Fisher Matrix Approach Research Articles

Cosmological forecasts from the combination of Stage-IV photometric galaxy surveys and the magnification from forthcoming GW observatories

In this work we have investigated the synergy between Stage-IV galaxy surveys and future GW observatories for constraining the underlying cosmological model of the Universe, focussing on photometric galaxy clustering, cosmic shear and GW magnification as cosmological probes. We have implemented a Fisher matrix approach for the evaluation of the full 6×2pt statistics composed by the angular power spectra of the single probes together with their combination. For our analysis, we have in particular considered dynamical dark energy and massive neutrino scenarios. We have found that the improvement to galaxy survey performance is below 1%, in the case of ℓ GW max=100 and a luminosity distance error of σ dL /dL =10%. However, when extending the analysis to ℓ GW max=1000, we find that the GW magnification improves the galaxy survey performance on all the cosmological parameters, reducing their errors by 3%-5%, when σ dL /dL =10%, and by 10%-18% when σ dL /dL =1%, especially for Mν , w 0 and wa . However, here our analysis is unavoidably optimistic: a much more detailed and realistic approach will be needed, especially by including systematic effects. But we can conclude that, in the case of future gravitational wave observatories, the inclusion of the gravitational wave magnification can improve Stage-IV galaxy surveys performance on constraining the underlying cosmological model of the Universe.

Improving precision and accuracy in cosmology with model-independent spectrum and bispectrum

A new and promising avenue was recently developed for analyzing large-scale structure data with a model-independent approach, in which the linear power spectrum shape is parametrized with a large number of freely varying wavebands rather than by assuming specific cosmological models. We call this method FreePower. Here we show, using a Fisher matrix approach, that precision of this method for the case of the one-loop power spectrum is greatly improved with the inclusion of the tree-level bispectrum. We also show that accuracy can be similarly improved by employing perturbation theory kernels whose structure is entirely determined by symmetries instead of evolution equations valid in particular models (like in the usual Einstein-de Sitter approximation). The main result is that with the Euclid survey one can precisely measure the Hubble function, distance and (k-independent) growth rate f(z) in seven redshift bins in the range z ∈ [0.6, 2.0]. The typical errors for the lower zbins are around 1% (for H), 0.7–1% (for D), and 2–3% (for f). The use of general perturbation theory allows us, for the first time, to study constraints on the nonlinear kernels of cosmological perturbations, that is, beyond the linear growth factor, showing that they can be probed at the 10–20% level. We find that the combination of spectrum and bispectrum is particularly effective in constraining the perturbation parameters, both at linear and quadratic order.

Constraining the evolution of Newton’s constant with slow inspirals observed from spaceborne gravitational-wave detectors

Spaceborne gravitational-wave (GW) detectors observing at milli-Hz and deci-Hz frequencies are expected to detect large numbers of quasi-monochromatic signals. The first and second time-derivative of the GW frequency ($\dot f_0$ and $\ddot f_0$) can be measured for the most favourable sources and used to look for negative post-Newtonian corrections, which can be induced by the source's environment or modifications of general relativity. We present an analytical, Fisher-matrix-based approach to estimate how precisely such corrections can be constrained. We use this method to estimate the bounds attainable on the time evolution of the gravitational constant $G(t)$ with different classes of quasi-monochromatic sources observable with LISA and DECIGO, two representative spaceborne detectors for milli-Hz and deci-Hz GW frequencies. We find that the most constraining source among a simulated population of LISA galactic binaries could yield $\dot G/G_0 \lesssim 10^{-6}\text{yr}^{-1}$, while the best currently known verification binary will reach $\dot G/G_0 \lesssim 10^{-4}\text{yr}^{-1}$. We also perform Monte-Carlo simulations using quasi-monochromatic waveforms to check the validity of our Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries that do not satisfy the quasi-monochromatic assumption. We find that our analytical Fisher matrix produces good order-of-magnitude constraints even for sources well beyond its regime of validity. Monte-Carlo investigations also show that chirping stellar-mass compact binaries detected by DECIGO-like detectors at cosmological distances of tens of Mpc can yield constraints as tight as $\dot G/G_0 \lesssim 10^{-11}\text{yr}^{-1}$.

Euclid: Forecasts from the void-lensing cross-correlation

The Euclid space telescope will survey a large dataset of cosmic voids traced by dense samples of galaxies. In this work we estimate its expected performance when exploiting angular photometric void clustering, galaxy weak lensing, and their cross-correlation. To this aim, we implemented a Fisher matrix approach tailored for voids from the Euclid photometric dataset and we present the first forecasts on cosmological parameters that include the void-lensing correlation. We examined two different probe settings, pessimistic and optimistic, both for void clustering and galaxy lensing. We carried out forecast analyses in four model cosmologies, accounting for a varying total neutrino mass, Mν, and a dynamical dark energy (DE) equation of state, w(z), described by the popular Chevallier-Polarski-Linder parametrization. We find that void clustering constraints on h and Ωb are competitive with galaxy lensing alone, while errors on ns decrease thanks to the orthogonality of the two probes in the 2D-projected parameter space. We also note that, as a whole, with respect to assuming the two probes as independent, the inclusion of the void-lensing cross-correlation signal improves parameter constraints by 10 − 15%, and enhances the joint void clustering and galaxy lensing figure of merit (FoM) by 10% and 25%, in the pessimistic and optimistic scenarios, respectively. Finally, when further combining with the spectroscopic galaxy clustering, assumed as an independent probe, we find that, in the most competitive case, the FoM increases by a factor of 4 with respect to the combination of weak lensing and spectroscopic galaxy clustering taken as independent probes. The forecasts presented in this work show that photometric void clustering and its cross-correlation with galaxy lensing deserve to be exploited in the data analysis of the Euclid galaxy survey and promise to improve its constraining power, especially on h, Ωb, the neutrino mass, and the DE evolution.

Toward establishing the presence or absence of horizons in coalescing binaries of compact objects by using their gravitational wave signals

The quest for distinguishing black holes (BH) from horizonless compact objects using gravitational wave (GW) signals from coalescing compact binaries can be helped by utilizing the phenomenon of tidal heating (TH), which leaves its imprint on binary waveforms through the horizon parameters. We investigate the effects of TH on GWs to probe the observability of the horizon parameters, mainly using Fisher matrix analysis to determine the errors and covariances between them. The horizon parameters are defined as $H_1$ and $H_2$ for the two binary components, with $H_{1,2} \in [0,1]$, and combined with the component masses and spins to form two new parameters, $H_{\rm eff5}$ and $H_{\rm eff8}$, to minimize their covariances in parameter estimation studies. In this work, we add the phase contribution due to TH in terms of $H_{\rm eff5}$ and $H_{\rm eff8}$ to a post-Newtonian waveform and examine the variation of their measurement errors with the binary's total mass, mass ratio, luminosity distance, and component spins. Since the Fisher matrix approach works well for high signal-to-noise ratio, we focus mainly on third-generation (3G) GW detectors Einstein Telescope and Cosmic Explorer and use LIGO and Virgo for comparison. We find that the region in the total binary mass where measurements of $H_{\rm eff5}$ and $H_{\rm eff8}$ are most precise are $\sim 20 - 30M_\odot$ for LIGO-Virgo and $\sim 50 - 80M_\odot$ for 3G detectors. Higher component spins allow more precise measurements of $H_{\rm eff5}$ and $H_{\rm eff8}$. For a binary situated at 200 Mpc with component masses $12M_\odot$ and $18M_\odot$, equal spins $\chi_1=\chi_2=0.8$, and $H_{\rm eff5}=0.6$, $H_{\rm eff8}=12$, the 1-$\sigma$ errors in these two parameters are $\sim 0.01$ and $\sim 0.04$, respectively, in 3G detectors. We substantiate our results from Fisher studies with a set of Bayesian simulations.

Forecasts on interacting dark energy from the 21-cm angular power spectrum with BINGO and SKA observations

ABSTRACT Neutral hydrogen (H i) intensity mapping is a promising technique to probe the large-scale structure of the Universe, improving our understanding of the late-time accelerated expansion. In this work, we first scrutinize how an alternative cosmology, interacting dark energy (IDE), can affect the 21-cm angular power spectrum relative to the concordance ΛCDM model. We re-derive the 21-cm brightness temperature fluctuation in the context of such an interaction and uncover an extra new contribution. Then we estimate the noise level of three upcoming H i intensity mapping surveys, namely Baryon Acoustic Oscillations from Integrated Neutral Gas Observations (BINGO), Square Kilometre Array (SKA1)-MID Band 1 and Band 2, and employ a Fisher matrix approach to forecast their constraints on the IDE model. We find that while Planck 2018 maintains its dominion over early-Universe parameter constraints, BINGO and SKA1-MID Band 2 provide complementary bounding to the latest cosmic microwave background measurements on the dark energy equation of state w, the interacting strength λi and the reduced Hubble constant h, and that SKA1-MID Band 1 even outperforms Planck 2018 in these late-Universe parameter constraints. The expected minimum uncertainties are given by SKA1-MID Band 1 + Planck: $\sim 0.34{{\ \rm per\ cent}}$ on w, $\sim 0.22{{\ \rm per\ cent}}$ on h, $\sim 0.64{{\ \rm per\ cent}}$ on H i bias bHi, and an absolute uncertainty of about 3 × 10−4 (7 × 10−4) on λ1 (λ2). Moreover, we quantify the effects from systematics of the redshift bin number, redshift-space distortions, foreground residuals and uncertainties on the measured H i fraction, ΩHi(z). Our results indicate a bright prospect for H i intensity mapping surveys in constraining IDE, whether on their own or by synergies with other measurements.

Validating the Fisher approach for stage IV spectroscopic surveys

In recent years, forecasting activities have become an important tool in designing and optimising large-scale structure surveys. To predict the performance of such surveys, the Fisher matrix formalism is frequently used as a fast and easy way to compute constraints on cosmological parameters. Among them lies the study of the properties of dark energy which is one of the main goals in modern cosmology. As so, a metric for the power of a survey to constrain dark energy is provided by the figure of merit (FoM). This is defined as the inverse of the surface contour given by the joint variance of the dark energy equation of state parameters {w0, wa} in the Chevallier-Polarski-Linder parameterization, which can be evaluated from the covariance matrix of the parameters. This covariance matrix is obtained as the inverse of the Fisher matrix. The inversion of an ill-conditioned matrix can result in large errors on the covariance coefficients if the elements of the Fisher matrix are estimated with insufficient precision. The conditioning number is a metric providing a mathematical lower limit to the required precision for a reliable inversion, but it is often too stringent in practice for Fisher matrices with sizes greater than 2 × 2. In this paper, we propose a general numerical method to guarantee a certain precision on the inferred constraints, such as the FoM. It consists of randomly vibrating (perturbing) the Fisher matrix elements with Gaussian perturbations of a given amplitude and then evaluating the maximum amplitude that keeps the FoM within the chosen precision. The steps used in the numerical derivatives and integrals involved in the calculation of the Fisher matrix elements can then be chosen accordingly in order to keep the precision of the Fisher matrix elements below this maximum amplitude. We illustrate our approach by forecasting stage IV spectroscopic surveys cosmological constraints from the galaxy power spectrum. We infer the range of steps for which the Fisher matrix approach is numerically reliable. We explicitly check that using steps that are larger by a factor of two produce an inaccurate estimation of the constraints. We further validate our approach by comparing the Fisher matrix contours to those obtained with a Monte Carlo Markov chain (MCMC) approach – in the case where the MCMC posterior distribution is close to a Gaussian – and finding excellent agreement between the two approaches.

Fisher matrix for multiple tracers: all you can learn from large-scale structure without assuming a model

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 ΛCDM 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,z1,z2), defined as the ratio of fσ8(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.

A semianalytic Fisher matrix for precessing binaries with a single significant spin

Gravitational waves from a binary with a single dynamically significant spin, notably including precessing black hole-neutron star binaries, let us constrain that binary’s properties: the two masses and the dominant black hole spin. Based on a straightforward fourier transform of enabled by the corotating frame, we show the Fisher matrix for precessing binaries can be well-approximated by an extremely simple semianalytic approximation. This approximation can be easily understood as a weighted average of independent information channels, each associated with one gravitational wave harmonic. Generalizing previous studies of nonprecessing binaries to include critical symmetry-breaking precession effects required to understand plausible astrophysical sources, our ansatz can be applied to address how well gravitational wave measurements can address a wide range of astrophysical and fundamental questions. This Fisher matrix approach provides a simple method to assess what parameters gravitational wave detectors can measure, how well, and why. Our study is the first analytically-tractable Fisher matrix calculation for precessing binaries.

The impact of relativistic effects on the 3D Quasar-Lyman-α cross-correlation

We study the impact of relativistic effects in the 3-dimensional cross-correlation between Lyman-α forest and quasars. Apart from the relativistic effects, which are dominated by the Doppler contribution, several systematic effects are also included in our analysis (intervening metals, unidentified high column density systems, transverse proximity effect and effect of the UV fluctuations). We compute the signal-to-noise ratio for the Baryonic Oscillation Spectroscopic Survey (BOSS), the extended Baryonic Oscillation Spectroscopic Survey (eBOSS) and the Dark Energy Spectroscopic Instrument (DESI) surveys, showing that DESI will be able to detect the Doppler contribution in a Large Scale Structure (LSS) survey for the first time, with a S/N >7 for rmin > 10 Mpc/h, where rmin denotes the minimum comoving separation between sources. We demonstrate that several physical parameters, introduced to provide a full modelling of the cross-correlation function, are affected by the Doppler contribution. By using a Fisher matrix approach, we establish that if the Doppler contribution is neglected in the data analysis, the derived parameters will be shifted by a non-negligible amount for the upcoming surveys.

Impact of 1/f noise on cosmological parameter constraints for SKA intensity mapping

ABSTRACT We investigate the impact of 1/f noise on cosmology for an intensity mapping survey with SKA1-MID Band 1 and Band 2. We use a Fisher matrix approach to forecast constraints on cosmological parameters under the influence of 1/f noise, adopting a semi-empirical model from an earlier work, which results from the residual 1/f noise spectrum after applying a component separation algorithm to remove smooth spectral components. Without 1/f noise, the projected constraints are $4{{\ \rm per\ cent}}$ on w0, $1{{\ \rm per\ cent}}$ on h, $2{{\ \rm per\ cent}}$ on bH i using Band 1+Planck, and $3{{\ \rm per\ cent}}$ on w0, $0.5{{\ \rm per\ cent}}$ on h, $2{{\ \rm per\ cent}}$ on bH i using Band 2+Planck. A representative baseline 1/f noise degrades these constraints by a factor of ∼1.5 for Band 1+Planck, and ∼1.2 for Band 2+Planck. On the power spectrum measurement, higher redshift and smaller scales are more affected by 1/f noise, with minimal contamination comes from z ≲ 1 and ℓ ≲ 100. Subject to the specific scan strategy of the adopted 1/f noise model, one prefers a correlation in frequency with minimized spectral slope, a low knee frequency, and a large telescope slew speed in order to reduce its impact.

J-PAS: forecasts on interacting dark energy from baryon acoustic oscillations and redshift-space distortions

ABSTRACT We estimate the constraining power of Javalambre-Physics of the Accelerated Universe Astrophysical Survey (J-PAS) for parameters of an interacting dark energy (DE) cosmology. The survey is expected to map several millions of luminous red galaxies, emission line galaxies, and quasars in an area of thousands of square degrees in the northern sky with precise photometric redshift measurements. Forecasts for the DESI and Euclid surveys are also evaluated and compared to J-PAS. Using the Fisher matrix approach, we find that J-PAS can place constraints on the interaction parameter comparable to those from DESI, with an absolute uncertainty of about 0.02, when the interaction term is proportional to the dark matter energy density, and almost as good, of about 0.01, when the interaction is proportional to the DE density. For the equation of state of DE, the constraints from J-PAS are slightly better in the two cases (uncertainties 0.04–0.05 against 0.05–0.07 around the fiducial value −1). Both surveys stay behind Euclid but follow it closely, imposing comparable constraints in all specific cases considered.

Forecasts for low spin black hole spectroscopy in Horndeski gravity

We investigate the prospect of using black hole spectroscopy to constrain the parameters of Horndeski gravity through observations of gravitational waves from perturbed black holes. We study the gravitational waves emitted during ringdown from black holes without hair in Horndeski gravity, demonstrating the qualitative differences between such emission in General Relativity and Horndeski theory. In particular, Quasi-Normal Mode frequencies associated with the scalar field spectrum can appear in the emitted gravitational radiation. Analytic expressions for error estimates for both the black hole and Horndeski parameters are calculated using a Fisher Matrix approach, with constraints on the `effective mass' of the Horndeski scalar field of order $\sim 10^{-17}$eV$c^{-2}$ or tighter being shown to be achievable in some scenarios. Estimates for the minimum signal-noise-ratio required to observe such a signal are also presented.

Testing scale-dependent perturbations in ΛCDM with future galaxy surveys

Abstract The quest for the origin of the present accelerated expansion of the Universe is still open. By means of the present geometrical and dynamical observational data, it is very hard to establish, from a statistical perspective, a clear preference among the vast majority of the proposed models for the dynamical dark energy and/or modified gravity theories alternative with respect to the standard Λ CDM scenario. On the other hand, on scales much smaller than present Hubble scale, there are possibly detectable differences in the growth of the matter perturbations for different modes of the perturbations, even in the context of the same Λ CDM model. In view of the new planned observations that will give insight into the perturbations of the dark sector, this issue is being worth of further investigation. Here, we analyze the evolution of the dark matter perturbations in the context of Λ CDM. We employ the scale-dependent perturbation equations for the growth function, and we abandon both the sub-Hubble approximation and the slowly varying potential assumption, which lead to the well known and most commonly used scale-independent solutions for the perturbations. We apply the Fisher Matrix approach to three future planned galaxy surveys e.g., DESI, Euclid, and WFirst-2.4, in order to have insights on the possibility to confute cosmological models through perturbations growth data in the next future. With the aforementioned surveys on hand, and only by dynamical probes, we will achieve multiple goals: 1 . the improvement in the accuracy of the determination of the f σ 8 will give the possibility to discriminate between Λ CDM and alternative dark energy models even in the scale-independent approach; 2 . it will be possible to test the goodness of the scale-independence finally, and also to quantify the necessity of a scale dependent approach to the growth of the perturbations, in particular using surveys which encompass redshift bins with scales k 0 . 005 h Mpc−1; 3 . the scale-dependence itself might add much more discriminating power in general, but further advanced surveys will be needed.

The Information Content in Cold Stellar Streams

Abstract Cold stellar streams—produced by tidal disruptions of globular clusters—are long-lived, coherent dynamical features in the halo of the Milky Way. They hold the promise of delivering precise information about the gravitational potential, including constraints on the shape of the dark matter halo. Because of their different ages and different positions in phase space, different streams tell us different things about the Galaxy. Here we employ a Cramér–Rao lower bound (CRLB) or Fisher-matrix approach to understand the quantitative information content in (toy versions of) 11 known streams: ATLAS, GD-1, Hermus, Kwando, Orinoco, PS1A, PS1C, PS1D, PS1E, Sangarius, and Triangulum. This approach depends on a generative model, which we have developed previously, and which permits calculation of derivatives of predicted stream properties with respect to Galaxy and stream parameters. We find that in simple analytic models of the Milky Way, streams on eccentric orbits contain the most information about the halo shape. For each stream, there are near degeneracies between dark matter halo properties and parameters of the bulge, the disk, and the stream progenitor itself, but simultaneous fitting of multiple streams will constrain all parameters at the percent level. At this precision, simulated dark matter halos deviate from simple analytic parameterizations, so we add an expansion of basis functions as a first step in giving the gravitational potential more freedom. As freedom increases, the information about the halo reduces overall, and it becomes more localized to the current position of the stream. In the limit of high model freedom, a stellar stream appears to measure the local acceleration at its current position; this motivates thinking about future nonparametric approaches. The CRLB formalism also permits us to assess the value of future measurements of stellar velocities, distances, and proper motions. We show that velocities of stream stars are essential for producing competitive constraints on the distribution of dark matter.

Multiband gravitational-wave astronomy: Observing binary inspirals with a decihertz detector, B-DECIGO

An evolving Japanese gravitational-wave (GW) mission in the deci-Hz band: B-DECIGO (DECihertz laser Interferometer Gravitational wave Observatory) will enable us to detect GW150914-like binary black holes, GW170817-like binary neutron stars, and intermediate-mass binary black holes out to cosmological distances. The B-DECIGO band slots in between the aLIGO-Virgo-KAGRA-IndIGO (hecto-Hz) and LISA (milli-Hz) bands for broader bandwidth; the sources described emit GWs for weeks to years across the multiband to accumulate high signal-to-noise ratios. This suggests the possibility that joint detection would greatly improve the parameter estimation of the binaries. We examine B-DECIGO's ability to measure binary parameters and assess to what extent multiband analysis could improve such measurement. Using non-precessing post-Newtonian waveforms with the Fisher matrix approach, we find for systems like GW150914 and GW170817 that B-DECIGO can measure the mass ratio to within $< 0.1\%$, the individual black-hole spins to within $< 10\%$, and the coalescence time to within $< 5\,$s about a week before alerting aLIGO and electromagnetic facilities. Prior information from B-DECIGO for aLIGO can further reduce the uncertainty in the measurement of, e.g., certain neutron star tidally-induced deformations by factor of $\sim 6$, and potentially determine the spin-induced neutron star quadrupole moment. Joint LISA and B-DECIGO measurement will also be able to recover the masses and spins of intermediate-mass binary black holes at percent-level precision. However, there will be a large systematic bias in these results due to post-Newtonian approximation of exact GW signals.

Binary neutron star mergers and third generation detectors: Localization and early warning

For third generation gravitational wave detectors, such as the Einstein Telescope, gravitational wave signals from binary neutron stars can last up to a few days before the neutron stars merge. To estimate the measurement uncertainties of key signal parameters, we develop a Fisher matrix approach which accounts for effects on such long duration signals of the time-dependent detector response and the earths rotation. We use this approach to characterize the sky localization uncertainty for gravitational waves from binary neutron stars at 40, 200, 400, 800 and 1600Mpc, for the Einstein Telescope and Cosmic Explorer individually and operating as a network. We find that the Einstein Telescope alone can localize the majority of detectable binary neutron stars at a distance of $\leq200$Mpc to within $100\text{deg}^2$ with 90% confidence. A network consisting of the Einstein Telescope and Cosmic Explorer can enhance the sky localization performance significantly - with the 90% credible region of $\mathcal{O}(1) \text{deg}^2$ for most sources at $\leq200$Mpc and $\leq100\text{deg}^2$ for most sources at $\leq1600$Mpc. We also investigate the prospects for third generation detectors identifying the presence of a signal prior to merger. To do this, we require a signal to have a network signal-to-noise ratio of $\geq12$ and $\geq5.5$ for at least two interferometers, and to have a 90% credible region for the sky localization that is no larger than $100 \text{deg}^2$. We find that the Einstein Telescope can send out such "early-warning" detection alerts 1 - 20 hours before merger for 100% of detectable binary neutron stars at 40Mpc and for $\sim58\%$ of sources at 200Mpc. For sources at a distance of 400Mpc, a network of the Einstein telescope and Cosmic Explorer can produce detection alerts up to $\sim 3$ hours prior to merger for 98% of detectable binary neutron stars.

Higgs-dilaton cosmology: An inflation–dark-energy connection and forecasts for future galaxy surveys

The Higgs-Dilaton model is a scale-invariant extension of the Standard Model non-minimally coupled to gravity and containing just one additional degree of freedom on top of the Standard Model particle content. This minimalistic scenario predicts a set of measurable consistency relations between the inflationary observables and the dark-energy equation-of-state parameter. We present an alternative derivation of these consistency relations that highlights the connections and differences with the $\alpha$-attractor scenario. We study in how far these constraints allow to distinguish the Higgs-Dilaton model from $\Lambda$CDM and $w$CDM cosmologies. To this end we first analyze existing data sets using a Markov Chain Monte Carlo approach. Second, we perform forecasts for future galaxy surveys using a Fisher matrix approach, both for galaxy clustering and weak lensing probes. Assuming that the best fit values in the different models remain comparable to the present ones, we show that both Euclid- and SKA2-like missions will be able to discriminate a Higgs-Dilaton cosmology from $\Lambda$CDM and $w$CDM.

A Halo Model Approach to the 21 cm and Lyα Cross-correlation

Abstract We present a halo-model-based approach to calculate the cross-correlation between H i intensity fluctuations and emitters (LAE) during the epoch of reionization (EoR). Ionizing radiation around dark matter halos are modeled as bubbles with the size and growth determined based on the reionization photon production, among other physical parameters. The cross-correlation shows a clear negative-to-positive transition, associated with transition from ionized to neutral hydrogen in the intergalactic medium during EoR. The cross-correlation is subject to several foreground contaminants, including foreground radio point sources important for experiments and low-z interloper emission lines, such as , O iii, and O ii, for experiments. Our calculations show that by masking out high fluxes in the measurement, the correlated foreground contamination on the – cross-correlation can be dramatically reduced. We forecast the detectability of – cross-correlation at different redshifts and adopt a Fisher matrix approach to estimate uncertainties on the key EoR parameters that have not been well constrained by other observations of reionization. This halo-model-based approach enables us to explore the EoR parameter space rapidly for different and experiments.

Improving Fisher matrix forecasts for galaxy surveys: window function, bin cross-correlation and bin redshift uncertainty

The Fisher matrix is a widely used tool to forecast the performance of future experiments and approximate the likelihood of large data sets. Most of the forecasts for cosmological parameters in galaxy clustering studies rely on the Fisher matrix approach for large-scale experiments like DES, Euclid, or SKA. Here we improve upon the standard method by taking into account three effects: the finite window function, the correlation between redshift bins, and the uncertainty on the bin redshift. The first two effects are negligible only in the limit of infinite surveys. The third effect, on the contrary, is negligible for infinitely small bins. Here we show how to take into account these effects and what the impact on forecasts of a Euclid-type experiment will be. The main result of this article is that the windowing and the bin cross-correlation induce a considerable change in the forecasted errors, of the order of 10-30% for most cosmological parameters, while the redshift bin uncertainty can be neglected for bins smaller than $\Delta z = 0.1$ roughly.