Coupled Dark Energy Research Articles

Testing the Interaction Between Baryons and Dark Energy with Recent Cosmological Observations

We study a modified interacting dark energy (MIDE) model as a candidate to describe possible interaction between dark energy and dark matter as well as that between dark energy and baryonic matter. More specifically, we introduce a new parameter γ b to quantify the extent of interaction between dark energy and baryons. With three classes of cosmological distance observations including CMB measurements from Planck and WMAP9 results, as well as the recent direct measurements of the Hubble parameter as a function of redshift, we study the allowable values of γ c and γ b and other cosmological parameters. The constraint results obtained by using the MCMC method show: (1) The interaction term γ b quantifying the extent of interaction between baryonic matter and dark energy is nearly equal to 0, which strongly support the whole coupled dark energy scenario based on the assumption that baryons should remain uncoupled in order to allow a non-negligible coupling to dark matter. (2) At the 95.4 % confidence level, we see the energy of dark energy is slightly transferring to that of dark matter; (3) Concerning the typical value of the present energy density ratio between baryonic matter and dark matter in the universe, we obtain a positive coupling between dark energy and matter at 2σ, which indicates that dark energy is leaking energy to matter. Finally, concerning the observational density parameter ratio Ω b /Ω m derived from the gas mass fraction data (f g a s ), within the framework of the phenomenological interaction model, we observe a good compatibility between the observational constraints from f g a s and other combined data.

Covariantizing the interaction between dark energy and dark matter

Coupling dark energy and dark matter through an effective fluid description is a very common procedure in cosmology, however it always remains in comoving coordinates in the special FLRW space. We construct a consistent, general, and covariant formulation, where the interaction is a natural implication of the imperfectness of the fluids. This imperfectness makes difficult the final step towards a robust formulation of interacting fluids, namely the construction of a Lagrangian whose variation would give rise to the interacting equations. Nevertheless, we present a formal solution to this problem for a single fluid, through the introduction of an effective metric.

Testing coupled dark energy with large scale structure observation

The coupling between the dark components provides a new approach to mitigate the coincidence problem of cosmological standard model. In this paper, dark energy is treated as a fluid with a constant equation of state, whose coupling with dark matter is Q̄=3Hξxρ̄x. In the frame of dark energy, we derive the evolution equations for the density and velocity perturbations. According to the Markov Chain Monte Carlo method, we constrain the model by currently available cosmic observations which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and fσ8(z) data points from redshift-space distortion. The results show the interaction rate in σ regions: ξx = 0.00328-0.00328-0.00328-0.00328+0.000736+0.00549+0.00816, which means that the recently cosmic observations favor a small interaction rate which is up to the order of 10-2, meanwhile, the measurement of redshift-space distortion could rule out the large interaction rate in the σ region.

Late evolution of relic gravitational waves in coupled dark energy models

In this paper we study the late evolution of Relic Gravitational Waves in coupled dark energy models, where dark energy interacts with cold dark matter. Relic Gravitational Waves are second tensorial order perturbations of the Lemaitre–Friedman–Robertson–Walker metric and experiment an evolution ruled by the scale factor of the metric. We find that the amplitude of Relic Gravitational Waves is smaller in coupled dark energy models than in models with non interacting dark energy. We also find that the amplitude of the waves predicted by the models with coupling term proportional to the dark energy density is smaller than those of the models with coupling term proportional to dark matter density.

Material models of dark energy

A new class of “dark energy” models is reviewed and developed, in which the relativistic theory of solids is used to construct material models of dark energy. These are models which include the effects of a continuous medium with well defined physical properties at the level of linearized perturbations. The formalism is constructed for a medium with arbitrary symmetry, and then specialised to isotropic media (which will be the case of interest for the majority of cosmological applications). The theory of relativistic isotropic viscoelastic media is developed whilst keeping in mind that we ultimately want to observationally constrain the allowed properties of the material model. This is done by obtaining the viscoelastic equations of state for perturbations (the entropy and anisotropic stress), as well as identifying the consistent corner of the theory which has constant equation of state parameter . A connection to the non‐relativistic theory of solids is obtained by identifying the two quadratic invariants that are needed to construct the energy‐momentum tensor, namely the Rayleigh dissipation function and Lagrangian for perturbations. Finally, the notion is developed that the viscoelastic behavior of the medium can be thought of as a non‐minimally coupled massive gravity theory. This also provides a tool‐kit for constructing consistent generalizations of coupled dark energy theories.

Can the coincidence problem be solved by a cosmological model of coupled dark energy and dark matter?

Motivated by the cosmological constant and the coincidence problems, we consider a cosmological model where the dark sectors are interacting together through a phenomenological decay law $\dot{\rho}_{\Lambda}=Q\rho_{\Lambda}^n$ in a FRW spacetime with spatial curvature. We show that the only value of $n$ for which the late-time matter energy density to dark energy density ratio ($r_m=\rho_m/\rho_{\Lambda}$) is constant (which could provide an explanation to the coincidence problem) is $n=3/2$. For each value of $Q$, there are two distinct solutions. One of them involves a spatial curvature approaching zero at late times ($\rho_k\approx0$) and is stable when the interaction is weaker than a critical value ${Q_0=-\sqrt{32\pi G/c^2}}$. The other one allows for a non-negligible spatial curvature ($\rho_k\napprox0$) at late times and is stable when the interaction is stronger than $Q_0$. We constrain the model parameters using various observational data (SNeIa, GRB, CMB, BAO, OHD). The limits obtained on the parameters exclude the regions where the cosmological constant problem is significantly ameliorated and do not allow for a completely satisfying explanation for the coincidence problem.

Dark energy coupling with electromagnetism as seen from future low-medium redshift probes

Beyond the standard cosmological model the late-time accelerated expansion of the universe can be reproduced by the introduction of an additional dynamical scalar field. In this case, the field is expected to be naturally coupled to the rest of the theory's fields, unless a (still unknown) symmetry suppresses this coupling. Therefore, this would possibly lead to some observational consequences, such as space-time variations of nature's fundamental constants. In this paper we investigate the coupling between a dynamical Dark Energy model and the electromagnetic field, and the corresponding evolution of the fine structure constant ($\alpha$) with respect to the standard local value $\alpha_0$. In particular, we derive joint constraints on two dynamical Dark Energy model parametrizations (the Chevallier-Polarski-Linder and Early Dark Energy model) and on the coupling with electromagnetism $\zeta$, forecasting future low-medium redshift observations. We combine supernovae and weak lensing measurements from the Euclid experiment with high-resolution spectroscopy measurements of fundamental couplings and the redshift drift from the European Extremely Large Telescope, highlighting the contribution of each probe. Moreover, we also consider the case where the field driving the $\alpha$ evolution is not the one responsible for cosmic acceleration and investigate how future observations can constrain this scenario.

MASSIVE GRAVITY WRAPPED IN THE COSMIC WEB

We study how the filamentary pattern of the cosmic web changes if the true gravity deviates from the general relativity (GR) on the large scale. The f(R) gravity whose strength is controlled to satisfy the current observational constraints on the cluster scale is adopted as our fiducial model and a large N-body simulation of high-resolution is utilized for this study. By applying the minimal spanning tree algorithm to the halo catalogs from the simulation at various epochs, we identify the main stems of the rich superclusters located in the most prominent filamentary section of the cosmic web and determine their spatial extents per member cluster as the degree of their straightness. It is found that the $f(R)$ gravity has an effect of significantly bending the superclusters and that the effect becomes stronger as the universe evolves. Even in the case where the deviation from GR is too small to be detectable by any other observables, the degree of the supercluster straightness exhibits conspicuous difference between the $f(R)$ and the GR models. Our results also imply that the supercluster straightness could be a useful discriminator of f(R) gravity from the coupled dark energy since it is shown to evolve differently between the two models. As a final conclusion, the degree of the straightness of the rich superclusters should provide a powerful cosmological test of large scale gravity.

Coupled three-form dark energy

Cosmology with a three-form field interacting with cold dark matter is considered. In particular, the mass of the dark matter particles is assumed to depend upon the amplitude of the three-form field invariant. In comparison to coupled scalar field quintessence, the new features include an effective pressure contribution to the field equations that manifests both in the background and perturbation level. The dynamics of the background is analyzed, and new scaling solutions are found. A simple example model leading to a de Sitter expansion without a potential is studied. The Newtonian limit of cosmological perturbations is derived, and it is deduced that the coupling can be very tightly constrained by the large-scale structure data. This is demonstrated with numerical solutions for a model with nontrivial coupling and a quadratic potential.

New limits on coupled dark energy from Planck

Recently, the Planck collaboration has released the first cosmological papers providing the high resolution, full sky, maps of the cosmic microwave background (CMB) temperature anisotropies. It is crucial to understand that whether the accelerating expansion of our universe at present is driven by an unknown energy component (Dark Energy) or a modification to general relativity (Modified Gravity). In this paper we study the coupled dark energy models, in which the quintessence scalar field nontrivially couples to the cold dark matter, with the strength parameter of interaction β. Using the Planck data alone, we obtain that the strength of interaction between dark sectors is constrained as β < 0.102 at 95% confidence level, which is tighter than that from the WMAP9 data alone. Combining the Planck data with other probes, like the Baryon Acoustic Oscillation (BAO), Type-Ia supernovae ``Union2.1 compilation'' and the CMB lensing data from Planck measurement, we find the tight constraint on the strength of interaction β < 0.052 (95% C.L.). Interestingly, we also find a non-zero coupling β = 0.078±0.022 (68% C.L.) when we use the Planck, the ``SNLS'' supernovae samples, and the prior on the Hubble constant from the Hubble Space Telescope (HST) together. This evidence for the coupled dark energy models mainly comes from a tension between constraints on the Hubble constant from the Planck measurement and the local direct H0 probes from HST.

DARK SECTOR COUPLING BENDS THE SUPERCLUSTERS

The galaxy clusters exhibit noticeably anisotropic pattern in their clustering, which is vividly manifested by the presence of rich filament-like superclusters. The more anisotropic the clustering of galaxy clusters is, the more straight the rich filament-like superclusters become. Given that the degree of the anisotropy in the largest-scale clustering depends sensitively on the nature of dark energy, the supercluster straightness may play a complimentary role in testing dynamic dark energy models. Here we focus on the coupled dark energy (cDE) models which assume the existence of dark sector coupling between scalar field dark energy and nonbaryonic dark matter. Determining the spines of the superclusters identified in the publicly available group catalogs from the CODECS (COupled Dark Energy Cosmological Simulations) for four different cDE models as well as for the LCDM model, we quantify the straightness of each supercluster as the spatial extent of its spine per member cluster where a supercluster spine represents the main stem of the minimal spanning tree constructed out of the member clusters. It is shown that the dark sector coupling plays a role in making the supercluster less straight relative to the LCDM case and that in a cDE model with supergravity potential the superclusters are least straight. We also find that the difference in the degree of the supercluster straightness between the cDE and the LCDM cases increases with redshifts. A physical interpretation of our result as well as its cosmological implication are discussed.

Testing modified gravity with Planck: The case of coupled dark energy

The Planck collaboration has recently published maps of the Cosmic Microwave Background (CMB) radiation, in good agreement with a LCDM model, a fit especially valid for multipoles l > 40. We explore here the possibility that dark energy is dynamical and gravitational attraction between dark matter particles is effectively different from the standard one in General Relativity: this is the case of coupled dark energy models, where dark matter particles feel the presence of a fifth force, larger than gravity by a factor beta^2. We investigate constraints on the strength of the coupling beta in view of Planck data. Interestingly, we show that a non-zero coupling is compatible with data and find a likelihood peak at beta = 0.036 \pm 0.016 (Planck + WP + BAO) (compatible with zero at 2sigma). The significance of the peak increases to beta = 0.066 \pm 0.018 (Planck + WP + HST) (around 3.6sigma) when Planck is combined to Hubble Space Telescope data. This peak comes mostly from the small difference between the Hubble parameter determined with CMB measurements and the one coming from astrophysics measurements. In this sense, future observations and further tests of current observations are needed to determine whether the discrepancy is due to systematics in any of the datasets. Our aim here is not to claim new physics but rather to show how Planck data can be used to provide information on dynamical dark energy and modified gravity, allowing us to test the strength of an effective fifth force between dark matter particles with precision smaller than 2%.

Maps of CMB lensing deflection from N-body simulations in Coupled Dark Energy Cosmologies

We produce lensing potential and deflection-angle maps in order to simulate the weak gravitational lensing of the Cosmic Microwave Background (CMB) via ray-tracing through the COupled Dark Energy Cosmological Simulations (CoDECS), the largest suite of N-body simulations to date for interacting Dark Energy cosmologies. The constructed maps faithfully reflect the N-body cosmic structures on a range of scales going from the arcminute to the degree scale, limited only by the resolution and extension of the simulations. We investigate the variation of the lensing pattern due to the underlying Dark Energy (DE) dynamics, characterised by different background and perturbation behaviours as a consequence of the interaction between the DE field and Cold Dark Matter (CDM). In particular, we study in detail the results from three cosmological models differing in the background and perturbations evolution at the epoch in which the lensing cross section is most effective, corresponding to a redshift of ∼ 1, with the purpose to isolate their imprints in the lensing observables, regardless of the compatibility of these models with present constraints. The scenarios investigated here include a reference ΛCDM cosmology, a standard coupled DE (cDE) scenario, and a ``bouncing" cDE scenario. For the standard cDE scenario, we find that typical differences in the lensing potential result from two effects: the enhanced growth of linear CDM density fluctuations with respect to the ΛCDM case, and the modified nonlinear dynamics of collapsed structures induced by the DE-CDM interaction. As a consequence, CMB lensing highlights the DE impact in the cosmological expansion, even in the degenerate case where the amplitude of the linear matter density perturbations, parametrised through σ8, is the same in both the standard cDE and ΛCDM cosmologies. For the ``bouncing" scenario, we find that the two opposite behaviours of the lens density contrast and of the matter abundance lead to a counter-intuitive effect, making the power of the lensing signal in this model lower by 10% than in the ΛCDM scenario. Moreover, we compare the behaviour of CDM and baryons in CoDECS separately, in order to isolate effects coming from the coupling with the DE component. We find that, in the bouncing scenario, baryons show an opposite trend with respect to CDM, due to the coupling of the latter with the DE component. These results confirm the relevance of CMB lensing as a probe for DE at the early stages of cosmic acceleration, and demonstrate the reliability of N-body based large scale CMB lensing simulations in the context of DE studies.

New constraints on coupled dark energy from the Planck satellite experiment

We present new constraints on coupled dark energy from the recent measurements of the cosmic microwave background anisotropies from the Planck satellite mission. We found that a coupled dark energy model is fully compatible with the Planck measurements, deriving a weak bound on the dark matter--dark energy coupling parameter $\ensuremath{\xi}=\ensuremath{-}{0.49}_{\ensuremath{-}0.31}^{+0.19}$ at 68% C.L. Moreover if Planck data are fitted to a coupled dark energy scenario, the constraint on the Hubble constant is relaxed to ${H}_{0}={72.1}_{\ensuremath{-}2.3}^{+3.2}\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$, solving the tension with the Hubble Space Telescope (HST) value. We show that a combined $\mathrm{\text{PLANCK}}+\mathrm{HST}$ analysis provides significant evidence for coupled dark energy finding a nonzero value for the coupling parameter $\ensuremath{\xi}$, with $\ensuremath{-}0.90&lt;\ensuremath{\xi}&lt;\ensuremath{-}0.22$ at 95% C.L. We also consider the combined constraints from the Planck data plus the baryon acoustic oscillation measurements of the 6dF Galaxy Survey, the Sloan Digital Sky Survey and the Baron Oscillation Spectroscopic Survey.

Characterizing dark interactions with the halo mass accretion history and structural properties

We study the halo mass accretion history (MAH) and its correlation with the internal structural properties in coupled dark energy cosmologies (cDE). To accurately predict all the non-linear effects caused by dark interactions, we use the COupled Dark Energy Cosmological Simulations (CoDECS). We measure the halo concentration at z=0 and the number of substructures above a mass resolution threshold for each halo. Tracing the halo merging history trees back in time, following the mass of the main halo, we develope a MAH model that accurately reproduces the halo growth in term of M_{200} in the {\Lambda}CDM Universe; we then compare the MAH in different cosmological scenarios. For cDE models with a weak constant coupling, our MAH model can reproduce the simulation results, within 10% of accuracy, by suitably rescaling the normalization of the linear matter power spectrum at z=0, {\sigma}_8. However, this is not the case for more complex scenarios, like the "bouncing" cDE model, for which the numerical analysis shows a rapid growth of haloes at high redshifts, that cannot be reproduced by simply rescaling the value of {\sigma}_8. Moreover, at fixed value of {\sigma}_8, cold dark matter (CDM) haloes in these cDE scenarios tend to be more concentrated and have a larger amount of substructures with respect to {\Lambda}CDM predictions. Finally, we present an accurate model that relates the halo concentration to the time at which it assembles half or 4% of its mass. Combining this with our MAH model, we show how halo concentrations change while varying only {\sigma}_8 in a {\Lambda}CDM Universe, at fixed halo mass.

Constraints on coupled dark energy using CMB data from WMAP and South Pole Telescope

We consider the case of a coupling in the dark cosmological sector, where a dark energy scalar field modifies the gravitational attraction between dark matter particles. We find that the strength of the coupling {\beta} is constrained using current Cosmic Microwave Background (CMB) data, including WMAP7 and SPT, to be less than 0.063 (0.11) at 68% (95%) confidence level. Further, we consider the additional effect of the CMB-lensing amplitude, curvature, effective number of relativistic species and massive neutrinos and show that the bound from current data on {\beta} is already strong enough to be rather stable with respect to any of these variables. The strongest effect is obtained when we allow for massive neutrinos, in which case the bound becomes slightly weaker, {\beta} < 0.084(0.14). A larger value of the effective number of relativistic degrees of freedom favors larger couplings between dark matter and dark energy as well as values of the spectral index closer to 1. Adding the present constraints on the Hubble constant, as well as from baryon acoustic oscillations and supernovae Ia, we find {\beta} < 0.050(0.074). In this case we also find an interesting likelihood peak for {\beta} = 0.041 (still compatible with 0 at 1{\sigma}). This peak comes mostly from a slight difference between the Hubble parameter HST result and the WMAP7+SPT best fit. Finally, we show that forecasts of Planck+SPT mock data can pin down the coupling to a precision of better than 1% and detect whether the marginal peak we find at small non zero coupling is a real effect.

The halo mass function in interacting dark energy models

We present a detailed investigation of the effects imprinted by a direct interaction between dark energy and cold dark matter particles on the halo mass function of groups and clusters of galaxies. Making use of the public halo catalogues of the codecs simulations, we derive the halo mass function for several different types of coupled dark energy scenarios, based on both the friends-of-friends algorithm and the spherical overdensity halo identification for different values of the overdensity threshold Δc. We compare the computed halo mass functions for coupled dark energy cosmologies with ΛCDM as well as with the predictions of the standard analytic fitting functions. Our results show that the standard fitting functions still reproduce both the friends-of-friends and spherical overdensity halo mass functions of interacting dark energy cosmologies reasonably well at intermediate masses and low redshifts, once rescaled to the characteristic amplitude of linear density perturbations of each specific model as given by σ8. However, we also find that such apparent degeneracy with σ8 is broken by both the high-mass tail and the redshift evolution of our halo mass functions, with deviations beyond ∼10 per cent for most of the models under investigation. Furthermore, the discrepancy with respect to the predictions of standard fitting functions rescaled with the characteristic value of σ8 shows - for some models - a strong dependence on the spherical overdensity threshold Δc used for the halo identification. We find that such an effect is due to a significant increase of halo concentration at low redshifts in these models that is, however, absent in the majority of the cosmological scenarios considered in this work. We can therefore conclude that the universality of the halo mass function is violated by cosmological models that feature a direct interaction between dark energy and cold dark matter.

Testing coupled dark energy with next-generation large-scale observations

Coupling dark energy to dark matter provides one of the simplest way to effectively modify gravity at large scales without strong constraints from local (i.e. solar system) observations. Models of coupled dark energy have been studied several times in the past and are already significantly constrained by cosmic microwave background experiments. In this paper we estimate the constraints that future large-scale observations will be able to put on the coupling and in general on all the parameters of the model. We combine cosmic microwave background, tomographic weak lensing, redshift distortions and power spectrum probes. We show that next-generation observations can improve the current constraint on the coupling to dark matter by two orders of magnitude; this constraint is complementary to the current solar-system bounds on a coupling to baryons.

THE SPIN ALIGNMENTS IN GALAXY PAIRS AS A TEST OF BOUNCING COUPLED DARK ENERGY

We investigate the effect of coupled dark energy (cDE) on the spin alignments in isolated pairs of galactic halos, using the publicly available data from the hydrodynamical cDE simulations (H-CoDECs) which were run for various cDE models such as EXP001, EXP002, EXP003 (with exponential potential and constant coupling), EXP008e3 (with exponential potential and exponential coupling) and SUGRA003 (with supergravity potential and negative constant coupling) as well as for a standard LCDM cosmology (with the WMAP7 parameters). Measuring the cosines of the angles between the spin axes in isolated pairs of galactic halos for each model and determining its probability density distribution, we show that for the SUGRA003 model with bouncing cDE the null hypothesis of no spin alignment in pairs of galactic halos is rejected at 99.999% confidence level. In contrast, the LCDM cosmology yields no significant signal of spin alignment and the other four cDE models also exhibit only weak signals of spin-alignments. The strength of the spin alignment signal is found to be almost independent of the total halo mass and separation distance in galaxy pairs. Showing also that no signal is detected from the Sloan Digital Sky Survey DR 7, we conclude that the spin alignments in galaxy pairs is in principle a unique test of bouncing cDE models.

Weak lensing predictions for coupled dark energy cosmologies at non-linear scales

We present non-linear weak lensing predictions for coupled dark energy models using the CoDECS simulations. We calculate the shear correlation function and error covariance expected for these models, for forthcoming ground-based (such as DES) and space-based (Euclid) weak lensing surveys. We obtain predictions for the discriminatory power of a ground-based survey similar to DES and a space-based survey such as Euclid in distinguishing between $\Lambda$CDM and coupled dark energy models; we show that using the non-linear lensing signal we could discriminate between $\Lambda$CDM and exponential constant coupling models with $\beta_0\geq0.1$ at $4\sigma$ confidence level with a DES-like survey, and $\beta_0\geq0.05$ at $5\sigma$ confidence level with Euclid. We also demonstrate that estimating the coupled dark energy models' non-linear power spectrum, using the $\Lambda$CDM Halofit fitting formula, results in biases in the shear correlation function that exceed the survey errors.