We consider a generic type of dark energy fluid, characterised by a constant equation of state parameter w and sound speed c s , and investigate the impact of dark energy clustering on cosmic structure formation using the spherical collapse model. Along the way, we also discuss in detail the evolution of dark energy perturbations in the linear regime. We find that the introduction of a finite sound speed into the picture necessarily induces a scale-dependence in the dark energy clustering, which in turn affects the dynamics of the spherical collapse in a scale-dependent way. As with other, more conventional fluids, we can define a Jeans scale for the dark energy clustering, and hence a Jeans mass M J for the dark matter which feels the effect of dark energy clustering via gravitational interactions. For bound objects (halos) with masses M ≫ M J , the effect of dark energy clustering is maximal. For those with M ≪ M J , the dark energy component is effectively homogeneous, and its role in the formation of these structures is reduced to its effects on the Hubble expansion rate. To compute quantitatively the virial density and the linearly extrapolated threshold density, we use a quasi-linear approach which is expected to be valid up to around the Jeans mass. We find an interesting dependence of these quantities on the halo mass M , given some w and c s . The dependence is the strongest for masses lying in the vicinity of M ∼ M J . Observing this M -dependence will be a tell-tale sign that dark energy is dynamic, and a great leap towards pinning down its clustering properties.

Abstract. We perform a detailed forecast on how well a Euclid-like survey will be able to constrain dark energy and neutrino parameters from a combination of its cosmic shear power spectrum, galaxy power spectrum, and cluster mass function measurements. We find that the combination of these three probes vastly improves the survey's potential to measure the time evolution of dark energy. In terms of a dark energy figure-of-merit defined as (σ(w p )σ(w a )) −1 , we find a value of 690 for Euclid-like data combined with Planck-like measurements of the cosmic microwave background (CMB) anisotropies in a 10-dimensional cosmological parameter space, assuming a ΛCDM fiducial cosmology. For the more commonly used 7-parameter model, we find a figure-of-merit of 1900 for the same data combination. We consider also the survey's potential to measure dark energy perturbations in models wherein the dark energy is parameterised as a fluid with a nonstandard non-adiabatic sound speed, and find that in an optimistic scenario in which w 0 deviates by as much as is currently observationally allowed from −1, models withĉ 2 s = 10 −6 andĉ 2 s = 1 can be distinguished at more than 2σ significance. We emphasise that constraints on the dark energy sound speed from cluster measurements are strongly dependent on the modelling of the cluster mass function; significantly weaker sensitivities ensue if we modify our model to include fewer features of nonlinear dark energy clustering. Finally, we find that the sum of neutrino masses can be measured with a 1σ precision of 0.015 eV, even in complex cosmological models in which the dark energy equation of state varies with time. The 1σ sensitivity to the effective number of relativistic species N ml eff is approximately 0.03, meaning that the small deviation of 0.046 from 3 in the standard value of N ml eff due to non-instantaneous decoupling and finite temperature effects can be probed with 1σ precision for the first time.

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PurposeThe purpose of this paper is to analyse the dividend policy of firms from a macroeconomic perspective. In order to do so inflation and real growth are also considered.Design/methodology/approachThe paper examines the relationship between dividends, corporate earnings, real growth and inflation in the USA by applying cointegration techniques. In this framework, impulse response analysis is used to test the two most popular theories of dividend determination.FindingsThe data indicate three cointegration relations among the four‐time series. Impulse response analysis then shows some interesting dynamics. Dividend smoothing seems to be a relevant phenomenon. Furthermore, inflation has a positive effect on dividends.Research limitations/implicationsThe most important finding of this paper is the indication of a positive relationship between inflation and dividend payments. This can be interpreted in two different ways: managers may try to follow a dividend policy, which is perceived to be optimal, believing that there is a desirable level of real dividend income to be paid to their investors. On the other hand, inflation may simply increase the nominal value of corporate earnings and therefore the dividends paid. Independently from the interpretation of the results, inflation should definitely be considered analysing dividend policy.Practical implicationsManagers should also examine the inflationary environment formulating an adequate dividend policy for their firm.Originality/valueThe paper provides an as of yet widely ignored link between the micro‐ and macroeconomic sphere examining one of the most important problems of financial economics. Neglecting the effects of inflation on dividends may, among others, be one reason for the mixed empirical findings testing theories of dividend determination.

We study the potential of a future, large-volume photometric survey to constrain the axion mass m a in the hot dark matter limit. Future surveys such as Euclid will have significantly more constraining power than current observations for hot dark matter. Nonetheless, the lowest accessible axion masses are limited by the fact that axions lighter than ∼ 0.15 eV decouple before the QCD epoch, assumed here to occur at a temperature T QCD ∼ 170 MeV; this leaves an axion population of such low density that its late-time cosmological impact is negligible. For larger axion masses, m a 0.15 eV, where axions remain in equilibrium until after the QCD phase transition, we find that a Euclid-like survey combined with Planck CMB data can detect m a at very high significance. Our conclusions are robust against assumptions about prior knowledge of the neutrino mass. Given that the proposed IAXO solar axion search is sensitive to m a 0.2 eV, the axion mass range probed by cosmology is nicely complementary.