Scalar Field Dark Energy Model Via Observational Constraints

In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text]. The model shows a flipping nature and redshift transition occurs at [Formula: see text], and the present value of decelerated parameter is computed to be [Formula: see text] for the combined dataset. We have explored characteristics like the universe’s age, particle horizon, deceleration parameter, and jerk parameter. The dynamical properties, such as energy density [Formula: see text], scalar field pressure [Formula: see text], and equation of state parameter [Formula: see text], are analyzed and presented. We have also described the behavior of the scalar potential [Formula: see text] and scalar field. Furthermore, the authors also described the behavior of energy conditions in scalar-tensor cosmology. The scenario of the present accelerated expansion of the universe is described by the contribution of the scalar field.

In this paper, we investigate the scalar field dark energy (DE) models within the context of [Formula: see text] gravity. Scalar field models are known for their dynamic nature. Parameters in the dynamical equation of state are responsible for the acceleration of the cosmos in recent epochs. We determined that the power-law cosmology fits the OHD and Pantheon data nicely. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo (MCMC) method, we examine the three sets of the model parameters [Formula: see text] [Formula: see text] obtained by 57 points of the [Formula: see text] data, [Formula: see text] [Formula: see text] 1048 points of the Pantheon data and [Formula: see text] [Formula: see text] by using joint data ([Formula: see text]), respectively. We solved the modified Einstein’s field equations by taking the bulk-viscosity component [Formula: see text]. We also establish a correspondence between the [Formula: see text] gravity model and scalar field DE models such as quintessence, [Formula: see text]-essence, and DBI-essence. The nature of scalar fields and their corresponding potentials are being graphically analyzed. To check the validity of [Formula: see text] gravity model, we also analyze the behavior of energy conditions.

In this paper, we have established a scalar field dark energy model in the flat FLRW universe, with the aim of studying the evolution of cosmic acceleration. A parameterization of the deceleration parameter [Formula: see text] is considered. We derive constraints on cosmological parameters by applying sophisticated Markov Chain Monte Carlo (MCMC) methods through the combination of various cosmological datasets such as Baryon Acoustic Oscillation (BAO) data points, Cosmic Chronometer (CC) measurements, and Standard Candle (SC) datasets from Pantheon Type Ia supernovae (SNe Ia), Quasars and gamma-ray bursts. This analysis allows us to determine a transition redshift, from the decelerated to the accelerated universe, with a value of [Formula: see text] and the current value of the deceleration parameter is [Formula: see text]. The dynamical behavior of quintessence is confirmed by the Equation of State (EoS) parameter, where [Formula: see text], indicating a subtle deviation from the cosmological constant. At lower redshifts [Formula: see text], our model shows strong agreement with the [Formula: see text]CDM model, while clear deviations are observed at higher redshifts [Formula: see text]. This study, through an analysis of cosmographic parameters such as energy density [Formula: see text], pressure [Formula: see text], and the scalar field EoS, emphasizes the potential of scalar field models as leading candidates for dark energy. Furthermore, we observe that the model yields a slightly higher value of the Hubble constant [Formula: see text] for certain dataset combinations, indicating that it may partially alleviate the Hubble tension.

The quest of deciphering the true nature of dark energy has proven to be one of the most exciting in recent times in cosmology. Various ideas have been put forward in this regard besides the usual cosmological constant approach, ranging from scalar field based models like Quintessence and Phantom dark energy to various modified gravity approaches as well. A very interesting idea then is to consider scalar field dark energy models in quantum gravitationally corrected cosmologies with the RS-II Braneworld being one of the most well known in this regard. So in this work, we consider RS-II Braneworld based scalar field dark energy models and try to look out for the existence of finite time singularities in these regimes both through a dynamical system perspective, for which we employ the Goriely–Hyde singularity analysis method, and a physical perspective. Our approach is general in the sense that it is not limited to any particular class of potentials or for any constrained parameter region for the brane tension and is valid for both Quintessence and phantom dark energy regimes. We firstly show through Goriely–Hyde procedure that finite time singularities can exist in these models for a limited set of initial conditions and that this result would hold irrespective of any consideration given to the swampland dS conjecture. We then discuss the physical nature of the singularities that can occur in this regime, where we use a well motivated ansatz for the Hubble parameter and show that these models of dark energy can allow for weak singularities like those of Type III and Type IV and can also allow for strong singularities like the Big Rip (Type I).

We investigate the prospect of constraining scalar field dark energy models\nusing HI 21-cm intensity mapping surveys. We consider a wide class of coupled\nscalar field dark energy models whose predictions about the background\ncosmological evolution are different from the $\\Lambda$CDM predictions by a few\npercent. We find that these models can be statistically distinguished from\n$\\Lambda$CDM through their imprint on the 21-cm angular power spectrum. At the\nfiducial $z= 1.5$, corresponding to a radio interferometric observation of the\npost-reionization HI 21 cm observation at frequency $568 \\rm MHz$, these models\ncan infact be distinguished from the $\\Lambda$CDM model at $ {\\rm SNR }> 3\n\\sigma$ level using a 10,000 hr radio observation distributed over 40 pointings\nof a SKA1-mid like radio-telescope. We also show that tracker models are more\nlikely to be ruled out in comparison with $\\Lambda$CDM than the thawer models.\nFuture radio observations can be instrumental in obtaining tighter constraints\non the parameter space of dark energy models and supplement the bounds obtained\nfrom background studies.\n

Most dark energy models have the varLambda CDM as their limit, and if future observations constrain our universe to be close to varLambda CDM Bayesian arguments about the evidence and the fine-tuning will have to be employed to discriminate between the models. Assuming a baseline varLambda CDM model we investigate a number of quintessence and phantom dark energy models, and we study how they would perform when compared to observational data, such as the expansion rate, the angular distance, and the growth rate measurements, from the upcoming Dark Energy Spectroscopic Instrument (DESI) survey. We sample posterior likelihood surfaces of these dark energy models with Monte Carlo Markov Chains while using central values consistent with the Planck varLambda CDM universe and covariance matrices estimated with Fisher information matrix techniques. We find that for this setup the Bayes factor provides a substantial evidence in favor of the varLambda CDM model over most of the alternatives. We also investigated how well the CPL parametrization approximates various scalar field dark energy models, and identified the location for each dark energy model in the CPL parameter space.

The persistent Hubble tension—marked by a notable disparity between early- and late-universe determinations of the Hubble constant H0—poses a serious challenge to the standard cosmological framework. Closely linked to this is the H0−rd tension, which stems from the fact that BAO-based estimates of H0 are intrinsically dependent on the assumed value of the sound horizon at the drag epoch, rd. In this study, we construct a scalar field dark energy model within the framework of a spatially flat Friedmann–Lemaitre–Robertson–Walker model to explore the dynamics of cosmic acceleration. To solve the field equations, we introduce a generalized extension of the standard Lambda Cold Dark Matter model that allows for deviations in the expansion history. Employing advanced Markov Chain Monte Carlo techniques, we constrain the model parameters using a comprehensive combination of observational data, including Baryon Acoustic Oscillations, Cosmic Chronometers, and Standard Candle datasets from Pantheon, Quasars, and Gamma-Ray Bursts (GRBs). Our analysis reveals a transition redshift from deceleration to acceleration at ztr=0.69 and a present-day deceleration parameter value of q0=−0.64. The model supports a dynamical scalar field interpretation, with an equation of state parameter satisfying −1<ω0ϕ<0, consistent with quintessence behavior, and signaling a deviation from the Λ. While the model aligns closely with the Lambda Cold Dark Matter scenario at lower redshifts (z≲0.65), notable departures emerge at higher redshifts (z≳0.65), offering a potential window into modified early-time cosmology. Furthermore, the evolution of key cosmographic quantities such as energy density ρϕ, pressure pϕ, and the scalar field equation of state highlights the robustness of scalar field frameworks in describing dark energy phenomenology. Importantly, our results indicate a slightly higher value of the Hubble constant H0 for specific data combinations, suggesting that the model may provide a partial resolution of the current H0 tension.

We studied the following scalar field ϕCDM models: ten quintessence models and seven phantom models. We reconstructed these models using the phenomenological method developed by our group. For each potential, the following ranges were found: (i) model parameters; (ii) EoS parameters; and (iii) the initial conditions for differential equations, which describe the dynamics of the universe. Using MCMC analysis, we obtained the constraints of scalar field models by comparing observations for the expansion rate of the universe, the angular diameter distance and the growth rate function, with corresponding data generated for the fiducial ΛCDM model. We applied Bayes statistical criteria to compare scalar field models. To this end, we calculated the Bayes factor, as well as the AIC and BIC information criteria. The results of this analysis show that we could not uniquely identify the preferable scalar field ϕCDM models compared to the fiducial ΛCDM model based on the predicted DESI data, and that the ΛCDM model is a true dark energy model. We investigated scalar field ϕCDM models in the w0–wa phase spaces of the CPL-ΛCDM contours. We identified subclasses of quintessence and phantom scalar field models that, in the present epoch: (i) can be distinguished from the ΛCDM model; (ii) cannot be distinguished from the ΛCDM model; and (iii) can be either distinguished or undistinguished from the ΛCDM model. We found that all the studied models can be divided into two classes: models that have attractor solutions and models whose evolution depends on initial conditions.

Quintessence or phantom: Study of scalar field dark energy models through a general parametrization of the Hubble parameter

We present an investigation of a scalar field dark energy model in the context of the FLRW universe, focusing on the parameterization of the deceleration parameter q(z) to study the evolution of cosmic acceleration. By employing extensive observational datasets—including 30 independent cosmic chronometer measurements, 17 additional baryon acoustic oscillation data points, and standard candle datasets from Pantheon Type Ia supernovae, Quasars, and Gamma-Ray Bursts—we provide constraints on cosmological parameters using advanced Markov chain Monte Carlo methods. Our analysis identifies a transition redshift of zt=0.62, marking the shift from decelerated to accelerated expansion, with a current deceleration parameter of q0=-0.59. The equation of state parameter confirms the dynamical behavior of quintessence, deviating slightly from a cosmological constant. Furthermore, the model demonstrates strong consistency with ΛCDM at lower redshifts while revealing distinct deviations at higher redshifts, which provides valuable insights into the late-time dynamics of the universe. By examining the evolution of cosmography parameters, energy density, pressure, and the scalar field equation of state, this study contributes the relevance of scalar field models as promising candidates for dark energy.

\n We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, K-essence, and general non-canonical scalar field models, change the dynamical variables from variables $$(x, y, \\lambda )$$ to observable related variables $$(w_{\\phi }, \\Omega _{\\phi }, \\lambda )$$, and show the intimate relationships between those scalar fields that the three-dimensional system of K-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and K-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in $$(w_{\\phi }, \\Omega _{\\phi }, \\lambda )$$ instead of variables $$(x, y, \\lambda )$$ and to investigate the dynamical system in three dimensions instead of two dimensions. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter.\n

This paper is devoted to study the scalar field dark energy models by taking its different aspects in the framework off(R,∇R)gravity. We consider flat FRW universe to construct the equation of state parameter governed byf(R,∇R)gravity. The stability of the model is discussed with the help of squared speed of sound parameter. It is found that models show quintessence behavior of the universe in stable as well as unstable modes. We also develop the correspondence off(R,∇R)model with some scalar field dark energy models like quintessence, tachyonic field,k-essence, dilaton, hessence, and DBI-essence. The nature of scalar fields and corresponding scalar potentials is being analyzed inf(R,∇R)gravity graphically which show consistency with the present day observations about accelerated phenomenon.

Dark energy and dark matter, two subjects of basic physics, have received a lot of attention in the 21st century. From the observational point of view, the interaction between dark energy and dark matter can significantly affect cosmological distances. This gives rise to the possibility of indirectly detecting such interaction through high-redshift cosmological probes. Theoretically, the introduction of interaction between dark energy and dark matter can assist in alleviating the coincidence problem of the standard cosmological model ($\Lambda$CDM model). Furthermore, this can provide a new method of studying the properties of dark matter particles. In this paper, based on the latest observations of multiple measurements of quasars (X-ray+UV quasars acting as standard candles, compact radio quasars acting as standard rulers) covering the redshift range of $0.04~<~z~<~5.1$ and baryonic acoustic oscillation between ($0.38~<~z~<~2.34$), we investigate the observational constraints on a variety of interacting dark energy models ($\gamma_d~$IDE model, $\gamma_m~$IDE model) and other cosmological models ($\Lambda$CDM model, XCDM model). The results provide us with a quantitative analysis of the possible interaction between dark energy and dark matter, as well as the possible range of the mass of dark matter particles. The joint analysis shows that: (1) Multiple measurements of quasars can provide more stringent constraints on the interacting dark energy models, which can further strengthen the potential of quasars acting as effective cosmological standard probes at higher redshifts; (2) In the framework of both $\gamma_m$IDE model and $\gamma_d$IDE model, the quasar data supports possible conversion of dark energy into dark matter at high redshift, which alleviates the coincidence problem to some extent. We also found that the interaction term is of a small value, which demonstrates the negligible interaction between dark matter and dark energy; (3) In the framework of $\Lambda$CDM model, which has shown the best consistency with quasar data, the density parameter of matter in the Universe is constrained at $\Omega_~m=0.317^{+0.007}_{-0.007}$, with the best-fit Hubble constant $H_0=68.177^{+0.497}_{-0.505}$ at 68.3% confidence level. These findings are consistent with the recent microwave background radiation (CMB) measurements from the Planck satellite; (4) If dark matter in the Universe exists in the form of scalar-field dark matter with $Z_2$ symmetry, we obtain the range of the mass of dark matter particles as $56~{\rm~GeV}\lesssim~m_S\lesssim~63~{\rm~GeV}$ or $m_S\gtrsim450~{\rm~GeV}$, based on the dark energy-dark matter coupling term from multiple measurements of quasars. Such conclusions agree well with the latest experimental results aimed at the direct detection of dark matter particles.

Likelihood analyses of the COBE-DMR sky maps are used to determine the normalization of the inverse-power-law-potential scalar field dark energy model. Predictions of the DMR-normalized model are compared to various observations to constrain the allowed range of model parameters. Although the derived constraints are restrictive, evolving dark energy density scalar field models remain an observationally-viable alternative to the constant cosmological constant model.

In modern cosmology, the curiosity of ultimately understanding the nature of the dark energy controlling the recent acceleration of the Universe motivates us to explore its properties by using some novel approaches. In this work, to explore the properties of dark energy we adopt the modified f(Q) gravity theory, where the non-metricity scalar Q, emerging from Weyl geometry, plays the dynamical role. For the function f(Q) we adopt the functional form f(Q)=Q+6γH02(Q/Q0)n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q)=Q+ 6\\gamma \\,H_0^2(Q/Q_0)^n$$\\end{document}, where n,γ,H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n,\\, \\gamma ,\\, H_0$$\\end{document} and Q0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_0$$\\end{document} are constants. Then, we test our constructed model against the various observational datasets, such as the Hubble, and the Pantheon+SHOES samples, and their combined sample, through the Markov Chain Monte Carlo (MCMC) statistical analysis. We also employ the parameter estimation technique to constrain the free parameters of the model. In addition, we use the constrained values of the model parameters to explore a few implications of the cosmological model. A detailed comparison of the predictions of our model with the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model is also performed. In particular, we discuss in detail some cosmographic parameters, like the deceleration, the jerk, and the snap parameters, as well as the behavior of the dark energy and matter energy densities to see the evolution of various energy/matter profiles. The Om diagnostics is also presented to test the dark energy nature of our model, as compared to the standard Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM paradigm. Our findings show that the considered version of the non-metric f(Q) type modified gravity theory, despite some differences with respect to the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM paradigm, can still explain the current observational results on the cosmological parameters, and provide a convincing and consistent account for the accelerating expansion of the Universe.