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Register a new userFisher matrix for multiple tracers: model independent constraints on the redshift distortion parameter
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We show how to obtain constraints on $beta=f/b$, the ratio of the matter growth rate and the bias that quantifies the linear redshift-space distortions, that are independent of the cosmological model, using multiple tracers of large-scale structure. For a single tracer the uncertainties on $beta$ are constrained by the uncertainties in the amplitude and shape of the power spectrum, which is limited by cosmic variance. However, for two or more tracers this limit does not apply, since taking the ratio of power spectra cosmic variance cancels out, and in the linear (Kaiser) approximation one measures directly the quantity $(1+ beta_1 mu^2)^2/(1+ beta_2 mu^2)^2$, where $mu$ is the angle of a given mode with the line of sight. We provide analytic formulae for the Fisher matrix for one and two tracers, and quantify the signal-to-noise ratio needed to make effective use of the multiple-tracer technique. We also forecast the errors on $beta$ for a survey like Euclid.
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This paper aims to put constraints on the transition redshift $z_t$, which determines the onset of cosmic acceleration, in cosmological-model independent frameworks. In order to perform our analyses, we consider a flat universe and {assume} a parametrization for the comoving distance $D_C(z)$ up to third degree on $z$, a second degree parametrization for the Hubble parameter $H(z)$ and a linear parametrization for the deceleration parameter $q(z)$. For each case, we show that {type Ia supernovae} and $H(z)$ data complement each other on the parameter {space} and tighter constrains for the transition redshift are obtained. By {combining} the type Ia supernovae observations and Hubble parameter measurements it is possible to constrain the values of $z_t$, for each approach, as $0.806pm 0.094$, $0.870pm 0.063$ and $0.973pm 0.058$ at 1$sigma$ c.l., respectively. Then, such approaches provide cosmological-model independent estimates for this parameter.
In a Bayesian context, theoretical parameters are correlated random variables. Then, the constraints on one parameter can be improved by either measuring this parameter more precisely - or by measuring the other parameters more precisely. Especially in the case of many parameters, a lengthy process of guesswork is then needed to determine the most efficient way to improve one parameters constraints. In this short article, we highlight an extremely simple analytical expression that replaces the guesswork and that facilitates a deeper understanding of optimization with interdependent parameters.
The galaxy power spectrum is one of the central quantities in cosmology. It contains information about the primordial inflationary process, the matter clustering, the baryon-photon interaction, the effects of gravity, the galaxy-matter bias, the cosmic expansion, the peculiar velocity field, etc.. Most of this information is however difficult to extract without assuming a specific cosmological model, for instance $Lambda$CDM and standard gravity. In this paper we explore instead how much information can be obtained that is independent of the cosmological model, both at background and linear perturbation level. We determine the full set of model-independent statistics that can be constructed by combining two redshift bins and two distinct tracers. We focus in particular on the statistics $r(k,z_1,z_2)$, defined as the ratio of $fsigma_8(z)$ at two redshift shells, and we show how to estimate it with a Fisher matrix approach. Finally, we forecast the constraints on $r$ that can be achieved by future galaxy surveys, and compare it with the standard single-tracer result. We find that $r$ can be measured with a precision from 3 to 11%, depending on the survey. Using two tracers, we find improvements in the constraints up to a factor of two.
We use current measurements of the expansion rate $H(z)$ and cosmic background radiation bounds on the spatial curvature of the Universe to impose cosmological model-independent constraints on cosmic opacity. To perform our analyses, we compare opacity-free distance modulus from $H(z)$ data with those from two supernovae Ia compilations: the Union2.1 plus the most distant spectroscopically confirmed SNe Ia (SNe Ia SCP-0401 $z=1.713$) and two Sloan Digital Sky Survey (SDSS) subsamples. The influence of different SNe Ia light-curve fitters (SALT2 and MLCS2K2) on the results is also verified. We find that a completely transparent universe is in agreement with the largest sample in our analysis (Union 2.1 plus SNe Ia SCP-0401). For SDSS sample a such universe it is compatible at $< 1.5sigma$ level regardless the SNe Ia light-curve fitting used.
The effective anisotropic stress or gravitational slip $eta=-Phi/Psi$ is a key variable in the characterisation of the physical origin of the dark energy, as it allows to test for a non-minimal coupling of the dark sector to gravity in the Jordan frame. It is however important to use a fully model-independent approach when measuring $eta$ to avoid introducing a theoretical bias into the results. In this paper we forecast the precision with which future large surveys can determine $eta$ in a way that only relies on directly observable quantities. In particular, we do not assume anything concerning the initial spectrum of perturbations, nor on its evolution outside the observed redshift range, nor on the galaxy bias. We first leave $eta$ free to vary in space and time and then we model it as suggested in Horndeski models of dark energy. Among our results, we find that a future large scale lensing and clustering survey can constrain $eta$ to within 10% if $k$-independent, and to within 60% or better at $k=0.1 h/$Mpc if it is restricted to follow the Horndeski model.
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