Dark Energy Equation Of State Research Articles

Constraints on parameterized dark energy properties from new observations with principal component analysis

For dark energy, the equation of state (EoS) is a critical parameter to depict its physical properties. In this paper, we mainly give constraints on the EoS of dark energy w with the latest observations of cosmic microwave background radiation (CMB) from Planck satellite, JLA Type Ia supernovae (SNIa) sample, baryon acoustic oscillation (BAO) and Hubble parameter measurements. We introduce a kind of parameterized dark energy model called “constant bin−w”, in which the whole redshift range is divided into several bins, and EoS w in each bin is assumed as an independent constant. The results show that EoS in all of the redshift bins are comparable with ΛCDM in the 2σ confidence regions, but some weak deviations from w=−1 are still indicated. In particular, in the framework of 7 bins, a slight oscillation behavior is shown in the redshift 0 < z < 0.75, especially around the range of 4th bin (0.25 < z < 0.35) and 5th bin (0.35 < z < 0.51). Additionally, we adopt the principal component analysis (PCA) method to do the model-independent analysis, which includes normal PCA and localized PCA methods. By implementing so called normal PCA method, the original oscillation behavior of EoS indicated in the framework of 7 bins becomes more significant after the best reconstruction, but such result still supports ΛCDM within the margin of 2σ errors. To further reduce the errors of constraints on EoS, and confirm such deviations from the cosmological constant scenario, we hope for more precise observational data in the future.

Structure formation simulations with momentum exchange: alleviating tensions between high-redshift and low-redshift cosmological probes

Persisting tensions between the cosmological constraints derived from low-redshift probes and the ones obtained from temperature and polarisation anisotropies of the Cosmic Microwave Background -- although not yet providing compelling evidence against the $\Lambda $CDM model -- seem to consistently indicate a slower growth of density perturbations as compared to the predictions of the standard cosmological scenario. Such behavior is not easily accommodated by the simplest extensions of General Relativity, such as f(R) models, which generically predict an enhanced growth rate. In the present work we present the outcomes of a suite of large N-body simulations carried out in the context of a cosmological model featuring a non-vanishing scattering cross section between the dark matter and the dark energy fields, for two different parameterisations of the dark energy equation of state. Our results indicate that these Dark Scattering models have very mild effects on many observables related to large-scale structures formation and evolution, while providing a significant suppression of the amplitude of linear density perturbations and the abundance of massive clusters. Our simulations therefore confirm that these models offer a promising route to alleviate existing tensions between low-redshift measurements and those of the CMB.

Aspects of late-time evolution in mimetic F(R) gravity

We demonstrate how to describe in an unified way early and late-time acceleration in the context of mimetic F(R) gravity. As we show, an exponential F(R) gravity model has appealing features, with regard to unification and we perform an analysis of the late-time evolution. The resulting picture is interesting since in the mimetic case, certain pathologies of some ordinary F(R) models are remedied in a consistent way, owing to the presence of the mimetic potential and the Lagrange multiplier. We quantify the late-time evolution analysis by studying the scaled dark energy density, the dark energy equation of state and the total effective equation of state, and as we show the late-time evolution is crucially affected by the functional form of the F(R) gravity. It is intriguing that the most appealing case corresponds to the exponential F(R) gravity which unifies late- and early-time acceleration. Finally, we study the behavior of the effective gravitational constant and the growth factor, and as we show, significant differences between the mimetic and ordinary F(R) exponential model are spotted in the growth factor.

Simultaneous constraints on cosmology and photometric redshift bias from weak lensing and galaxy clustering

Abstract We investigate the expected cosmological constraints from a combination of cosmic shear and large-scale galaxy clustering using realistic photometric redshift distributions. Introducing a systematic bias in the lensing distributions (of 0.05 in redshift) produces a &amp;gt;2σ bias in the recovered matter power spectrum amplitude and dark energy equation of state for preliminary Stage III surveys. We demonstrate that cosmological error can be largely removed by marginalizing over biases in the assumed weak-lensing redshift distributions. Furthermore, the cosmological constraining power is retained despite removing much of the information on the lensing redshift biases. This finding relies upon high-quality redshift estimates for the clustering sample, but does not require spectroscopy. All galaxies in this analysis can thus be assumed to come from a single photometric survey. We show that this internal constraint on redshift biases arises from complementary degeneracy directions between cosmic shear and the combination of galaxy clustering and shear–density cross-correlations. Finally we examine a case where the assumed redshift distributions differ from the truth by more than a simple uniform bias. We find that the effectiveness of this self-calibration method will depend on the survey details and the nature of the uncertainties on the estimated redshift distributions.

Cosmology with photometric weak lensing surveys: Constraints with redshift tomography of convergence peaks and moments

Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(\Omega_m,w,\sigma_8)$ for an LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the $1\sigma$ confidence interval in $(\Omega_m,w)$ space by a factor of 8 with respect to the case of the single highest redshift bin. We also find that adding non-Gaussian information from the peak counts and higher-order moments of the convergence field and its spatial derivatives further reduces the constrained area in $(\Omega_m,w)$ by a factor of 3 and 4, respectively. When we add cosmic microwave background parameter priors from Planck to our analysis, tomography improves power spectrum constraints by a factor of 3. Adding moments yields an improvement by an additional factor of 2, and adding both moments and peaks improves by almost a factor of 3, over power spectrum tomography alone. We evaluate the effect of uncorrected systematic photometric redshift errors on the parameter constraints. We find that different statistics lead to different bias directions in parameter space, suggesting the possibility of eliminating this bias via self-calibration.

Constraining neutrinos and dark energy with galaxy clustering in the dark energy survey

We determine the forecast errors on the absolute neutrino mass scale and the equation of state of dark energy by combining synthetic data from the Dark Energy Survey (DES) and the Cosmic Microwave Background (CMB) Planck surveyor. We use angular clustering of galaxies for DES in 7 redshift shells up to $z\sim 1.7$ including cross-correlations between different redshift shells. We study models with massless and massive neutrinos and three different dark energy models: $\Lambda$CDM ($w=-1$), wCDM (constant $w$), and waCDM (evolving equation of state parameter $w(a)=w_0 + w_{a}(1-a)$). We include the impact of uncertainties in modeling galaxy bias using a constant and a redshift-evolving bias model. For the $\Lambda$CDM model we obtain an upper limit for the sum of neutrino masses from DES+Planck of $\Sigma m_\nu < 0.08$ eV (95\% C.L.) for a fiducial mass of $\Sigma m_\nu = 0.047$ eV, with a 1$\sigma$ error of 0.02 eV, assuming perfect knowledge of galaxy bias. For the wCDM model the limit is $\Sigma m_\nu < 0.10 $ eV. For a wCDM model where galaxy bias evolves with redshift, the upper limit on the sum of neutrino masses increases to 0.19 eV. DES will be able to place competitive upper limits on the sum of neutrino masses of 0.1-0.2 eV and could therefore strongly constrain the inverted mass hierarchy of neutrinos. In a wCDM model the 1$\sigma$ error on constant $w$ is $\Delta w= 0.03$ from DES galaxy clustering and Planck. Allowing $\Sigma m_\nu$ as a free parameter increases the error on $w$ by a factor of 2, with $\Delta w=0.06$. In a waCDM model, in which the dark energy equation of state varies with time, the errors are $\Delta w_0 = 0.2$ and $\Delta w_a = 0.42$. Including neutrinos and redshift dependent galaxy bias increases the errors to $\Delta w_0 = 0.35$ and $\Delta w_a = 0.89$.

The H ii galaxy Hubble diagram strongly favoursRh=ctover ΛCDM

We continue to build support for the proposal to use HII galaxies (HIIGx) and giant extragalactic HII regions (GEHR) as standard candles to construct the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae. Using a sample of 25 high-redshift HIIGx, 107 local HIIGx, and 24 GEHR, we confirm that the correlation between the emission-line luminosity and ionized-gas velocity dispersion is a viable luminosity indicator, and use it to test and compare the standard model $\Lambda$CDM and the $R_{\rm h}=ct$ Universe by optimizing the parameters in each cosmology using a maximization of the likelihood function. For the flat $\Lambda$CDM model, the best fit is obtained with $\Omega_{\rm m}= 0.40_{-0.09}^{+0.09}$. However, statistical tools, such as the Akaike (AIC), Kullback (KIC) and Bayes (BIC) Information Criteria favor $R_{\rm h}=ct$ over the standard model with a likelihood of $\approx 94.8\%-98.8\%$ versus only $\approx 1.2\%-5.2\%$. For $w$CDM (the version of $\Lambda$CDM with a dark-energy equation of state $w_{\rm de}\equiv p_{\rm de}/\rho_{\rm de}$ rather than $w_{\rm de}=w_{\Lambda}=-1$), a statistically acceptable fit is realized with $\Omega_{\rm m}=0.22_{-0.14}^{+0.16}$ and $w_{\rm de}= -0.51_{-0.25}^{+0.15}$ which, however, are not fully consistent with their concordance values. In this case, $w$CDM has two more free parameters than $R_{\rm h}=ct$, and is penalized more heavily by these criteria. We find that $R_{\rm h}=ct$ is strongly favored over $w$CDM with a likelihood of $\approx 92.9\%-99.6\%$ versus only $0.4\%-7.1\%$. The current HIIGx sample is already large enough for the BIC to rule out $\Lambda$CDM/$w$CDM in favor of $R_{\rm h}=ct$ at a confidence level approaching $3\sigma$.

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to non-trivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling $G_{\rm eff}$ with matter density perturbations under a quasi-static approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing $G_{\rm eff}$. In fact, within the parameter space, $G_{\rm eff}$ can be even smaller than the Newton gravitational constant $G$ at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter $\eta$ and the evolution of growth rate $f\sigma_8$ are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the $\Lambda$CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

Constraining the dark energy equation of state with H ii galaxies

We use the HII galaxies $L - \sigma$ relation and the resulting Hubble expansion cosmological probe of a sample of just 25 high-$z$ (up to $z \sim 2.33$) HII galaxies, in a joint likelihood analysis with other well tested cosmological probes (CMB, BAOs) in an attempt to constrain the dark energy equation of state (EoS). The constraints, although still weak, are in excellent agreement with those of a similar joint analysis using the well established SNIa Hubble expansion probe. Interestingly, even with the current small number of available high redshift HII galaxies, the HII/BAO/CMB joint analysis gives a 13% improvement of the quintessence dark energy cosmological constraints compared to the BAO/CMB joint analysis. We have further performed extensive Monte Carlo simulations, with a realistic redshift sampling, to explore the extent to which the use of the $L - \sigma$ relation, observed in HII galaxies, can constrain effectively the parameter space of the dark energy EoS. The simulations predict substantial improvement in the constraints when increasing the sample of high-$z$ HII galaxies to 500, a goal that can be achieved in reasonable observing times with existing large telescopes and state-of-the-art instrumentation.

Modified Brans–Dicke cosmology with matter-scalar field interaction

We discuss the cosmological implications of an extended Brans–Dicke theory presented recently, in which there is an energy exchange between the scalar field and ordinary matter, determined by the theory. A new mass scale is generated in the theory which modifies the Friedmann equations with field-dependent corrected kinetic terms. In a radiation Universe the general solutions are found and there are branches with complete removal of the initial singularity, while at the same time a transient accelerating period can occur within deceleration. Entropy production is also possible in the early Universe. In the dust era, late-times acceleration has been found numerically in agreement with the correct behavior of the density parameters and the dark energy equation of state, while the gravitational constant has only a slight variation over a large redshift interval in agreement with observational bounds.

Cosmological and astrophysical constraints on tachyon dark energy models

Rolling tachyon field models are among the candidates suggested as explanations for the recent acceleration of the Universe. In these models the field is expected to interact with gauge fields and lead to variations of the fine-structure constant $\alpha$. Here we take advantage of recent observational progress and use a combination of background cosmological observations of Type Ia supernovas and astrophysical and local measurements of $\alpha$ to improve constraints on this class of models. We show that the constraints on $\alpha$ imply that the field dynamics must be extremely slow, leading to a constraint of the present-day dark energy equation of state $(1+w_0)<2.4\times10^{-7}$ at the $99.7\%$ confidence level. Therefore current and forthcoming standard background cosmology observational probes can't distinguish this class of models from a cosmological constant, while detections of $\alpha$ variations could possibly do so since they would have a characteristic redshift dependence.

Model-independent dark energy equation of state from unanchored baryon acoustic oscillations

Abstract Ratios of line of sight baryon acoustic oscillation (BAO) peaks at two redshifts only depend upon the average dark energy equation of states between those redshifts, as the dependence on anchors such as the BAO scale or the Hubble constant is canceled in a ratio. As a result, BAO ratios provide a probe of dark energy which is independent of both the cosmic distance ladder and the early evolution of universe. In this note, we use ratios to demonstrate that the known tension between the Lyman alpha forest BAO measurement and other probes arises entirely from recent ( 0.57 z 2.34 ) cosmological expansion. Using ratios of the line of sight Lyman alpha forest and BOSS CMASS BAO scales, we show that there is already more than 3 σ tension with the standard Λ CDM cosmological model which implies that either (i) The BOSS Lyman alpha forest measurement of the Hubble parameter was too low as a result of a statistical fluctuation or systematic error or else (ii) the dark energy equation of state falls steeply at high redshift.

Comparison of thawing and freezing dark energy parametrizations

Dark energy equation of state $w(z)$ parametrizations with two parameters and given monotonicity are generically either convex or concave functions. This makes them suitable for fitting either freezing or thawing quintessence models but not both simultaneously. Fitting a dataset based on a freezing model with an unsuitable (concave when increasing) $w(z)$ parametrization (like CPL) can lead to significant misleading features like crossing of the phantom divide line, incorrect $w(z=0)$, incorrect slope \etc that are not present in the underlying cosmological model. To demonstrate this fact we generate scattered cosmological data both at the level of $w(z)$ and the luminosity distance $D_L(z)$ based on either thawing or freezing quintessence models and fit them using parametrizations of convex and of concave type. We then compare statistically significant features of the best fit $w(z)$ with actual features of the underlying model. We thus verify that the use of unsuitable parametrizations can lead to misleading conclusions. In order to avoid these problems it is important to either use both convex and concave parametrizations and select the one with the best $\chi^2$ or use principal component analysis thus splitting the redshift range into independent bins. In the latter case however, significant information about the slope of $w(z)$ at high redshifts is lost. Finally, we propose a new family of parametrizations (nCPL) $w(z)=w_0+w_a (\frac{z}{1+z})^n$ which generalizes the CPL and interpolates between thawing and freezing parametrizations as the parameter $n$ increases to values larger than 1.

Is the effective field theory of dark energy effective?

The effective field theory of cosmic acceleration systematizes possible contributions to the action, accounting for both dark energy and modifications of gravity. Rather than making model dependent assumptions, it includes all terms, subject to the required symmetries, with four (seven) functions of time for the coefficients. These correspond respectively to the Horndeski and general beyond Horndeski class of theories. We address the question of whether this general systematization is actually effective, i.e. useful in revealing the nature of cosmic acceleration when compared with cosmological data. The answer is no and yes: there is no simple time dependence of the free functions—assumed forms in the literature are poor fits, but one can derive some general characteristics in early and late time limits. For example, we prove that the gravitational slip must restore to general relativity in the de Sitter limit of Horndeski theories, and why it doesn't more generally. We also clarify the relation between the tensor and scalar sectors, and its important relation to observations; in a real sense the expansion history H(z) or dark energy equation of state w(z) is 1/5 or less of the functional information! In addition we discuss the de Sitter, Horndeski, and decoupling limits of the theory utilizing Goldstone techniques.

Dodging the dark matter degeneracy while determining the dynamics of dark energy

One of the key issues in cosmology is to establish the nature of dark energy, and to determine whether the equation of state evolves with time. When estimating this from distance measurements there is a degeneracy with the matter density. We show that there exists a simple function of the dark energy equation of state and its first derivative which is independent of this degeneracy at all redshifts, and so is a much more robust determinant of the evolution of dark energy than just its derivative. We show that this function can be well determined at low redshift from supernovae using Gaussian Processes, and that this method is far superior to a variety of parameterisations which are also subject to priors on the matter density. This shows that parametrised models give very biased constraints on the evolution of dark energy.

A COMPREHENSIVE INVESTIGATION ON THE SLOWING DOWN OF COSMIC ACCELERATION

ABSTRACT Shafieloo et al. first proposed the possibility that the current cosmic acceleration (CA) is slowing down. However, this is rather counterintuitive because a slowing down CA cannot be accommodated in most mainstream cosmological models. In this work, by exploring the evolutionary trajectories of the dark energy equation of state w(z) and deceleration parameter q(z), we present a comprehensive investigation on the slowing down of CA from both the theoretical and the observational sides. For the theoretical side, we study the impact of different w(z) using six parametrization models, and then we discuss the effects of spatial curvature. For the observational side, we investigate the effects of different type Ia supernovae (SNe Ia), baryon acoustic oscillation (BAO), and cosmic microwave background (CMB) data. We find that (1) the evolution of CA is insensitive to the specific form of w ( z ) ; in contrast, a non-flat universe favors a slowing down CA more than a flat universe. (2) SNLS3 SNe Ia data sets favor a slowing down CA at a 1σ confidence level, while JLA SNe Ia samples prefer an eternal CA; in contrast, the effects of different BAO data are negligible. (3) Compared with CMB distance prior data, full CMB data favor a slowing down CA more. (4) Due to the low significance, the slowing down of CA is still a theoretical possibility that cannot be confirmed by the current observations.

Bi-scalar modified gravity and cosmology with conformal invariance

We investigate the cosmological applications of a bi-scalar modified gravity that exhibits partial conformal invariance, which could become full conformal invariance in the absence of the usual Einstein-Hilbert term and introducing additionally either the Weyl derivative or properly rescaled fields. Such a theory is constructed by considering the action of a non-minimally conformally-coupled scalar field, and adding a second scalar allowing for a nonminimal derivative coupling with the Einstein tensor and the energy-momentum tensor of the first field. At a cosmological framework we obtain an effective dark-energy sector constituted from both scalars. In the absence of an explicit matter sector we extract analytical solutions, which for some parameter regions correspond to an effective matter era and/or to an effective radiation era, thus the two scalars give rise to “mimetic dark matter” or to “dark radiation” respectively. In the case where an explicit matter sector is included we obtain a cosmological evolution in agreement with observations, that is a transition from matter to dark energy era, with the onset of cosmic acceleration. Furthermore, for particular parameter regions, the effective dark-energy equation of state can transit to the phantom regime at late times. These behaviors reveal the capabilities of the theory, since they arise purely from the novel, bi-scalar construction and the involved couplings between the two fields.

External priors for the next generation of CMB experiments

Planned cosmic microwave background (CMB) experiments will improve what we know about neutrino physics, inflation, and dark energy. The low level of noise, together with improved angular resolution, will increase the signal-to-noise ratio of the CMB polarized data as well as the reconstructed lensing potential of large scale structure. Projected constraints on cosmological parameters are tight, but these can be improved even further with information from external experiments. Here, we examine quantitatively the extent to which external priors can lead to improvement in projected constraints from a CMB-Stage IV (S4) experiment on neutrino and dark energy properties. We find that CMB S4 constraints on neutrino mass could be strongly enhanced by external constraints on the cold dark matter density ${\mathrm{\ensuremath{\Omega}}}_{c}{h}^{2}$ and the Hubble constant ${H}_{0}$. If polarization on the largest scales ($\ensuremath{\ell}&lt;50$) will not be measured, an external prior on the primordial amplitude ${A}_{s}$ or the optical depth $\ensuremath{\tau}$ will also be important. A CMB constraint on the number of relativistic degrees of freedom, ${N}_{\mathrm{eff}}$, will benefit from an external prior on the spectral index ${n}_{s}$ and the baryon energy density ${\mathrm{\ensuremath{\Omega}}}_{b}{h}^{2}$. Finally, an external prior on ${H}_{0}$ will help constrain the dark energy equation of state ($w$).

Redshift-space distortions in massive neutrino and evolving dark energy cosmologies

Large-scale structure surveys in the coming years will measure the redshift-space power spectrum to unprecedented accuracy, allowing for powerful new tests of the LambdaCDM picture as well as measurements of particle physics parameters such as the neutrino masses. We extend the Time-RG perturbative framework to redshift space, computing the power spectrum P_s(k,mu) in massive neutrino cosmologies with time-dependent dark energy equations of state w(z). Time-RG is uniquely capable of incorporating scale-dependent growth into the P_s(k,mu) computation, which is important for massive neutrinos as well as modified gravity models. Although changes to w(z) and the neutrino mass fraction both affect the late-time scale-dependence of the non-linear power spectrum, we find that the two effects depend differently on the line-of-sight angle mu. Finally, we use the HACC N-body code to quantify errors in the perturbative calculations. For a LambdaCDM model at redshift z=1, our procedure predicts the monopole~(quadrupole) to 1% accuracy up to a wave number 0.19h/Mpc (0.28h/Mpc), compared to 0.08h/Mpc (0.07h/Mpc) for the Kaiser approximation and 0.19h/Mpc (0.16h/Mpc) for the current state-of-the-art perturbation scheme. Our calculation agrees with the simulated redshift-space power spectrum even for neutrino masses above the current bound, and for rapidly-evolving dark energy equations of state, |dw/dz| ~ 1. Along with this article, we make our redshift-space Time-RG implementation publicly available as the code redTime.

Measuring the distance–redshift relation with the baryon acoustic oscillations of galaxy clusters

We analyse the largest spectroscopic samples of galaxy clusters to date, and provide observational constraints on the distance-redshift relation from baryon acoustic oscillations. The cluster samples considered in this work have been extracted from the Sloan Digital Sky Survey at three median redshifts, $z=0.2$, $z=0.3$, and $z=0.5$. The number of objects is $12910$, $42215$, and $11816$, respectively. We detect the peak of baryon acoustic oscillations for all the three samples. The derived distance constraints are: $r_s/D_V(z=0.2)=0.18 \pm 0.01$, $r_s/D_V(z=0.3)=0.124 \pm 0.004$ and $r_s/D_V(z=0.5)=0.080 \pm 0.002$. Combining these measurements, we obtain robust constraints on cosmological parameters. Our results are in agreement with the standard $\Lambda$ cold dark matter model. Specifically, we constrain the Hubble constant in a $\Lambda$CDM model, $H_0 = 64_{-9}^{+14} \, \mathrm{km} \, \mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, the density of curvature energy, in the $o\Lambda$CDM context, $\Omega_K = -0.015_{-0.36}^{+0.34}$, and finally the parameter of the dark energy equation of state in the $ow$CDM case, $w = -1.01_{-0.44}^{+0.44}$. This is the first time the distance-redshift relation has been constrained using only the peak of baryon acoustic oscillations of galaxy clusters.