Simplest Dark Energy Models Research Articles

Partition function approach to non-Gaussian likelihoods: physically motivated convergence criteria for Markov chains

ABSTRACT Non-Gaussian distributions in cosmology are commonly evaluated with Monte Carlo Markov chain methods, as the Fisher matrix formalism is restricted to the Gaussian case. The Metropolis–Hastings algorithm will provide samples from the posterior distribution after a burn-in period, and the corresponding convergence is usually quantified with the Gelman–Rubin criterion. In this paper, we investigate the convergence of the Metropolis–Hastings algorithm by drawing analogies to statistical Hamiltonian systems in thermal equilibrium for which a canonical partition sum exists. Specifically, we quantify virialization, equipartition, and thermalization of Hamiltonian Monte Carlo Markov chains for a toy model and for the likelihood evaluation for a simple dark energy model constructed from supernova data. We follow the convergence of these criteria to the values expected in thermal equilibrium, in comparison to the Gelman–Rubin criterion. We find that there is a much larger class of physically motivated convergence criteria with clearly defined target values indicating convergence. As a numerical tool, we employ physics-informed neural networks for speeding up the sampling process.

Coupled multi-Proca vector dark energy

We study a new class of vector dark energy models where multi-Proca fields $A_\mu^a$ are coupled to cold dark matter by the term $f(X)\tilde{\mathcal{L}}_{m}$ where $f(X)$ is a general function of $X\equiv -\frac{1}{2}A^\mu_ a A^a_\mu$ and $\tilde{\mathcal{L}}_{m}$ is the cold dark matter Lagrangian. From here, we derive the general covariant form of the novel interaction term sourcing the field equations. This result is quite general in the sense that encompasses Abelian and non-Abelian vector fields. In particular, we investigate the effects of this type of coupling in a simple dark energy model based on three copies of canonical Maxwell fields to realize isotropic expansion. The cosmological background dynamics of the model is examined by means of a dynamical system analysis to determine the stability of the emergent cosmological solutions. As an interesting result, we find that the coupling function leads to the existence of a novel scaling solution during the dark matter dominance. Furthermore, the critical points show an early contribution of the vector field in the form of dark radiation and a stable de Sitter-type attractor at late times mimicking dark energy. The cosmological evolution of the system as well as the aforementioned features are verified by numerical computations. Observational constraints are also discussed to put the model in a more phenomenological context in the light of future observations.

A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension

Abstract Motivated by the current status of cosmological observations and significant tensions in the estimated values of some key parameters assuming the standard ΛCDM model, we propose a simple but radical phenomenological emergent dark energy model where dark energy has no effective presence in the past and emerges at later times. Theoretically, in this phenomenological dark energy model with zero degrees of freedom (similar to a ΛCDM model), one can derive that the equation of state of dark energy increases from in the past to −1 in the future. We show that by setting a hard-cut 2σ lower bound prior for H 0 associated with a 97.72% probability from recent local observations, this model can satisfy different combinations of cosmological observations at low and high redshifts (SNe Ia, baryon acoustic oscillation (BAO), Lyα BAO, and cosmic microwave background (CMB)) substantially better than the concordance ΛCDM model with and Δ DIC ∼ −35.38. If there are no substantial systematics in SN Ia, BAO, or Planck CMB data, and assuming the reliability of current local H 0 measurements, there is a very high probability that with more precise measurements of the Hubble constant our proposed phenomenological model rules out the cosmological constant with decisive statistical significance and is a strong alternative to explain the combination of different cosmological observations. This simple phenomenologically emergent dark energy model can guide theoretically motivated dark energy model building activities.

Gravitational Collapse and Structure Formation in an Expanding Universe with Dark Energy

Observations show that the expansion of the Universe is accelerating. This requires that the dominant constituent of matter in the Universe has some unusual properties like negative pressure. This exotic component has been given the name dark energy. We work with the simplest model of dark energy, the cosmological constant introduced by Einstein. We study the evolution of spherical over-densities in such a model and show that there is a minimum over-density required for collapse; perturbations with a smaller amplitude do not collapse. This threshold is interesting as even perturbations with a positive over-density and negative energy do not collapse in finite time. Further, we show that perturbations with an amplitude larger than, but comparable to the threshold value, take a very long time to collapse. We compare the solutions with the case when dark energy is absent.

No evidence for the evolution of mass density power-law index γ from strong gravitational lensing observation

In this paper, we consider the singular isothermal sphere lensing model that has a spherically symmetric power-law mass distribution $\rho_{tot}(r)\sim r^{-\gamma}$. We investigate whether the mass density power-law index $\gamma$ is cosmologically evolutionary by using the strong gravitational lensing (SGL) observation, in combination with other cosmological observations. We also check whether the constraint result of $\gamma$ is affected by the cosmological model, by considering several simple dynamical dark energy models. We find that the constraint on $\gamma$ is mainly decided by the SGL observation and independent of the cosmological model, and we find no evidence for the evolution of $\gamma$ from the SGL observation.

Impacts of dark energy on weighing neutrinos after Planck 2015

We investigate how dark energy properties impact the cosmological limits on the total mass of active neutrinos. We consider two typical, simple dark energy models (that have only one more additional parameter than $\Lambda$CDM), i.e., the $w$CDM model and the holographic dark energy (HDE) model, as examples, to make an analysis. In the cosmological fits, we use the Planck 2015 temperature and polarization data, in combination with other low-redshift observations, including the baryon acoustic oscillations, type Ia supernovae, and Hubble constant measurement, as well as the Planck lensing measurements. We find that, once dynamical dark energy is considered, the degeneracy between $\sum m_\nu$ and $H_0$ will be changed, i.e., in the $\Lambda$CDM model, $\sum m_\nu$ is anti-correlated with $H_0$, but in the $w$CDM and HDE models, $\sum m_\nu$ becomes positively correlated with $H_0$. Compared to $\Lambda$CDM, in the $w$CDM model the limit on $\sum m_\nu$ becomes much looser, but in the HDE model the limit becomes much tighter. In the HDE model, we obtain $\sum m_\nu<0.113$ eV ($95\%$ CL) with the combined data sets, which is perhaps the most stringent upper limit by far on neutrino mass. Thus, our result in the HDE model is nearly ready to diagnose the neutrino mass hierarchy with the current cosmological observations.

Exploring the evolution of color-luminosity parameterβand its effects on parameter estimation

It has been found in previous studies that, for the Supernova Legacy Survey three-year (SNLS3) data, there is strong evidence for the redshift-evolution of color-luminosity parameter $\beta$. In this paper, using three simplest dark energy models ($\Lambda$CDM, $w$CDM, and CPL), we further explore the evolution of $\beta$ and its effects on parameter estimation. In addition to the SNLS3 data, we also take into account the Planck distance priors data, as well as the latest galaxy clustering (GC) data extracted from SDSS DR7 and BOSS. We find that, for all the models, adding a parameter of $\beta$ can reduce $\chi^2_{min}$ by $\sim$ 36, indicating that $\beta_1 = 0$ is ruled out at 6$\sigma$ confidence levels. In other words, $\beta$ deviates from a constant at 6$\sigma$ confidence levels. This conclusion is insensitive to the dark energy models considered, showing the importance of considering the evolution of $\beta$ in the cosmology-fits. Furthermore, it is found that varying $\beta$ can significantly change the fitting results of various cosmological parameters: using the SNLS3 data alone, varying $\beta$ yields a larger $\Omega_m$ for the $\Lambda$CDM model; using the SNLS3+CMB+GC data, varying $\beta$ yields a larger $\Omega_m$ and a smaller $h$ for all the models. Moreover, we find that these results are much closer to those given by the CMB+GC data, compared to the cases of treating $\beta$ as a constant. This indicates that considering the evolution of $\beta$ is very helpful for reducing the tension between supernova and other cosmological observations.

A one-parameter formula for testing slow-roll dark energy: observational prospects

Numerous upcoming observations, such as Wide-Field Infrared Survey Telescope, Baryon Oscillation Spectroscopic Survey (BOSS), BigBOSS, Large Synoptic Survey Telescope, Euclid and Planck, will constrain dark energy (DE)'s equation of state with great precision. They may well find that the ratio of pressure to energy density, w, is −1, meaning DE is equivalent to a cosmological constant. However, many time-varying DE models have also been proposed. A single parametrization to test a broad class of them and that is itself motivated by a physical picture is therefore desirable. We suggest that the simplest model of DE has the same mechanism as inflation, likely a scalar field slowly rolling down its potential. If this is so, DE will have a generic equation of state and the Universe will have a generic dependence of the Hubble constant on redshift, independent of the potential's starting value and shape. This equation of state and expression for the Hubble constant offer the desired model-independent but physically motivated parametrization, because they will hold for most of the standard scalar field models of DE such as quintessence and phantom DE. Up until now two-parameter descriptions of w have been available, but this work finds an additional approximation that leads to a single-parameter model. Using it, we conduct a χ2 analysis and find that experiments in the next seven years should be able to distinguish any of these time-varying DE models on the one hand from a cosmological constant on the other to 73 per cent confidence if w today differs from −1 by 3.5 per cent. In the limit of perfectly accurate measurements of Ωm and H0, this confidence would rise to 96 per cent. We also include discussion of the current status of DE experiments, a table compiling the techniques each will use and tables of the precisions of the experiments for which this information was available at the time of publication.

CFHTLenS: combined probe cosmological model comparison using 2D weak gravitational lensing

We present cosmological constraints from 2D weak gravitational lensing by the large-scale structure in the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) which spans 154 square degrees in five optical bands. Using accurate photometric redshifts and measured shapes for 4.2 million galaxies between redshifts of 0.2 and 1.3, we compute the 2D cosmic shear correlation function over angular scales ranging between 0.8 and 350 arcmin. Using non-linear models of the dark-matter power spectrum, we constrain cosmological parameters by exploring the parameter space with Population Monte Carlo sampling. The best constraints from lensing alone are obtained for the small-scale density-fluctuations amplitude sigma_8 scaled with the total matter density Omega_m. For a flat LambdaCDM model we obtain sigma_8(Omega_m/0.27)^0.6 = 0.79+-0.03. We combine the CFHTLenS data with WMAP7, BOSS and an HST distance-ladder prior on the Hubble constant to get joint constraints. For a flat LambdaCDM model, we find Omega_m = 0.283+-0.010 and sigma_8 = 0.813+-0.014. In the case of a curved wCDM universe, we obtain Omega_m = 0.27+-0.03, sigma_8 = 0.83+-0.04, w_0 = -1.10+-0.15 and Omega_K = 0.006+0.006-0.004. We calculate the Bayesian evidence to compare flat and curved LambdaCDM and dark-energy CDM models. From the combination of all four probes, we find models with curvature to be at moderately disfavoured with respect to the flat case. A simple dark-energy model is indistinguishable from LambdaCDM. Our results therefore do not necessitate any deviations from the standard cosmological model.

Inhomogeneous vacuum energy

Vacuum energy remains the simplest model of dark energy which could drive the accelerated expansion of the Universe without necessarily introducing any new degrees of freedom. Inhomogeneous vacuum energy is necessarily interacting in general relativity. Although the 4-velocity of vacuum energy is undefined, an interacting vacuum has an energy transfer and the vacuum energy defines a particular foliation of spacetime. In particular we will discuss cosmological solutions where the background vacuum energy is spatially homogeneous. It is possible to give a consistent description of vacuum dynamics and in particular the relativistic equations of motion for spatially inhomogeneous perturbations given a covariant prescription for the vacuum energy, or equivalently the energy transfer 4-vector, and we construct gauge-invariant vacuum perturbations. We show that any dark energy cosmology can be decomposed into an interacting vacuum+matter cosmology whose inhomogeneous perturbations obey simple first-order equations.

DARK ENERGY, WITH SIGNATURES

We propose a class of simple dark energy models which predict a late-time dark radiation component and a distinctive time-dependent equation of state w(z) for redshift z &lt; 3. The dark energy field can be coupled strongly enough to standard model particles to be detected in colliders, and the model requires only modest additional particle content and little or no fine-tuning other than a new energy scale of order milli-electron volts.

Bayesian model comparison in cosmology with Population Monte Carlo

We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence in favour of each model using Population Monte Carlo (PMC), a new adaptive sampling technique which was recently applied in a cosmological context. The Bayesian evidence is immediately available from the PMC sample used for parameter estimation without further computational effort, and it comes with an associated error evaluation. Besides, it provides an unbiased estimator of the evidence after any fixed number of iterations and it is naturally parallelizable, in contrast with MCMC and nested sampling methods. By comparison with analytical predictions for simulated data, we show that our results obtained with PMC are reliable and robust. The variability in the evidence evaluation and the stability for various cases are estimated both from simulations and from data. For the cases we consider, the log-evidence is calculated with a precision of better than 0.08. Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive evidence between flat LambdaCDM and simple dark-energy models. A curved Universe is moderately to strongly disfavoured with respect to a flat cosmology. Using physically well-motivated priors within the slow-roll approximation of inflation, we find a weak preference for a running spectral index. A Harrison-Zel'dovich spectrum is weakly disfavoured. With the current data, tensor modes are not detected; the large prior volume on the tensor-to-scalar ratio r results in moderate evidence in favour of r=0. [Abridged]

Roles of Dark Energy Perturbations in Dynamical Dark Energy Models: Can We Ignore Them?

We show the importance of properly including the perturbations of the dark energy component in the dynamical dark energy models based on a scalar field and modified gravity theories in order to meet with present and future observational precisions. Based on a simple scaling scalar field dark energy model, we show that observationally distinguishable substantial differences appear by ignoring the dark energy perturbation. By ignoring it the perturbed system of equations becomes inconsistent and deviations in (gauge-invariant) power spectra depend on the gauge choice.

Majorana neutrino superfluidity and stability of neutrino dark energy

We demonstrate that Majorana neutrinos can form Cooper pairs due to long-range attractive forces and show BCS superfluidity in a class of mass varying neutrino dark energy models. We describe the condensates for Majorana neutrinos and estimate the value of the gap, critical temperature and Pippard coherence length for a simple neutrino dark energy model. In the strong coupling regime bosonic degree of freedom can become important and Bose-Einstein condensate may govern the dynamics for the mass varying neutrino models. Formation of the condensates can significantly alter the instability scenario in the mass varying neutrino models.

Friedmann Cosmology with Bulk Viscosity: A Concrete Model for Dark Energy

The universe content is considered as a non-perfect fluid with bulk viscosity and can be described by a general equation of state (endowed some deviation from the conventionally assumed cosmic perfect fluid model). An explicitly bulk viscosity dark energy model is proposed to confront consistently with the current observational data sets by statistical analysis and is shown consistent with (not deviated away much from) the concordant Λ Cold Dark Matter (CDM) model by comparing the decelerating parameter. Also we compare our relatively simple viscosity dark energy model with a more complicated one by contrast with the concordant Λ CDM model and find our model improves for the viscosity dark energy model building. Finally we discuss the perspectives of dark energy probes for the coming years with observations.

Dark radiation as a signature of dark energy

We propose a simple dark energy model with the following properties: the model predicts a late-time dark radiation component that is not ruled out by current observational data, but which produces a distinctive time-dependent equation of state w(z) for z < 3. The dark energy field can be coupled strongly enough to Standard Model particles to be detected in colliders, and the model requires only modest additional particle content and little or no fine-tuning other than a new energy scale of order milli-electron volts.

The Hubble constant and dark energy from cosmological distance measures

We study how the determination of the Hubble constant from cosmological distancemeasures is affected by models of dark energy and vice versa. For this purpose, constraintson the Hubble constant and dark energy are investigated using the cosmologicalobservations of cosmic microwave background, baryon acoustic oscillations and type Iasupernovae. When one investigates dark energy, the Hubble constant is often a nuisanceparameter; thus it is usually marginalized over. On the other hand, when one focuses onthe Hubble constant, simple dark energy models such as a cosmological constant and aconstant equation of state are usually assumed. Since we do not know the nature ofdark energy yet, it is interesting to investigate the Hubble constant assumingsome types of dark energy and see to what extent the constraint on the Hubbleconstant is affected by the assumption concerning dark energy. We show thatthe constraint on the Hubble constant is not affected much by the assumptionfor dark energy. We furthermore show that this holds true even if we removethe assumption that the universe is flat. We also discuss how the prior on theHubble constant affects the constraints on dark energy and/or the curvature of theuniverse.

Constraining dark energy evolution with gravitational lensing by large scale structures

We study the sensitivity of weak lensing by large scale structures as a probe of the evolution of dark energy. We explore a two-parameters model of dark energy evolution, inspired by tracking quintessence models. To this end, we compute the likelihood of a few fiducial models with varying and nonvarying equation of states. For the different models, we investigate the dark energy parameter degeneracies with the mass power spectrum shape $\ensuremath{\Gamma}$, normalization ${\ensuremath{\sigma}}_{8}$, and with the matter mean density ${\ensuremath{\Omega}}_{M}$. We find that degeneracies are such that weak lensing turns out to be a good probe of dark energy evolution, even with limited knowledge on $\ensuremath{\Gamma}$, ${\ensuremath{\sigma}}_{8}$, and ${\ensuremath{\Omega}}_{M}$. This result is a strong motivation for performing large scale structure simulations beyond the simple constant dark energy models, in order to calibrate the nonlinear regime accurately. Such calibration could then be used for any large scale structure tests of dark energy evolution. Prospective for the Canada France Hawaii Telescope Legacy Survey and Super-Novae Acceleration Probe are given. These results complement nicely the cosmic microwave background and supernovae constraints.

Observational bounds on cosmic doomsday

Recently it was found, in abroad class of models, that the dark energy density may change its signduring the evolution of the universe. This may lead to a global collapseof the universe within the time tc ~ 1010–1011 years. Ourgoal is to find what bounds on the future lifetime of the universe can beplaced by the next generation of cosmological observations. As an example,we investigate the simplest model of dark energy with a linear potentialV(ϕ) = V0(1 + αϕ). This model can describe the present stageof acceleration of the universe if α is small enough. However,eventually the field ϕ rolls down, V(ϕ) becomes negative, andthe universe collapses. The existing observational data indicate that theuniverse described by this model will collapse not earlier than tc ≳ 10 billion years from the present moment. We show thatthe data from SNAP and Planck satellites may extend the bound on the `doomsday' time to tc ≳ 40 billion years at the 95% confidence level.