Dark Energy Perturbations Research Articles

New MGCAMB tests of gravity with CosmoMC and Cobaya

We present a new version of MGCAMB, a patch for the Einstein-Boltzmann solver CAMB for cosmological tests of gravity. New features include a new cubic-spline parameterization allowing for a simultaneous reconstruction of μ, Σ and the dark energy density fraction Ω X as functions of redshift, the option to work with a direct implementation of μ, Σ (instead of converting to μ, γ first), along with the option to test models with a scalar field coupled only to dark matter, and the option to include dark energy perturbations when working with w ≠ -1 backgrounds, to restore consistency with CAMB in the GR limit. This version of MGCAMB comes with a Python wrapper to run it directly from the Python interface, an implementation in the latest version of CosmoMC, and can be used with Cobaya.

Growth of matter perturbations in some parametrization of dark energy models

In this work, we investigate the growth of matter perturbations in some known parameterizations of dark energy (DE) models i.e, CPL, JBP, BA, and a new parameterization of DE introduced in this study. We examine the growth of perturbations in the linear region by assuming the possibility of perturbations in DE. Then, we follow an overall likelihood analysis to put the same constraints on models using background and growth rate data, and we conclude that the reviewed DE parameterizations are compatible with the observational data at both background and perturbation levels. Furthermore, we find that DE parameterizations are comparable with each other, and with the Lambda CDM model. In particular, we obtain the following significant results: (i) the growth rate of matter perturbations in the homogeneous DE case is smaller than its value in the clustered case for CPL and BA models, while it is the opposite for JBP and the new model. (ii) The growth rate of matter perturbations related to the CPL and BA models have very similar behavior for both homogeneous and clustered DE cases at all redshift z. This is also true for JBP and the new model. (iii) We show that the growth rate of matter perturbations relevant to the models is lower than its value in the Lambda CDM model at low redshifts, and at high redshifts, the difference between them is insignificant. Finally, using AIC and BIC analysis, we conclude that the selection of a model that has better compatible with the observational data depends on the background and perturbation data.

An effective fluid description of scalar-vector-tensor theories under the sub-horizon and quasi-static approximations

We consider scalar-vector-tensor (SVT) theories with second-order equations of motion and tensor propagation speed equivalent to the speed of light. Under the sub-horizon and the quasi-static approximations we find analytical formulae for an effective dark energy fluid, i.e., sound speed, anisotropic stress as well as energy density and pressure. We took advantage of our general, analytical fluid description and showed that it is possible to design SVT cosmological models which are degenerate with ΛCDM at the background level while having gravity strength G eff < G N at late-times as well as non-vanishing dark energy perturbations. We implemented SVT designer models in the widely used Boltzmann solver CLASS thus making it possible to test SVT models against astrophysical observations. Our effective fluid approach to SVT models reveals non trivial behaviour in the sound speed and the anisotropic stress well worth an investigation in light of current discrepancies in cosmological parameters such as H 0 and σ 8.

Skewness as a test of dark energy perturbations

We investigate the role played by dark energy perturbations in the skewness ${S}_{3}$ of large-scale matter distribution. We consider a two-fluid universe composed by matter and dark energy, with perturbations in both components, and we estimate numerically the skewness of the matter density field as a function of the dark energy parameters. We characterize today's ${S}_{3}$ value for quintessence and phantom dark energy cosmologies as well as its dependence on the matter density parameter ${\mathrm{\ensuremath{\Omega}}}_{m0}$ and the dark energy sound speed ${c}_{s}^{2}$ with accurate numerical fitting. These fits can be used to test cosmology against future high quality data on large scale structure.

Cosmic evolution in DHOST theory with scaling solutions

We study cosmic evolution based on the fixed points in the dynamical analysis of the degenerate higher-order scalar-tensor (DHOST) theories. We consider the DHOST theory in which the propagation speed of gravitational waves is equal to the speed of light, the tensor perturbations do not decay to dark energy perturbations, and the scaling solutions exist. The scaling fixed point associated with late-time acceleration of the universe can be either stable or saddle depending on the parameters of the theory. For some ranges of the parameters, this scaling fixed point and field-dominated fixed point can be simultaneously stable. Cosmic evolution will reach either the scaling attractor or the field-dominated attractor depending on the sign of the time derivative of the scalar field in the theory during the matter domination. The density parameter of dark matter can be larger than unity before reaching the scaling attractor if the deviation from Einstein’s theory of gravity is too large. For this DHOST theory, stabilities of {phi }-matter-dominated epoch (phi MDE) and field-dominated solutions are similar to the coupled dark energy models in Einstein gravity even though gravity is described by different theories. In our consideration, the universe can only evolve from the phi MDE regime to the field-dominated regime. The ghost and gradient instabilities up to linear order in cosmological perturbations have been investigated. There is no gradient instability, while the ghost instability can be avoided for some range of the model parameters.

A Short Review on Clustering Dark Energy

We review dark energy models that can present non-negligible fluctuations on scales smaller than Hubble radius. Both linear and nonlinear evolutions of dark energy fluctuations are discussed. The linear evolution has a well-established framework, based on linear perturbation theory in General Relativity, and is well studied and implemented in numerical codes. We highlight the main results from linear theory to explain how dark energy perturbations become important on the scales of interest for structure formation. Next, we review some attempts to understand the impact of clustering dark energy models in the nonlinear regime, usually based on generalizations of the Spherical Collapse Model. We critically discuss the proposed generalizations of the Spherical Collapse Model that can treat clustering dark energy models and their shortcomings. Proposed implementations of clustering dark energy models in halo mass functions are reviewed. We also discuss some recent numerical simulations capable of treating dark energy fluctuations. Finally, we summarize the observational predictions based on these models.

Tachyonic vs quintessence dark energy: linear perturbations and CMB data

We use linear perturbation theory to study perturbations in dynamical dark energy (DE) models. We compare quintessence and tachyonic DE models with identical background evolution. We rewrite the perturbation equations for quintessence and tachyonic models in a form that makes it easier to see that these models are very hard to distinguish in the linear regime, especially when the equation of state w is close to that of Λ (i.e. in the limit (1 + w) ≪ 1). We use cosmic microwave background data and parametric representations for the two models to illustrate that current observations cannot distinguish between models with the same background evolution. Further, we constrain tachyonic models with the Planck data. We do this analysis for exponential and inverse square potentials and find that the intrinsic parameters of the potentials remain very weakly constrained. In particular, this is true in the regime allowed by low redshift observations.

Interacting dynamical dark energy with stable high-scale cosmological perturbations at radiation-dominated epoch

In this paper, the cosmological perturbations of dynamical dark energy and dark matter, which interact non-gravitationally are studied. This dark energy–dark matter non-gravitational interaction is linearly dependent on the energy densities of dark components. However, in the interacting quintessence dark energy models with such type of interaction, the non-adiabatic instabilities of cosmological perturbations at radiation-dominated epoch arise. To avoid this problem, the model of dynamical dark energy was chosen as the basis. Here, the equation of state parameter of dark energy evolves in time but can be assumed constant at early epoch, so this model can be tuned in such a way that the non-adiabatic instabilities would not appear. The drawback of this cosmological model is that the energy densities of dark components can take the negative values for the certain range of interaction parameter, so the conditions for positivity of dark components densities were derived. Using obtained constraints on the model parameters, the impact of coupling parameter on modification of cosmological perturbations’ evolution is analyzed.

Multi-field dark energy: Cosmic acceleration on a steep potential

We argue that dark energy with multiple fields is theoretically well-motivated and predicts distinct observational signatures, in particular when cosmic acceleration takes place along a trajectory that is highly non-geodesic in field space. Such models provide novel physics compared to ΛCDM and quintessence by allowing cosmic acceleration on steep potentials. From the theoretical point of view, these theories can easily satisfy the conjectured swampland constraints and may in certain cases be technically natural, potential problems which are endemic to standard single-field dark energy. Observationally, we argue that while such multi-field models are likely to be largely indistinguishable from the concordance cosmology at the background level, dark energy perturbations can cluster, leading to an enhanced growth of large-scale structure that may be testable as early as the next generation of cosmological surveys.

Euclid preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

ABSTRACT We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent level accurate emulation is now supported in the eight-dimensional parameter space of w0waCDM+∑mν models between redshift z = 0 and z = 3 for spatial scales within the range $0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy, and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 30003 particles in boxes of 1(h−1 Gpc)3 volumes based on paired-and-fixed initial conditions, and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter wa significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors such as HALOFIT, HMCode, and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of $1{{\ \rm per\ cent}}$ or better for $0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$ and z ≤ 3 compared to high-resolution dark-matter-only simulations. EuclidEmulator2 is publicly available at https://github.com/miknab/EuclidEmulator2.

Effects of Rastall parameter on perturbation of dark sectors of the Universe

In recent years, Rastall gravity is undergoing a considerable surge in popularity. This theory purports to be a modified gravity theory with a non-conserved energy–momentum tensor (EMT) and an unusual non-minimal coupling between matter and geometry. This work looks for the evolution of homogeneous spherical perturbations within the Universe in the context of Rastall gravity. Using the spherical Top-Hat collapse model, we seek for exact solutions in linear regime for density contrast of dark matter (DM) and dark energy (DE). We find that the Rastall parameter affects crucially the dynamics of density contrasts for DM and DE and the fate of spherical collapse is different in comparison to the case of general relativity (GR). Numerical solutions for perturbation equations in nonlinear regime reveal that DE perturbations could amplify the rate of growth of DM perturbations depending on the values of Rastall parameter.

Measurements of H_0 and reconstruction of the dark energy properties from a model-independent joint analysis

Gaussian processes (GP) provide an elegant and model-independent method for extracting cosmological information from the observational data. In this work, we employ GP to perform a joint analysis by using the geometrical cosmological probes such as Supernova Type Ia (SN), Cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the H0LiCOW lenses sample to constrain the Hubble constant H_0, and reconstruct some properties of dark energy (DE), viz., the equation of state parameter w, the sound speed of DE perturbations c^2_s, and the ratio of DE density evolution X = rho _mathrm{de}/rho _mathrm{de,0}. From the joint analysis SN+CC+BAO+H0LiCOW, we find that H_0 is constrained at 1.1% precision with H_0 = 73.78 pm 0.84 hbox {km} hbox {s}^{-1},hbox {Mpc}^{-1}, which is in agreement with SH0ES and H0LiCOW estimates, but in sim 6.2 sigma tension with the current CMB measurements of H_0. With regard to the DE parameters, we find c^2_s < 0 at sim 2 sigma at high z, and the possibility of X to become negative for z > 1.5. We compare our results with the ones obtained in the literature, and discuss the consequences of our main results on the DE theoretical framework.

Relativistic corrections to the growth of structure in modified gravity

We present a method to introduce relativistic corrections including linear dark energy perturbations in Horndeski theory into Newtonian simulations based on the N-body gauge approach. We assume that standard matter species (cold dark matter, baryons, photons and neutrinos) are only gravitationally-coupled with the scalar field and we then use the fact that one can include modified gravity effects as an effective dark energy fluid in the total energy-momentum tensor. In order to compute the scalar field perturbations, as well as the cosmological background and metric perturbations, we use the Einstein-Boltzmann code hi_class. As an example, we study the impact of relativistic corrections on the matter power spectrum in k-essence, a subclass of Horndeski theory, including the effects of massless and massive neutrinos. For massive neutrinos with ∑ mν = 0.1 eV, the corrections due to relativistic species (photons, neutrinos and dark energy) can introduce a maximum deviation of approximately 7% to the power spectrum at k ∼ 10−3 Mpc−1 at z=0, for a scalar field with sound speed cs2∼0.013 during matter domination epoch. Our formalism makes it possible to test beyond \\lcdm models probed by upcoming large-scale structure surveys on very large scales.

Clustering dark energy imprints on cosmological observables of the gravitational field

ABSTRACT We study cosmological observables on the past light-cone of a fixed observer in the context of clustering dark energy. We focus on observables that probe the gravitational field directly, namely the integrated Sachs–Wolfe and non-linear Rees–Sciama effect (ISW-RS), weak gravitational lensing, gravitational redshift, and Shapiro time delay. With our purpose-built N-body code ‘k-evolution’ that tracks the coupled evolution of dark matter particles and the dark energy field, we are able to study the regime of low speed of sound cs where dark energy perturbations can become quite large. Using ray tracing, we produce two-dimensional sky maps for each effect and we compute their angular power spectra. It turns out that the ISW-RS signal is the most promising probe to constrain clustering dark energy properties coded in $w-c_\mathrm{ s}^2$, as the linear clustering of dark energy would change the angular power spectrum by ${\sim}30{{\ \rm per\ cent}}$ at low ℓ when comparing two different speeds of sound for dark energy. Weak gravitational lensing, Shapiro time delay, and gravitational redshift are less sensitive probes of clustering dark energy, showing variations of only a few per cent. The effect of dark energy non-linearities in all the power spectra is negligible at low ℓ, but reaches about $2{{\ \rm per\ cent}}$ and $3{{\ \rm per\ cent}}$, respectively, in the convergence and ISW-RS angular power spectra at multipoles of a few hundred when observed at redshift ∼0.85. Future cosmological surveys achieving per cent precision measurements will allow us to probe the clustering of dark energy to a high degree of confidence.

Cosmological constraints on nonadiabatic 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.

Non-linear spherical collapse in tachyon models and a comparison of collapse in tachyon and quintessence models of dark energy

We study evolution of perturbations in dark matter and dark energy for spherical collapse using a completely self consistent, relativistic approach. We study tachyon models of dark energy using the approach outlined in Rajvanshi and Bagla (2018). We work with models that are allowed by current observations. We find that as with quintessence models allowed by observations, dark energy perturbations do not affect evolution of perturbations in dark matter in a significant manner. Perturbations in dark energy remain small for such models. We then take two different Lagrangians for dark energy: tachyon and quintessence models, reconstruct potentials to have same expansion history and then compare if two can be distinguished in the nonlinear regime. Any variations we find are only due to a different Lagrangian density, and allow a comparison of different classes of models in a fair manner. We find that dark matter perturbations carry no imprint of the class of dark energy models for the same expansion history: this is significant in that we can work with any convenient model to study clustering of dark matter. We find that the evolution of dark energy perturbations carries an imprint of the class of models and dark energy perturbations grow differently in tachyon models and quintessence models for the same expansion history. However, the difference between these diminishes for (1 + w) ≪ 1 and hence prospects for differentiating between models using characteristics of perturbations are limited in our Universe.

General formulation of cosmological perturbations in scalar-tensor dark energy coupled to dark matter

For a scalar field ϕ coupled to cold dark matter (CDM), we provide a general framework for studying the background and perturbation dynamics on the isotropic cosmological background. The dark energy sector is described by a Horndeski Lagrangian with the speed of gravitational waves equivalent to that of light, whereas CDM is dealt as a perfect fluid characterized by the number density nc and four-velocity ucμ. For a very general interacting Lagrangian f(nc, ϕ, X, Z), where f depends on nc, ϕ, X=−∂μ ϕ ∂μ ϕ/2, and Z=ucμ ∂μ ϕ, we derive the full linear perturbation equations of motion without fixing any gauge conditions. To realize a vanishing CDM sound speed for the successful structure formation, the interacting function needs to be of the form f=−f1(ϕ, X, Z)nc+f2(ϕ, X, Z). Employing a quasi-static approximation for the modes deep inside the sound horizon, we obtain analytic formulas for the effective gravitational couplings of CDM and baryon density perturbations as well as gravitational and weak lensing potentials. We apply our general formulas to several interacting theories and show that, in many cases, the CDM gravitational coupling around the quasi de-Sitter background can be smaller than the Newton constant G due to a momentum transfer induced by the Z-dependence in f2.

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 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.

Evolution of dark energy perturbations for Slotheon field and power spectrum

Within the framework of modified gravity model namely Slotheon model, inspired by the theory of extra dimensions, we explore the behaviour of Dark Energy and the perturbations thereof. The Dark Energy and matter perturbations equations are then derived and solved numerically by defining certain dimensionless variables and properly chosen initial conditions. The results are compared with those for standard quintessence model and varLambda CDM model. The matter power spectrum is obtained and also compared with that for varLambda CDM model. It appears that Dark Energy in Slotheon model is more akin to that for varLambda CDM model than the standard quintessence model.

Perturbations in tachyon dark energy and their effect on matter clustering

A non-canonical scalar tachyon field is a viable candidate for dark energy and has been found to be in good agreement with observational data. Background data alone cannot completely rule out degeneracy between this model and others. To further constrain the parameters, apart from the distance measurements, we study perturbations in tachyon scalar field and how they affect matter clustering. We consider two tachyon potentials for this study, an inverse square potential and an exponential potential. We study the evolution of the gravitational potential, matter density contrast and dark energy density contrast, and compare them with the evolution in the ΛCDM model. Although perturbations in dark energy at sub-Hubble scales are negligible in comparison with matter perturbations, they cannot be ignored at Hubble and super-Hubble scales (λp > 1000 Mpc). We also study the evolution of growth function and growth rate of matter, and find that the growth rate is significantly suppressed in dark energy dominated era with respect to the growth rate for Λ CDM model. A comparison of these models with Redshift Space Distortion growth rate data is presented by way of calculating fσ8(z). There is a tension of 2.9σ (2.26σ) between growth rate data and Planck-2015 (Planck-2018) Cosmic Microwave Background Radiation data for Λ CDM model. We present constraints on free parameters of these models and show that perturbations in tachyon scalar field reduce this tension between different data sets.