Background Expansion History Research Articles

The CIDER simulations: non-linear structure formation in the constrained interacting dark energy scenario

ABSTRACTWe present for the first time a suite of cosmological simulations for a particular class of interacting Dark Energy cosmologies characterized by a background expansion history constrained to be indistinguishable from ΛCDM. Such Constrained Interacting Dark Energy scenario – or CIDER – has been recently proposed in the literature and has the appealing feature of suppressing structure formation at late times, thereby possibly alleviating the persisting σ8 tension while leaving background observables unaffected. A crucial step to assess the viability of such scenarios is then represented by quantifying their impact on structure formation at non-linear scales, which is what we start investigating with the simulations discussed in the present work. We show that – for reasonable parameter choices – the reconstructed scalar potential is close to an exponential for most of the matter dominated epoch, and that the non-linear evolution of structures in these models imprints specific footprints on matter and halo statistics that may allow to break degeneracies with standard cosmological parameters.

Perturbations in Bianchi-V Spacetimes with Varying Λ, G and Viscous Fluids

As a follow-up of a recent article in which we investigated the cosmological background expansion history of the universe in Bianchi type-V cosmological models with bulk viscous fluid and evolving cosmological Λ and Newtonian G parameters, we study the evolution of the cosmological perturbations in the current work. In particular, we analyse the evolution of the viscous matter over-density that leads to formation of large-scale structures in the Bianchi-V model, and compare the results with standard ΛCDM solutions. Our results suggest that introducing viscous fluid in the background described by Bianchi-V geometry with evolving Λ and G amplifies the structure-growth rate.

Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions: Dark energy beyond Λ

Combining supernovae, baryon acoustic oscillations, and redshift-space distortions data from the next generation of (stage-IV) cosmological surveys, we aim to reconstruct the expansion history up to large redshifts using forward-modeling of ${f}_{\mathrm{DE}}(z)={\ensuremath{\rho}}_{\mathrm{DE}}(z)/{\ensuremath{\rho}}_{\mathrm{DE},0}$ with Gaussian processes (GP). In order to reconstruct cosmological quantities at high redshifts where few or no data are available, we adopt a new approach to GP which enforces the following minimal assumptions: (a) Our cosmology corresponds to a flat Friedman-Lema\^{\i}tre-Robertson-Walker universe; (b) An Einstein de Sitter (EdS) universe is obtained on large redshifts. This allows us to reconstruct the perturbations growth history from the reconstructed background expansion history. Assuming various DE models, we show the ability of our reconstruction method to differentiate them from $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ at $\ensuremath{\gtrsim}2\ensuremath{\sigma}$.

Towards a universal model for the density profiles of dark matter haloes

ABSTRACT It is well established from cosmological simulations that dark matter (DM) haloes are not precisely self-similar and an additional parameter, beyond their concentration, is required to accurately describe their spherically averaged mass density profiles. We present, for the first time, a model to consistently predict both halo concentration, c, and this additional ‘shape’ parameter, α, for a halo of given mass and redshift for a specified cosmology. Following recent studies, we recast the dependence on mass, redshift, and cosmology to a dependence on ‘peak height’. We show that, when adopting the standard definition of peak height, which employs the so-called spherical top hat (STH) window function, the concentration–peak height relation has a strong residual dependence on cosmology (i.e. it is not uniquely determined by peak height), whereas the α–peak height relation is approximately universal when employing the STH window function. Given the freedom in the choice of window function, we explore a simple modification of the STH function, constraining its form so that it produces universal relations for concentration and α as a function of peak height using a large suite of cosmological simulations. It is found that universal relations for the two density profile parameters can indeed be derived and that these parameters are set by the linear power spectrum, P(k), filtered on different scales. We show that the results of this work generalize to any (reasonable) combination of P(k) and background expansion history, H($z$), resulting in accurate predictions of the density profiles of DM haloes for a wide range of cosmologies.

Proca-stinated cosmology. Part II. Matter, halo, and lensing statistics in the vector Galileon

The generalised Proca (GP) theory is a modified gravity model in which the acceleration of the cosmic expansion rate can be explained by self interactions of a cosmological vector field. In this paper we study a particular sub-class of the GP theory, with up to cubic order Lagrangian, known as the cubic vector Galileon (cvG) model. This model is similar to the cubic scalar Galileon (csG) in many aspects, including a fifth force and the Vainshtein screening mechanism, but with the additional flexibility that the strength of the fifth force depends on an extra parameter — interpolating between zero and the full strength of the csG model — while the background expansion history is independent of this parameter. It offers an interesting alternative to ΛCDM in explaining the cosmic acceleration, as well as a solution to the tension between early- and late-time measurements of the Hubble constant H 0. To identify the best ways to test this model, in this paper we conduct a comprehensive study of the phenomenology of this model in the nonlinear regime of large-scale structure formation, using a suite of N-body simulations run with the modified gravity code ECOSMOG. By inspecting thirteen statistics of the dark matter field, dark matter haloes and weak lensing maps, we find that the fifth force in this model can have particularly significant effects on the large-scale velocity field and lensing potential at late times, which suggest that redshift-space distortions and weak lensing can place strong constraints on it.

Will cosmic gravitational wave sirens determine the Hubble constant?

Incorrect assumptions about the background expansion history of the Universe can induce significant biases when estimating the Hubble constant H0 and other key cosmological parameters from cosmic (z≳ 0.1) gravitational wave standard sirens, even with electromagnetic counterpart redshifts. Future gravitational wave experiments such as the Einstein Telescope can provide us with a compilation of gravitational wave sirens that can be used to determine these cosmological parameters with very high precision. In such a future, the statistical precision can reach to the level of 1% uncertainty on H0. However, such datasets would include a large number of cosmic gravitational wave sirens, and not only sources at very low redshifts of z≲0.1. We show that wrong assumptions about the background expansion history of the Universe (e.g. form of dark energy) can introduce substantial bias in estimation of the Hubble constant and the other key parameters. Such biases would occur in non-ΛCDM cosmologies that can be degenerate with the standard ΛCDM model. To avoid model-dependent biases, statistical techniques that are appropriately agnostic about model assumptions need to be employed.

K-mouflage imprints on cosmological observables and data constraints

We investigate cosmological constraints on K-mouflage models of modified gravity. We consider two scenarios: one where the background evolution is free to deviate from ΛCDM (K-mouflage) and another one which reproduces a ΛCDM expansion (K-mimic), implementing both of them into the EFTCAMB code. We discuss the main observational signatures of these models and we compare their cosmological predictions to different datasets, including CMB, CMB lensing, SNIa and different galaxy catalogues. We argue about the possibility of relieving the H0 and weak lensing tensions within these models, finding that K-mouflage scenarios effectively ease the tension on the Hubble Constant. Our final 95% C.L. bounds on the ϵ2,0 parameter that measures the overall departure from ΛCDM (corresponding to ϵ2,0 = 0) are −0.04⩽ ϵ2,0 ⩽ 0 for K-mouflage and 0 ⩽ ϵ2,0 ⩽ 0.002 for K-mimic. These translate into an upper bound for the coupling strength: β <0.22 for K-mouflage and β < 0.026 for K-mimic. In the former case the main constraining power comes from changes in the background expansion history, while in the latter case the model is strongly constrained by measurements of the amplitude of matter perturbations. The sensitivity of these cosmological constraints closely matches that of solar system probes. We show that these constraints could be significantly tightened with future ideal probes like CORE.

Observational constraints in nonlocal gravity: the Deser-Woodard case

We study the cosmology of a specific class of nonlocal model of modified gravity, the so-called Deser-Woodard (DW) model, modifying the Einstein-Hilbert action by a term ∼ R f(−1R), where f is a free function. Choosing f so as to reproduce the ΛCDM cosmological background expansion history within the nonlocal model, we implement the model in a cosmological linear Einstein-Boltzmann solver and study the deviations to GR the model induces in the scalar and tensor perturbations. We observe that the DW nonlocal model describes a modified propagation for the gravitational waves, as well as a lower linear growth rate and a stronger lensing power as compared to ΛCDM, up to several percents. Such prominent growth and lensing features lead to the inference of a significantly smaller value of σ8 with respect to the one in ΛCDM, given Planck CMB+lensing data. The prediction for the linear growth rate fσ8 within the DW model is therefore significantly smaller than the one in ΛCDM and the addition of growth rate data fσ8 from Redshift-space distortion measurements to Planck CMB+lensing, opens a (dominant) tension between Redshift-space distortion data and the reconstructed Planck CMB lensing potential. However, model selection issues only result in “weak” evidences for ΛCDM against the DW model given the data. Such a fact shows that the joined datasets we consider are not constraining enough for distinguishing between the models on firm grounds. As we discuss, the addition of galaxy WL data or the consideration of cosmological constraints from future galaxy clustering, weak lensing surveys, but also third generation gravitational wave interferometers, prove to be useful for discriminating modified gravity models such as the DW one from ΛCDM, within the close future.

Large-scale structure in mimetic Horndeski gravity

In this paper, we propose to use the mimetic Horndeski model as a model for the dark universe. Both cold dark matter (CDM) and dark energy (DE) phenomena are described by a single component, the mimetic field. In linear theory, we show that this component effectively behaves like a perfect fluid with zero sound speed and clusters on all scales. For the simpler mimetic cubic Horndeski model, if the background expansion history is chosen to be identical to a perfect fluid DE (PFDE) then the mimetic model predicts the same power spectrum of the Newtonian potential as the PFDE model with zero sound speed. In particular, if the background is chosen to be the same as that of LCDM, then also in this case the power spectrum of the Newtonian potential in the mimetic model becomes indistinguishable from the power spectrum in LCDM on linear scales. A different conclusion may be found in the case of non-adiabatic perturbations. We also discuss the distinguishability, using power spectrum measurements from LCDM N-body simulations as a proxy for future observations, between these mimetic models and other popular models of DE. For instance, we find that if the background has an equation of state equal to −0.95 then we will be able to distinguish the mimetic model from the PFDE model with unity sound speed. On the other hand, it will be hard to do this distinction with respect to the LCDM model.

Cosmological histories in bimetric gravity: a graphical approach

The bimetric generalization of general relativity has been proven to be able to give an accelerated background expansion consistent with observations. Apart from the energy densities coupling to one or both of the metrics, the expansion will depend on the cosmological constant contribution to each of them, as well as the three parameters describing the interaction between the two metrics. Even for fixed values of these parameters can several possible solutions, so called branches, exist. Different branches can give similar background expansion histories for the observable metric, but may have different properties regarding, for example, the existence of ghosts and the rate of structure growth. In this paper, we outline a method to find viable solution branches for arbitrary parameter values. We show how possible expansion histories in bimetric gravity can be inferred qualitatively, by picturing the ratio of the scale factors of the two metrics as the spatial coordinate of a particle rolling along a frictionless track. A particularly interesting example discussed is a specific set of parameter values, where a cosmological dark matter background is mimicked without introducing ghost modes into the theory.

Quintessential scale dependence from separate universe simulations

By absorbing fluctuations into a local background, separate universe simulations provide a powerful technique to characterize the response of small-scale observables to the long-wavelength density fluctuations, for example those of the power spectrum and halo mass function which lead to the squeezed-limit $n$-point function and halo bias, respectively. Using quintessence dark energy as the paradigmatic example, we extend these simulation techniques to cases where non-gravitational forces in other sectors establish a Jeans scale across which the growth of density fluctuations becomes scale dependent. By characterizing the separate universes with matching background expansion histories, we show that the power spectrum and mass function responses depend on whether the long-wavelength mode is above or below the Jeans scale. Correspondingly, the squeezed bispectrum and halo bias also become scale dependent. Models of bias that are effectively local in the density field at a single epoch, initial or observed, cannot describe this effect which highlights the importance of temporal nonlocality in structure formation. Validated by these quintessence tests, our techniques are applicable to a wide range of models where the complex dynamics of additional fields affect the clustering of matter in the linear regime and it would otherwise be difficult to simulate their impact in the nonlinear regime.

Constraints on decaying early modified gravity from cosmological observations

Most of the information on our cosmos stems from either late-time observations or the imprint of early-time inhomogeneities on the cosmic microwave background. We explore to what extent early modifications of gravity, which become significant after recombination but then decay towards the present, can be constrained by current cosmological observations. For the evolution of the gravitational modification, we adopt the decaying mode of a hybrid-metric Palatini $f(\mathcal{R})$ gravity model which is designed to reproduce the standard cosmological background expansion history and due to the decay of the modification is naturally compatible with Solar-System tests. We embed the model in the effective field theory description of Horndeski scalar-tensor gravity with an early-time decoupling of the gravitational modification. Since the quasistatic approximation for the perturbations in the model breaks down at high redshifts, where modifications remain relevant, we introduce a computationally efficient correction to describe the evolution of the scalar field fluctuation in this regime. We compare the decaying early-time modification against geometric probes and recent Planck measurements and find no evidence for such effects in the observations. Current data constrains the scalar field value at $|f_{\mathcal{R}}(z=z_{\rm on})| \lesssim 10^{-2}$ for modifications introduced at redshifts $z_{\rm on}\sim(500-1000)$ with present-day value $|f_{\mathcal{R}0}|\lesssim10^{-8}$. Finally, we comment on constraints that will be achievable with future 21~cm surveys and gravitational wave experiments.

Can background cosmology hold the key for modified gravity tests?

Modified gravity theories are a popular alternative to dark energy as a possible explanation for the observed accelerating cosmic expansion, and their cosmological tests are currently an active research field. Studies in recent years have been increasingly focused on testing these theories in the nonlinear regime, which is computationally demanding. Here we show that, under certain circumstances, a whole class of theories can be ruled out by using background cosmology alone. This is possible because certain classes of models (i) are fundamentally incapable of producing specific background expansion histories, and (ii) said histories are incompatible with local gravity tests. As an example, we demonstrate that a popular class of models, $f(R)$ gravity, would not be viable if observations suggest even a slight deviation of the background expansion history from that of the $\Lambda$CDM paradigm.

New constraints onf(R)gravity from clusters of galaxies

The abundance of massive galaxy clusters is a powerful probe of departures from general relativity (GR) on cosmic scales. Despite current stringent constraints placed by stellar and galactic tests, on larger scales alternative theories of gravity such as $f(R)$ can still work as effective theories. Here we present constraints on two popular models of $f(R)$, Hu-Sawicki and ``designer,'' derived from a fully self-consistent analysis of current samples of x-ray selected clusters and accounting for all the covariances between cosmological and astrophysical parameters. Using cluster number counts in combination with recent data from the cosmic microwave background (CMB) and the CMB lensing potential generated by large scale structures, as well as with other cosmological constraints on the background expansion history and its mean matter density, we obtain the upper bounds ${\mathrm{log}}_{10}|{f}_{R0}|&lt;4.79$ and ${\mathrm{log}}_{10}{B}_{0}&lt;3.75$ at the 95.4% confidence level, for the Hu-Sawicki (with $n=1$) and designer models, respectively. The robustness of our results derives from high-quality cluster growth data for the most massive clusters known out to redshifts $z\ensuremath{\sim}0.5$, a tight control of systematic uncertainties including an accurate and precise mass calibration from weak gravitational lensing data, and the use of the full shape of the halo mass function over the mass range of our data.

Constraints onf(R)gravity through the redshift space distortion

In this paper, a specific family of $f(R)$ models that can produce the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ background expansion history is constrained by using the currently available geometric and dynamic probes. The scale dependence of the growth rate $f(z,k)$ in this specific family of $f(R)$ model is shown. Therefore to eliminate the scale dependence of $f{\ensuremath{\sigma}}_{8}(z)$ in theory, which usually is defined as the product of $f(z,k)$ and ${\ensuremath{\sigma}}_{8}(z)$, we define $f{\ensuremath{\sigma}}_{8}(z)=d{\ensuremath{\sigma}}_{8}(z)/d\mathrm{ln}a$, which is obviously scale independent and reproduces the conventional definition in the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology. In doing so, under the assumption that future probes having the same best fit values as the current ten data points of $f{\ensuremath{\sigma}}_{8}(z)$, even having 20% error bars enlarged, we find a preliminary constraint ${f}_{R0}=\ensuremath{-}2.5{8}_{\ensuremath{-}0.58}^{+2.14}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ in $1\ensuremath{\sigma}$ regions. This indicates the great potential that redshift space distortions have in constraining modified gravity theories. We also discuss the nonlinear matter power spectrum based on different halo fit models.

Classifying linearly shielded modified gravity models in effective field theory.

We study the model space generated by the time-dependent operator coefficients in the effective field theory of the cosmological background evolution and perturbations of modified gravity and dark energy models. We identify three classes of modified gravity models that reduce to Newtonian gravity on the small scales of linear theory. These general classes contain enough freedom to simultaneously admit a matching of the concordance model background expansion history. In particular, there exists a large model space that mimics the concordance model on all linear quasistatic subhorizon scales as well as in the background evolution. Such models also exist when restricting the theory space to operators introduced in Horndeski scalar-tensor gravity. We emphasize that whereas the partially shielded scenarios might be of interest to study in connection with tensions between large and small scale data, with conventional cosmological probes, the ability to distinguish the fully shielded scenarios from the concordance model on near-horizon scales will remain limited by cosmic variance. Novel tests of the large-scale structure remedying this deficiency and accounting for the full covariant nature of the alternative gravitational theories, however, might yield further insights on gravity in this regime.

Brane-world and loop cosmology from a gravity–matter coupling perspective

We show that the effective brane-world and the loop quantum cosmology background expansion histories can be reproduced from a modified gravity perspective in terms of an f(R) gravity action plus a g(R) term non-minimally coupled with the matter Lagrangian. The reconstruction algorithm that we provide depends on a free function of the matter density that must be specified in each case and allows to obtain analytical solutions always. In the simplest cases, the function f(R) is quadratic in the Ricci scalar, R, whereas g(R) is linear. Our approach is compared with recent results in the literature. We show that working in the Palatini formalism there is no need to impose any constraint that keeps the equations second-order, which is a key requirement for the successful implementation of the reconstruction algorithm.

Effective field theory of cosmic acceleration: Constraining dark energy with CMB data

We introduce EFTCAMB/EFTCosmoMC as publicly available patches to the commonly used camb/CosmoMC codes. We briefly describe the structure of the codes, their applicability and main features. To illustrate the use of these patches, we obtain constraints on parametrized pure effective field theory and designer $f(R)$ models, both on $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ and $w\mathrm{CDM}$ background expansion histories, using data from Planck temperature and lensing potential spectra, WMAP low-$\ensuremath{\ell}$ polarization spectra (WP), and baryon acoustic oscillations (BAO). Upon inspecting the theoretical stability of the models on the given background, we find nontrivial parameter spaces that we translate into viability priors. We use different combinations of data sets to show their individual effects on cosmological and model parameters. Our data analysis results show that, depending on the adopted data sets, in the $w\mathrm{CDM}$ background case these viability priors could dominate the marginalized posterior distributions. Interestingly, with $\mathrm{Planck}+\mathrm{WP}+\mathrm{BAO}+\mathrm{lensing}$ data, in $f(R)$ gravity models, we get very strong constraints on the constant dark energy equation of state, ${w}_{0}\ensuremath{\in}(\ensuremath{-}1,\ensuremath{-}0.9997)$ (95% C.L.).

Cosmological perturbations and observational constraints on nonlocal massive gravity

Nonlocal massive gravity can provide an interesting explanation for the late-time cosmic acceleration, with a dark energy equation of state $w_{\rm DE}$ smaller than $-1$ in the past. We derive the equations of linear cosmological perturbations to confront such models with the observations of large-scale structures. The effective gravitational coupling to nonrelativistic matter associated with galaxy clusterings is close to Newton's gravitational constant $G$ for a mass scale $m$ slightly smaller than today's Hubble parameter $H_0$. Taking into account the background expansion history as well as the evolution of matter perturbations $\delta_m$, we test for these models with Type Ia Supernovae (SnIa) from Union 2.1, the cosmic microwave background (CMB) measurements from Planck, a collection of baryon acoustic oscillations (BAO), and the growth rate data of $\delta_m$. Using a higher value of $H_0$ derived from its direct measurement ($H_0 \gtrsim 70$ km s$^{-1}$ Mpc$^{-1}$) the data strongly support the nonlocal massive gravity model ($-1.1 \lesssim w_{\rm DE} \lesssim -1.04$ in the past) over the $\Lambda$CDM model ($w_{\rm DE}=-1$), whereas for a lower prior (67 km s$^{-1}$ Mpc$^{-1}$ $\lesssim$ $H_0 \lesssim 70$ km s$^{-1}$ Mpc$^{-1}$) the two models are statistically comparable.

Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity

We present a turnkey solution, ready for implementation in numerical codes, for the study of linear structure formation in general scalar-tensor models involving a single universally coupled scalar field. We show that the totality of cosmological information on the gravitational sector can be compressed — without any redundancy — into five independent and arbitrary functions of time only and one constant. These describe physical properties of the universe: the observable background expansion history, fractional matter density today, and four functions of time describing the properties of the dark energy. We show that two of those dark-energy property functions control the existence of anisotropic stress, the other two — dark-energy clustering, both of which are can be scale-dependent. All these properties can in principle be measured, but no information on the underlying theory of acceleration beyond this can be obtained. We present a translation between popular models of late-time acceleration (e.g. perfect fluids, f(R), kinetic gravity braiding, galileons), as well as the effective field theory framework, and our formulation. In this way, implementing this formulation numerically would give a single tool which could consistently test the majority of models of late-time acceleration heretofore proposed.