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 ΛCDM 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 ΛCDM model. Finally, we show that the viscosity parameter c 2 vis 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.

We present a family of designer Horndeski models, i.e. models that have a background exactly equal to that of the ΛCDM 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 ∼ 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 ΛCDM 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 ΛCDM 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 2σ tension between the growth data and Planck 18 due to a degeneracy between σ8 and one of its model parameters that indicates the deviation from the ΛCDM model.

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 HðzÞ datasets. We obtain model independent and nonparametric reconstructions of the luminosity distance d L ðzÞ and Hubble parameter HðzÞ without assuming any dark energy model or a flat Universe. We then estimate the deceleration parameter qðzÞ, a measure of the acceleration of the Universe, and we make a ∼4.5σ model independent detection of the accelerated expansion, but we also place constraints on the transition redshift of the acceleration phase ðz tr ¼ 0.662 AE 0.027Þ. We also find a deviation from ΛCDM at high redshifts, albeit within the errors, hinting toward the recently alleged tension between the SnIa/quasar data and the cosmological constant ΛCDM model at high redshifts (z ≳ 1.5). Finally, we show the GA can be used in complementary null tests of the ΛCDM via reconstructions of the Hubble parameter and the luminosity distance.

Recent analyses of the Planck data and quasars at high redshifts have suggested possible deviations from the flat Λ cold dark matter model (ΛCDM), where Λ is the cosmological constant. Here we use machine learning methods to investigate any possible deviations from ΛCDM 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 γ(z), the linear DE anisotropic stress ηDE(z) and the adiabatic sound speed cs,DE2(z) of DE perturbations. We find a ∼ 2σ deviation of w(z) from -1 at high redshifts, the adiabatic sound speed is negative at the ∼ 2.5σ level at z = 0.1 and a ∼ 2σ deviation of the anisotropic stress from unity at low redshifts and ∼ 4σ 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 ΛCDM model.

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 last, measurements of redshift space distortions (RSDs) of the growth rate of matter perturbations. We find that the amplitude of the nonadiabatic pressure perturbation is consistent with zero within 1σ. Finally, we also present a new, publicly available, RSD likelihood for MONTE PYTHON based on the "Gold 2018" growth-rate data compilation.

We present a model independent and non-parametric reconstruction with a Machine Learning algorithm of the redshift evolution of the Cosmic Microwave Background (CMB) temperature from a wide redshift range z ∈ [0, 3] without assuming any dark energy model, an adiabatic universe or photon number conservation. In particular we use the genetic algorithms which avoid the dependency on an initial prior or a cosmological fiducial model. Through our reconstruction we constrain new physics at late times. We provide novel and updated estimates on the β parameter from the parametrisation T(z) = T 0 (1+z) 1−β , the duality relation η(z) and the cosmic opacity parameter τ (z). Furthermore we place constraints on a temporal varying fine structure constant α, which would have signatures in a broad spectrum of physical phenomena such as the CMB anisotropies. Overall we find no evidence of deviations within the 1σ region from the well established ΛCDM model, thus confirming its predictive potential.

We use simulated strongly lensed gravitational wave events from the Einstein telescope to demonstrate how the luminosity and angular diameter distances, d L ðzÞ and d A ðzÞ, respectively, can be combined to test in a model independent manner for deviations from the cosmic distance duality relation and the standard cosmological model. In particular, we use two machine learning approaches, the genetic algorithms and Gaussian processes, to reconstruct the mock data and we show that both approaches are capable of correctly recovering the underlying fiducial model and can provide percent-level constraints at intermediate redshifts when applied to future Einstein telescope data.

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