Designing Horndeski and the effective fluid approach

We present a family of designer Horndeski models, i.e. models that have a background exactly equal to that of the $\Lambda$CDM model but perturbations given by the Horndeski theory. Then, we extend the effective fluid approach to Horndeski theories, providing simple analytic formulae for the equivalent dark energy effective fluid pressure, density and velocity. We implement the dark energy effective fluid formulae in our code EFCLASS, a modified version of the widely used Boltzmann solver CLASS, and compare the solution of the perturbation equations with those of the code hi_CLASS which already includes Horndeski models. We find that our simple modifications to the vanilla code are accurate to the level of $\sim 0.1\%$ with respect to the more complicated hi_CLASS code. Furthermore, we study the kinetic braiding model both on and off the attractor and we find that even though the full case has a proper $\Lambda$CDM model limit for large $n$, it is not appropriately smooth, thus causing the quasistatic approximation to break down. Finally, we focus on our designer model (HDES), which has both a smooth $\Lambda$CDM limit and well-behaved perturbations, and we use it to perform Markov Chain Monte Carlo analyses to constrain its parameters with the latest cosmological data. We find that our HDES model can also alleviate the soft $2\sigma$ tension between the growth data and Planck 18 due to a degeneracy between $\sigma_8$ and one of its model parameters that indicates the deviation from the $\Lambda$CDM model.Comment: 31 pages, 9 figures, 5 tables, comments welcome. The codes used in the analysis of this paper can be found at https://members.ift.uam-csic.es/savvas.nesseris/efclass.html and at https://github.com/wilmarcardonac/EFCLAS

Machine Learning and cosmographic reconstructions of quintessence and the Swampland conjectures

We present model independent reconstructions of quintessence and the Swampland conjectures (SC) using both Machine Learning (ML) and cosmography. In particular, we demonstrate how the synergies between theoretical analyses and ML can provide key insights on the nature of dark energy and modified gravity. Using the Hubble parameter $H(z)$ data from the cosmic chronometers we find that the ML and cosmography reconstructions of the SC are compatible with observations at low redshifts. Finally, including the growth rate data $f\sigma_8(z)$ we perform a model independent test of modified gravity cosmologies through two phase diagrams, namely $H-f\sigma_8$ and $\eta-f\sigma_8$, where the anisotropic stress parameter $\eta$ is obtained via the $E_g$ statistics, which is related to gravitational lensing data. While the first diagram is consistent within the errors with the $\Lambda$CDM model, the second one has a $\sim 2\sigma$ deviation of the anisotropic stress from unity at $z\sim 0.3$ and a $\sim 4\sigma$ deviation at $z\sim 0.9$, thus pointing toward mild deviations from General Relativity, which could be further tested with upcoming large-scale structure surveys.Comment: 13 pages, 6 figures, 4 tables. Changes match published versio

Novel null tests for the spatial curvature and homogeneity of the Universe and their machine learning reconstructions

A plethora of observational data obtained over the last couple of decades has allowed cosmology to enter into a precision era and has led to the foundation of the standard cosmological constant and cold dark matter paradigm, known as the $\Lambda$CDM model. Given the many possible extensions of this concordance model, we present here several novel consistency tests which could be used to probe for deviations from $\Lambda$CDM. First, we derive a joint consistency test for the spatial curvature $\Omega_{k,0}$ and the matter density $\Omega_\textrm{m,0}$ parameters, constructed using only the Hubble rate $H(z)$, which can be determined directly from observations. Second, we present a new test of possible deviations from homogeneity using the combination of two datasets, either the baryon acoustic oscillation (BAO) and $H(z)$ data or the transversal and radial BAO data, while we also introduce two consistency tests for $\Lambda$CDM which could be reconstructed via the transversal and radial BAO data. We then reconstruct the aforementioned tests using the currently available data in a model independent manner using a particular machine learning approach, namely the Genetic Algorithms. Finally, we also report on a $\sim 4\sigma$ tension on the transition redshift as determined by the $H(z)$ and radial BAO data.Comment: 13 pages, 5 figures, 1 table. Changes match published versio

What can Machine Learning tell us about the background expansion of the Universe?

Machine learning (ML) algorithms have revolutionized the way we interpret data in astronomy, particle physics, biology and even economics, since they can remove biases due to a priori chosen models. Here we apply a particular ML method, the genetic algorithms (GA), to cosmological data that describes the background expansion of the Universe, namely the Pantheon Type Ia supernovae and the Hubble expansion history $H(z)$ datasets. We obtain model independent and nonparametric reconstructions of the luminosity distance $d_L(z)$ and Hubble parameter $H(z)$ without assuming any dark energy model or a flat Universe. We then estimate the deceleration parameter $q(z)$, a measure of the acceleration of the Universe, and we make a $\sim4.5\sigma$ model independent detection of the accelerated expansion, but we also place constraints on the transition redshift of the acceleration phase $(z_{\textrm{tr}}=0.662\pm0.027)$. We also find a deviation from $\Lambda$CDM at high redshifts, albeit within the errors, hinting toward the recently alleged tension between the SnIa/quasar data and the cosmological constant $\Lambda$CDM model at high redshifts $(z\gtrsim1.5)$. Finally, we show the GA can be used in complementary null tests of the $\Lambda$CDM via reconstructions of the Hubble parameter and the luminosity distance.Comment: 9 pages, 4 figures, 2 tables, comments welcome. Changes match published versio

Hints of dark energy anisotropic stress using Machine Learning

Recent analyses of the Planck data and quasars at high redshifts have suggested possible deviations from the flat $\Lambda$ cold dark matter model ($\Lambda$CDM), where $\Lambda$ is the cosmological constant. Here we use machine learning methods to investigate any possible deviations from $\Lambda$CDM at both low and high redshifts by using the latest cosmological data. Specifically, we apply the Genetic Algorithms to explore the nature of dark energy (DE) in a model independent fashion by reconstructing its equation of state $w(z)$, the growth index of matter density perturbations $\gamma(z)$, the linear DE anisotropic stress $\eta_\textrm{DE}(z)$ and the adiabatic sound speed $c_\textrm{s,DE}^2(z)$ of DE perturbations. We find a $\sim2\sigma$ deviation of $w(z)$ from -1 at high redshifts, the adiabatic sound speed is negative at the $\sim2.5\sigma$ level at $z=0.1$ and a $\sim2\sigma$ deviation of the anisotropic stress from unity at low redshifts and $\sim4 \sigma$ at high redshifts. These results hint towards either the presence of an non-adiabatic component in the DE sound speed or the presence of DE anisotropic stress, thus hinting at possible deviations from the $\Lambda$CDM model.Comment: 28 pages, 6 figures, 3 tables, changes match published versio

Testing the Λ\LambdaCDM paradigm with growth rate data and machine learning

The cosmological constant $\Lambda$ and cold dark matter (CDM) model ($\Lambda\text{CDM}$) is one of the pillars of modern cosmology and is widely used as the de facto theoretical model by current and forthcoming surveys. As the nature of dark energy is very elusive, in order to avoid the problem of model bias, here we present a novel null test at the perturbation level that uses the growth of matter perturbation data in order to assess the concordance model. We analyze how accurate this null test can be reconstructed by using data from forthcoming surveys creating mock catalogs based on $\Lambda\text{CDM}$ and three models that display a different evolution of the matter perturbations, namely a dark energy model with constant equation of state $w$ ($w$CDM), the Hu \& Sawicki and designer $f(R)$ models, and we reconstruct them with a machine learning technique known as the Genetic Algorithms. We show that with future LSST-like mock data our consistency test will be able to rule out these viable cosmological models at more than 5$\sigma$, help to check for tensions in the data and alleviate the existing tension of the amplitude of matter fluctuations $S_8=\sigma_8\left(\Omega_m/0.3\right)^{0.5}$.Comment: 9 pages, 4 figures. Comments welcom

Unraveling the effective fluid approach for f(R)f(R) models in the subhorizon approximation

We provide explicit formulas for the effective fluid approach of $f(R)$ theories, such as the Hu & Sawicki and the designer models. Using the latter and simple modifications to the CLASS code, which we call EFCLASS, in conjunction with very accurate analytic approximations for the background evolution, we obtain competitive results in a much simpler and less error-prone approach. We also derive the initial conditions in matter domination and we find they differ from those already found in the literature for a constant $w$ model. A clear example is the designer model that behaves as $\Lambda$CDM in the background, but has nonetheless dark energy perturbations. We then use the aforementioned models to derive constraints from the latest cosmological data, including supernovae, BAO, CMB, $H(z)$ and growth-rate data, and find they are statistically consistent to the $\Lambda$CDM model. Finally, we show that the viscosity parameter $c_{vis}^2$ in realistic models is not constant as commonly assumed, but rather evolves significantly over several orders of magnitude, something which could affect forecasts of upcoming surveys.Comment: 24 pages, 12 figures, 5 tables. Changes match published version. The codes used in the analysis can be found at https://members.ift.uam-csic.es/savvas.nesseris/efclass.html and https://github.com/wilmarcardonac/EFCLAS

Lensing convergence and anisotropic dark energy in galaxy redshift surveys

Analyses of upcoming galaxy surveys will require careful modelling of relevant observables such as the power spectrum of galaxy counts in harmonic space $C_\ell(z,z')$. We investigate the impact of disregarding relevant relativistic effects by considering a model of dark energy including constant sound speed, constant equation of state $w_0$, and anisotropic stress. Here we show that neglecting the effect of lensing convergence will lead to substantial shifts in cosmological parameters such as the galaxy bias $b_0$, the value of the dark energy equation of state today $w_0$, and the Hubble constant $H_0$. Interestingly, neglecting the effect of lensing convergence in this kind of models results in shifting $H_0$ downwards, something which could shed light on the current tension between local and CMB determinations of the Hubble constant.Comment: 13 pages, 3 figures, comments welcom

Cosmological constraints on non-adiabatic dark energy perturbations

The exact nature of dark energy is currently unknown and its cosmological perturbations, when dark energy is assumed not to be the cosmological constant, are usually modeled as adiabatic. Here we explore the possibility that dark energy might have a nonadiabatic component and we examine how it would affect several key cosmological observables. We present analytical solutions for the growth rate and growth index of matter density perturbations and compare them to both numerical solutions of the fluid equations and an implementation in the Boltzmann code CLASS, finding that they all agree to well below one percent. We also perform a Monte Carlo analysis to derive constraints on the parameters of the nonadiabatic component using the latest cosmological data, including the temperature and polarization spectra of the Cosmic Microwave Background as observed by Planck, the Baryon Acoustic Oscillations, the Pantheon type Ia supernovae compilation and lastly, measurements of Redshift Space Distortions (RSD) of the growth rate of matter perturbations. We find that the amplitude of the nonadiabatic pressure perturbation is consistent with zero within $1\sigma$. Finally, we also present a new, publicly available, RSD likelihood for MontePython based on the "Gold 2018" growth rate data compilation.Comment: 17 pages, 8 figures, 5 tables, changes match published version. The RSD Montepython likelihood can be found at https://github.com/snesseris/RSD-growt