Cosmic Microwave Background Shift Parameter Research Articles

Bayesian analysis of f(T) gravity using fσ8 data

We use observational data from Supernovae (SNIa) Pantheon sample, from direct Hubble constant measurements with cosmic chronometers (CC), from the Cosmic Microwave Background shift parameter $\text{CMB}_{\text{shift}}$, and from redshift space distortion ($f\sigma_8$) measurements, in order to constrain $f(T)$ gravity. We do not follow the common $\gamma$ parameterization within the semi-analytical approximation of the growth rate, in order to avoid model-dependent uncertainties. Up to our knowledge this is the first time that $f(T)$ gravity is analyzed within a Bayesian framework, and with background and perturbation behaviour considered jointly. We show that all three examined $f(T)$ models are able to describe adequately the $f\sigma_8$ data. Furthermore, applying the Akaike, Bayesian and Deviance Information Criteria, we conclude that all considered models are statistically equivalent, however the most efficient candidate is the exponential model, which additionally presents a small deviation from $\Lambda$CDM paradigm.

Updated constraints on f(T) models using direct and indirect measurements of the Hubble parameter

We extract observational constraints on f(T) gravity, using the recently proposed statistical method which is not affected by the value of H0 and thus it bypasses the problem of the disagreement in its exact numerical value between Planck and direct measurements. We use direct measurements of the Hubble parameter with the corresponding covariance matrix, and for completeness we perform a joint analysis using the latest data from Supernovae type Ia based on JLA sample, quasi-stellar objects, and Cosmic Microwave Background shift parameter from Planck. We analyze a large family of f(T) models, and we compare the fitting results with ΛCDM cosmology using the AIC statistical test. Utilizing only the Hubble parameter data we find that in the case of the power-law f(T) model a small but non-zero deviation from ΛCDM cosmology is slightly favored at 1-σ, nevertheless the corresponding AIC value shows a statistical equivalence with it. Finally, the join analysis reveals that all f(T) models are very efficient and in very good agreement with observations.

Reconstruction of interaction rate in holographic dark energy

The present work is based on the holographic dark energy model with Hubble horizon as the infrared cut-off. The interaction rate between dark energy and dark matter has been reconstructed for three different parameterizations of the deceleration parameter. Observational constraints on the model parameters have been obtained by maximum likelihood analysis using the observational Hubble parameter data (OHD), type Ia supernovab data (SNe), baryon acoustic oscillation data (BAO) and the distance prior of cosmic microwave background (CMB) namely the CMB shift parameter data (CMBShift). The interaction rate obtained in the present work remains always positive and increases with expansion. It is very similar to the result obtained by Sen and Pavon [1] where the interaction rate has been reconstructed for a parametrization of the dark energy equation of state. Tighter constraints on the interaction rate have been obtained in the present work as it is based on larger data sets. The nature of the dark energy equation of state parameter has also been studied for the present models. Though the reconstruction is done from different parametrizations, the overall nature of the interaction rate is very similar in all the cases. Different information criteria and the Bayesian evidence, which have been invoked in the context of model selection, show that the these models are at close proximity of each other.

Acceleration of the universe: a reconstruction of the effective equation of state

The present work is based upon a parametric reconstruction of the effective or total equation of state in a model for the universe with accelerated expansion. The constraints on the model parameters are obtained by maximum likelihood analysis using the supernova distance modulus data, observational Hubble data, baryon acoustic oscillation data and cosmic microwave background shift parameter data. For statistical comparison, the same analysis has also been carried out for the wCDM dark energy model. Different model selection criteria (Akaike information criterion (AIC)) and (Bayesian Information Criterion (BIC)) give the clear indication that the reconstructed model is well consistent with the wCDM model. Then both the models (w_{eff}(z) model and wCDM model) have also been presented through (q_0 ,j_0 ) parameter space. Tighter constraint on the present values of dark energy equation of state parameter (w_{DE}(z = 0)) and cosmological jerk (j_0) have been achieved for the reconstructed model.

How clustering dark energy affects matter perturbations

The rate of structure formation in the Universe is different in homogeneous and clustered dark energy models. The degree of dark energy clustering depends on the magnitude of its effective sound speed |$c^{2}_{\rm eff}$| and for |$c^{2}_{\rm eff}=0$| dark energy clusters in a similar fashion to dark matter while for |$c^{2}_{\rm eff}=1$| it stays (approximately) homogeneous. In this paper we consider two distinct equations of state for the dark energy component, wd = const and |$w_{\rm d}=w_0+w_1\left(\frac{z}{1+z}\right)$| with |$c^{2}_{\rm eff}$| as a free parameter and we try to constrain the dark energy effective sound speed using current available data including Type Ia supernovae, baryon acoustic oscillation, cosmic microwave background shift parameter (Planck and WMAP), Hubble parameter, big bang nucleosynthesis and the growth rate of structures fσ8(z). At first we derive the most general form of the equations governing dark matter and dark energy clustering under the assumption that |$c^{2}_{\rm eff}={\rm const}$|⁠. Finally, performing an overall likelihood analysis we find that the likelihood function peaks at |$c^{2}_{\rm eff}=0$|⁠; however, the dark energy sound speed is degenerate with respect to the cosmological parameters, namely Ωm and wd.

Observational constraint on the interacting dark energy models including the Sandage–Loeb test

Two types of interacting dark energy models are investigated using the type Ia supernova (SNIa), observational $H(z)$ data (OHD), cosmic microwave background (CMB) shift parameter and the secular Sandage-Loeb (SL) test. We find that the inclusion of SL test can obviously provide more stringent constraint on the parameters in both models. For the constant coupling model, the interaction term including the SL test is estimated at $\delta=-0.01 \pm 0.01 (1\sigma) \pm 0.02 (2\sigma)$, which has been improved to be only a half of original scale on corresponding errors. Comparing with the combination of SNIa and OHD, we find that the inclusion of SL test directly reduces the best-fit of interaction from 0.39 to 0.10, which indicates that the higher-redshift observation including the SL test is necessary to track the evolution of interaction. For the varying coupling model, we reconstruct the interaction $\delta (z)$, and find that the interaction is also negative similar as the constant coupling model. However, for high redshift, the interaction generally vanishes at infinity. The constraint result also shows that the $\Lambda$CDM model still behaves a good fit to the observational data, and the coincidence problem is still quite severe. However, the phantom-like dark energy with $w_X<-1$ is slightly favored over the $\Lambda$CDM model.

Decaying vacuum cosmology and its scalar field description

We discuss the cosmological consequences of an interacting model in the dark sector in which the Λ component evolves as a truncated power series of the Hubble parameter. We also discuss some of the thermodynamic features of this model. In order to constrain the free parameters of the model we carry out a joint statistical analysis involving observational data from current type Ia supernovae, recent estimates of the cosmic microwave background shift parameter and baryon acoustic oscillations measurements. Finally, we adopt a theoretical method to derive the coupled scalar field version for this non-equilibrium decaying vacuum accelerating cosmology.

On the equivalence of [formula omitted] and gravitationally induced particle production cosmologies

The correspondence between cosmological models powered by a decaying vacuum energy density and gravitationally induced particle production is investigated. Although being physically different in the physics behind them we show that both classes of cosmologies under certain conditions can exhibit the same dynamic and thermodynamic behavior. Our method is applied to obtain three specific models that may be described either as Λ(t)CDM or gravitationally induced particle creation. In the point of view of particle production models, such cosmologies can be interpreted as a kind of one-component unification of the dark sector. By using current type Ia supernovae data, recent estimates of the cosmic microwave background shift parameter and baryon acoustic oscillations measurements we also perform a statistical analysis to test the observational viability within the two equivalent classes of models and we obtain the best-fit of the free parameters. By adopting the Akaike information criterion we also determine the rank of the models considered here. Finally, the particle production cosmologies (and the associated decaying Λ(t)-models) are modeled in the framework of field theory by a phenomenological scalar field model.

Redshift drift reconstruction for some cosmological models from observations

Redshift drift is a tool to directly probe the expansion history of the universe. Based on the Friedmann-Robertson-Walker framework, we reconstruct the velocity drift and deceleration factor for several cosmological models using observational H(z) data from the differential ages of galaxies and baryon acoustic oscillation peaks, luminosity distance of Type Ia supernovae, cosmic microwave background shift parameter, and baryon acoustic oscillation distance parameter. They can, for the first time, provide an objective and quantifiable measure of the redshift drift. We find that reconstructed velocity drift with different peak values and corresponding redshifts can potentially provide a method to distinguish the quality of competing dark energy models at low redshifts. Better fitting between models and observational data indicate that current data are insufficient to distinguish the quality of these models. However, by comparing with the simulated velocity drift from Liske et al, we find that the Dvali-Gabadadze-Porrati model is inconsistent with the data at high redshift, which originally piqued the interest of researchers in the topic of redshift drift. Considering the deceleration factor, we are able to give a stable instantaneous estimation of a transition redshift of zt ∼ 0.7 from joint constraints, which incorporates a more complete set of values than the previous study that used a single data set.

Cosmological tests on Visser’s massive graviton dark matter cosmology

We present the constraints on the Massive Graviton Dark Matter scenario (MGCDM) using the cosmological observations, including type Ia supernovae (SNe Ia), Gamma Ray Bursts (GRB), Observational Hubble Parameter Data (OHD), Cosmic Microwave Background shift parameter, and the Radial Baryon Acoustic Oscillation. In order to compare the goodness of the data samples and their combinations, we adopt the Fisher matrix analysis and the figure of merit (FoM) diagnostic. Based on the constraint results, we further discuss the cosmic age problem in MGCDM. The calculation shows that the universe in MGCDM frame is older than that in standard ΛCDM model, but the cosmic age crisis is still unresolved with just an alleviation.

THE ΛCDM GROWTH RATE OF STRUCTURE REVISITED

We re-examine the growth index of the concordance Λ cosmology in the light of the latest 6dF and WiggleZ data. In particular, we investigate five different models for the growth index γ, by comparing their cosmological evolution using observational data of the growth rate of structure formation at different redshifts. Performing a joint likelihood analysis of the recent supernovae type Ia data, the Cosmic Microwave Background shift parameter, Baryonic Acoustic Oscillations and the growth rate data, we determine the free parameters of the γ(z) parametrizations and we statistically quantify their ability to represent the observations. We find that the addition of the 6dF and WiggleZ growth data in the likelihood analysis improves significantly the statistical results. As an example, considering a constant growth index we find Ωm0 = 0.273 ± 0.011 and [Formula: see text].

Scalar field description for parametric models of dark energy

We investigate theoretical and observational aspects of a time-dependent parameterization for the dark energy equation of state (EoS) $w(z)$, which is a well behaved function of the redshift $z$ over the entire cosmological evolution, i.e., $z \in [-1,\infty)$. By using a theoretical algorithm of constructing the quintessence potential directly from the effective EoS parameter, we derive and discuss the general features of the resulting potential for this $w(z)$ function. Since the parameterization here discussed allows us to divide the parametric plane in defined regions associated to distinct classes of dark energy models, we use the most recent observations from type Ia supernovae, baryon acoustic oscillation peak and Cosmic Microwave Background shift parameter to check which class is observationally prefered. We show that the largest portion of the confidence contours lies into the region corresponding to a possible crossing of the so-called phanton divide line at some point of the cosmic evolution.

Cosmological tests of sudden future singularities

We discuss combined constraints, coming from the cosmic microwave background shift parameter $\mathcal{R}$, baryon acoustic oscillations (BAO) distance parameter $\mathcal{A}$, and from the latest type Ia supernovae data, imposed on cosmological models which allow sudden future singularities of pressure. We show that due to their weakness such sudden singularities may happen in the very near future and that at present they can mimic standard dark energy models.

Einstein-aether theory as an alternative to dark energy model?

In the generalized Einstein-aether theories by taking a special form of the Lagrangian density of aether field, the possibility of Einstein-aether theory as an alternative to dark energy model is discussed in detail, that is, taking a special aether field as a dark energy candidate. We compute the joint statistic constraints on this special modelʼs parameters by using the recent type Ia supernovae (SNe Ia) data, the Cosmic Microwave Background (CMB) shift parameter data, and the Baryonic Acoustic Oscillations (BAOs) data traced by the Sloan Digital Sky Survey (SDSS). Furthermore, we analyze other constrains from the Observational Hubble parameter Data (OHD). The comparison with the standard cosmological model (cosmological constant Λ Cold Dark Matter (ΛCDM) model) is clearly shown with new features; also we comment on an interesting relation between the coupling constant M in this model and the possible existence of a special accelerating scale in the MOdified Newtonian Dynamics (MOND) model initially given by Milgrom with the hope for interpreting the galaxy rotation curves without introducing mysterious dark matter.

A Specific Case of Generalized Einstein-aether Theories

With the dark energy phenomena explored over a decade, in this present work we discuss a specific case of the generalized Einstein-aether theories, in which the modified Friedmann equation is similar to that in the Dvali—Gabadadze—Porrati (DGP) brane world model. We compute the joint statistic constraints on model parameters in this specific case by using the recent type Ia supernovae (SNe Ia) data, the cosmic microwave background (CMB) shift parameter data, and the baryonic acoustic oscillations (BAOs) data traced by the Sloan Digital Sky Survey (SDSS). Furthermore, we analyze other constrains from the observational Hubble parameter data (OHD). The comparison with the standard cosmological model (cosmological constant Λ cold dark matter (ΛCDM) model) is clearly shown; also we comment on the interesting relation between the coupling constant M in this model and the special accelerate scale in the modified Newtonian dynamics (MOND) model initially given by Milgrom with the hope for interpreting the galaxy rotation curves without introducing mysterious dark matter.

Observational constraints on the normal branch of a warped DGP cosmology

We investigate observational constraints on the normal branch of the warped DGP braneworld cosmology by using observational data from Type Ia Supernovae (SNIa), baryon acoustic oscillations (BAO), cosmic microwave background (CMB) and baryon gas mass fraction of cluster of galaxies. The best fit values of model free parameters are: Ω m = 0.240 - 0.130 + 0.050 and Ω r c = 0.000 + 0.014 at 1 σ confidence interval by using gold sample SNIa + CMB shift parameter + BAO + gas mass fraction of baryons in cluster of galaxies. The results for essence sample SNIa combined with CMB shift parameter, BAO and baryon gas mass fraction correspond to: Ω m = 0.220 - 0.170 + 0.020 and Ω r c = 0.000 + 0.025 at 68.3% confidence interval. We determine the age of the universe by using these best fit values. We also study the effective cosmological dynamics on the brane via an effective equation of state parameter and the deceleration parameter to conclude that an effective phantom-like behavior arises in this scenario.

Lookback time as a test for f(R) gravity in the Palatini approach

We use the recently released data of lookback time (LT)-redshift relation, the cosmic microwave background shift parameter and the baryon acoustic oscillation measurements to constrain cosmological parameters of f(R) gravity in the Palatini formalism by considering the f(R) form of type (a) f(R) = R − β/Rn and (b) f(R) = R + αln R − β. Under the assumption of a Friedmann-Robertson-Walker universe, we achieved the best fitting results of the free parameters (Ωm0, n) for (a) and (Ωm0, α) for (b). We find that current LT data can provide interesting and effective constraints on gravity models. Compared with other data, the LT constraints favor a smaller value of the non-relativistic matter energy density.

Hubble expansion and structure formation in the ``running FLRW model'' of the cosmic evolution

A new class of Friedmann-Lemaître-Robertson-Walker (FLRW)cosmological models with time-evolving fundamental parameters shouldemerge naturally from a description of the expansion of the universebased on the first principles of quantum field theory and stringtheory. Within this general paradigm, one expects that both thegravitational Newton's coupling G and the cosmological term Λshould not be strictly constant but appear rather as smoothfunctions of the Hubble rate H(t).This scenario (``running FLRW model'') predicts, in a natural way,the existence of dynamical dark energy without invoking theparticipation of extraneous scalar fields.In this paper, we perform a detailed study of some of these modelsin the light of the latest cosmological data, which serves toillustrate the phenomenological viability of the new dark energyparadigm as a serious alternative to the traditional scalar fieldapproaches. By performing a joint likelihood analysis of the recentsupernovae type Ia data (SNIa), the Cosmic Microwave Background(CMB) shift parameter, and the Baryonic Acoustic Oscillations (BAOs)traced by the Sloan Digital Sky Survey (SDSS), we put tightconstraints on the main cosmological parameters. Furthermore, wederive the theoretically predicted dark-matter halo mass functionand the corresponding redshift distribution of cluster-size halosfor the ``running'' models studied. Despite the fact that thesemodels closely reproduce the standard ΛCDM Hubble expansion,their normalization of the perturbation's power-spectrum varies,imposing, in many cases, a significantly different cluster-sizehalo redshift distribution. This fact indicates that it should berelatively easy to distinguish between the ``running'' models andthe ΛCDM using realistic future X-ray and Sunyaev-Zeldovichcluster surveys.

Analysis of recent type Ia supernova data based on evolving dark energy models

We study characters of recent type Ia supernova (SNIa) data using evolving dark energy models with changing equation of state parameter w. We consider sudden-jump approximation of w for some chosen redshift spans with double transitions, and constrain these models based on Markov Chain Monte Carlo (MCMC) method using the SNIa data (Constitution, Union, Union2) together with baryon acoustic oscillation A parameter and cosmic microwave background shift parameter in a flat background. In the double-transition model the Constitution data shows deviation outside 1 sigma from LCDM model at low (z < 0.2) and middle (0.2 < z < 0.4) redshift bins whereas no such deviations are noticeable in the Union and Union2 data. By analyzing the Union members in the Constitution set, however, we show that the same difference is actually due to different calibration of the same Union sample in the Constitution set, and is not due to new data added in the Constitution set. All detected deviations are within 2 sigma from the LCDM world model. From the LCDM mock data analysis, we quantify biases in the dark energy equation of state parameters induced by insufficient data with inhomogeneous distribution of data points in the redshift space and distance modulus errors. We demonstrate that location of peak in the distribution of arithmetic means (computed from the MCMC chain for each mock data) behaves as an unbiased estimator for the average bias, which is valid even for non-symmetric likelihood distributions.

Constraints of f(R) gravity in Palatini approach with observational Hubble data

We use the newly released observational H(z) data (OHD), the Cosmic Microwave Background (CMB) shift parameter, and the Baryon Acoustic Oscillation (BAO) measurements data to constrain cosmological parameters of f(R) gravity in Palatini formalism in which the f(R) form is defined as f(R) = R − β/Rn. Under the assumption of a spatially flat FRW universe, we get the best fitting results of the free parameters (Ωm0, n). In the calculation, we marginalize the likelihood function over H0 by integrating the probability density \(P \propto e^{{{ - \chi ^2 } \mathord{\left/ {\vphantom {{ - \chi ^2 } 2}} \right. \kern-\nulldelimiterspace} 2}} \) to obtain the best fitting results and the confidence regions in the Ωm0-n plane. The constraints results of (Ωm0, n) = (0.33, 0.41) by OHD only and (Ωm0, n) = (0.23, 0.08) by the combination of OHD+CMB+BAO both indicate that the universe goes through three last phases, i.e., radiation dominated, matter-dominated, and late time accelerated expansion without introduction of dark energy.