equations with constant coefficients. The new equations are then solved by means of Laplace transformation, assuming that the gas and dark matter trace the same density field before a sudden heating epoch. In a dark matter-dominated Universe, the ratio of baryonic to dark matter density perturbation decays with time roughly as exp(5 /4) t ^5/6 to the limiting value 1/[1+( k k _J)²]. For wavenumbers the decay is accompanied by oscillations with a period in . In comparison, as increases in a baryonic matter-dominated Universe, the ratio approaches 1( k k _J)² for k k _J, and zero otherwise.     

A constant dark matter halo surface density in galaxies

We confirm and extend the recent finding that the central surface density  μ_0D≡ r ₀ρ₀  of galaxy dark matter haloes, where r ₀ and  ρ₀  are the halo core radius and central density, is nearly constant and independent of galaxy luminosity. Based on the co-added rotation curves (RCs) of ∼1000 spiral galaxies, the mass models of individual dwarf irregular and spiral galaxies of late and early types with high-quality RCs, and the galaxy–galaxy weak-lensing signals from a sample of spiral and elliptical galaxies, we find that  log μ_0D= 2.15 ± 0.2  in units of  log(M_⊙ pc⁻²)  . We also show that the observed kinematics of Local Group dwarf spheroidal galaxies are consistent with this value. Our results are obtained for galactic systems spanning over 14 mag, belonging to different Hubble types and whose mass profiles have been determined by several independent methods. In the same objects, the approximate constancy of  μ_0D  is in sharp contrast to the systematical variations, by several orders of magnitude, of galaxy properties, including  ρ₀  and central stellar surface density.     

Implications of primordial black holes on the first stars and the origin of the super-massive black holes

If the cosmological dark matter has a component made of small primordial black holes (BHs), they may have a significant impact on the physics of the first stars and on the subsequent formation of massive BHs. Primordial BHs would be adiabatically contracted into these stars and then would sink to the stellar centre by dynamical friction, creating a larger BH which may quickly swallow the whole star. If these primordial BHs are heavier than  ∼10²² g  , the first stars would likely live only for a very short time and would not contribute much to the reionization of the Universe. They would instead become  10–10³ M_⊙  BHs which (depending on subsequent accretion) could serve as seeds for the super-massive BHs seen at high redshifts as well as those inside galaxies today.     

The Lyman α forest in a truncated hierarchical structure formation

The Lyman α forest provides important constraints on the smoothness of the Universe on large scales. We calculate the flux distribution along the line of sight to quasars in a universe made of randomly distributed clumps, each of them with a Rayleigh–L'evy fractal structure with dimension D <2. We consider the probability distribution function of the normalized flux in the line of sight to quasars. We illustrate that the truncated clustering hierarchy model with D <2 shows far too many voids along the line of sight to quasars compared with the observed flux distribution and the distribution in a cold dark matter model. This supports the common view that on large scales the Universe is homogeneous, rather than fractal-like.     

lemomaf: Lensed Mock Map Facility

We present the Lensed Mock Map Facility ( lemomaf ), a tool designed to perform mock weak-lensing measurements on numerically simulated chunks of the Universe. Coupling N -body simulations to a semi-analytical model of galaxy formation, lemomaf can create realistic lensed images and mock catalogues of galaxies, at wavelengths ranging from the ultraviolet to the submillimetre. To demonstrate the power of such a tool, we compute predictions of the source–lens clustering (SLC) effect on the convergence statistics, and quantify the impact of weak lensing on galaxy counts in two different filters. We find that the SLC effect skews the probability density function of the convergence towards low values, with an intensity which strongly depends on the redshift distribution of galaxies. On the other hand, the degree of enhancement or depletion in galaxy counts due to weak lensing is independent of the SLC effect. We discuss the impact on the two-point shear statistics to be measured by future missions like SNAP and LSST . The SLC effect would bias the estimation of σ₈ from two-point statistics up to 5 per cent for a narrow redshift distribution of mean   z ∼ 0.5  , and up to 2 per cent in small angular scales for a redshift distribution of mean   z ∼ 1.5  . We conclude that accurate photometric redshifts for individual galaxies are necessary in order to quantify and isolate the SLC effect.     

Recovering the initial conditions of our local Universe from NOG and PSCz catalogues

We apply the ztrace algorithm to the optical NOG and infrared PSC z galaxy catalogues to reconstruct the pattern of primordial fluctuations that have generated our local Universe. We check that the density fields traced by the two catalogues are well correlated, and consistent with a linear relation [either in δ or in  log (1 +δ)  ] with relative bias (of NOG with respect to PSC z )   b _rel= 1.1 ± 0.1  . The relative bias relation is used to fill the optical zone of avoidance at  | b | < 20°  using the PSC z galaxy density field.
We perform extensive testing on simulated galaxy catalogues to optimize the reconstruction. The quality of the reconstruction is predicted to be good at large scales, up to a limiting wavenumber   k _lim≃ 0.4 h Mpc⁻¹  beyond which all information is lost. We find that the improvement arising from the denser sampling of the optical catalogue is compensated by the uncertainties connected to the larger zone of avoidance.
The initial conditions reconstructed from the NOG catalogue are found (analogously to those from the PSC z ) to be consistent with a Gaussian paradigm. We use the reconstructions to produce sets of initial conditions ready to be used for constrained simulations of our local Universe.     

The existence and detection of optically dark galaxies by 21-cm surveys

One explanation for the disparity between cold dark matter (CDM) predictions of galaxy numbers and observations could be that there are numerous dark galaxies in the Universe. These galaxies may still contain baryons, but no stars, and may be detectable in the 21-cm line of atomic hydrogen. The results of surveys for such objects, and simulations that do/do not predict their existence, are controversial. In this paper, we use an analytical model of galaxy formation, consistent with CDM, to first show that dark galaxies are certainly a prediction of the model. Secondly, we show that objects like VIRGOHI21, a dark galaxy candidate recently discovered by us, while rare are predicted by the model. Thirdly, we show that previous 'blind' H  i surveys have placed few constraints on the existence of dark galaxies. This is because they have either lacked the sensitivity and/or velocity resolution or have not had the required detailed optical follow up. We look forward to new 21-cm blind surveys [Arecibo Legacy Fast ALFA (ALFALFA) survey and Arecibo Galactic Environments Survey (AGES)] using the Arecibo multibeam instrument which should find large numbers of dark galaxies if they exist.     

Testing dark energy with the Advanced Liquid-mirror Probe of Asteroids, Cosmology and Astrophysics

The Advanced Liquid-mirror Probe of Asteroids, Cosmology and Astrophysics (ALPACA) is a proposed 8-m liquid-mirror telescope surveying  ∼1000 deg²  of the Southern hemisphere sky. It will be a remarkably simple and inexpensive telescope that none the less will deliver a powerful sample of optical data for studying dark energy. The bulk of the cosmological data consist of nightly, high signal-to-noise ratio, multiband light curves of Type Ia supernovae (SNe Ia). At the end of the 3-yr run, ALPACA is expected to collect  ≳100 000  SNe Ia up to   z ∼ 1  . This will allow us to reduce present systematic uncertainties affecting the standard-candle relation. The survey will also provide several other data sets such as the detection of baryon acoustic oscillations in the matter power spectrum and shear weak-lensing measurements. In this preliminary analysis, we forecast constraints on dark energy parameters from SNe Ia and baryon acoustic oscillations. The combination of these two data sets will provide competitive constraints on the dark energy parameters under minimal prior assumptions. Further studies are needed to address the accuracy of weak-lensing measurements.     

Rydberg matter in space: low-density condensed dark matter

Here Rydberg matter is proposed as a candidate for the missing dark matter or dark baryonic matter in the Universe. Spectroscopic and other experimental studies give valuable information on the properties of Rydberg matter, especially its very weak interaction with light caused by the very small overlap with low states, and because of the necessary two-electron transitions even for disturbed matter. Recently, the unidentified infrared (UIR) bands have been shown to agree well with calculations and experiments on Rydberg matter. This is the reason for the present, somewhat speculative, proposal that dark matter has, at least partially, the form of Rydberg matter. The UIR bands have also been observed directly in emission from Rydberg matter in the laboratory. The unique space-filling properties of Rydberg matter are described: a hydrogen atom in this matter occupies a volume  5×10¹²  times larger than in its ground state or in a hydrogen molecule.