Cosmological tests of the osculating Barthel–Kropina dark energy model

Abstract

We further investigate the dark energy model based on the Finsler geometry inspired osculating Barthel–Kropina cosmology. The Barthel–Kropina cosmological approach is based on the introduction of a Barthel connection in an osculating Finsler geometry, with the connection having the property that it is the Levi-Civita connection of a Riemannian metric. From the generalized Friedmann equations of the Barthel–Kropina model, obtained by assuming that the background Riemannian metric is of the Friedmann–Lemaitre–Robertson–Walker type, an effective geometric dark energy component can be generated, with the effective, geometric type pressure, satisfying a linear barotropic type equation of state. The cosmological tests, and comparisons with observational data of this dark energy model are considered in detail. To constrain the Barthel–Kropina model parameters, and the parameter of the equation of state, we use 57 Hubble data points, and the Pantheon Supernovae Type Ia data sample. The st statistical analysis is performed by using Markov Chain Monte Carlo (MCMC) simulations. A detailed comparison with the standard $$\Lambda $$ Λ CDM model is also performed, with the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) used as the two model selection tools. The statefinder diagnostics consisting of jerk and snap parameters, and the Om(z) diagnostics are also considered for the comparative study of the Barthel–Kropina and $$\Lambda $$ Λ CDM cosmologies. Our results indicate that the Barthel–Kropina dark energy model gives a good description of the observational data, and thus it can be considered a viable alternative of the $$\Lambda $$ Λ CDM model.

Observational Constraining Study of New Deceleration Parameters in FRW Universe

“…The χ 2 function for these measurements, denoted by $$\chi _{\mathrm{H(z)}}^{2}$$, is $$$$\begin{equation} \chi _{\mathrm{H(z)}}^{2}=\sum _{i=1}^{57} \frac{{\left[H^{t h}{\left(z_i\right)}-H^{o b s}{\left(z_i\right)}\right]}^2}{\sigma _{H^{\mathrm{obs}}{\left(z_{i}\right)}}^{2}}, \end{equation}$$$$where $$H^{\mathrm{th}}(z_{i})$$ represent the theoretical value obtained from our cosmological model, $$H^{\text{obs }}(z_{i})$$ and represent the observed value of HP with a standard deviation $$\sigma _{H^{\mathrm{obs}}(z_{i})}^{2}$$ (to see more and rundown all measurements see ref. [ 60 ] ).…”

Hyperbolic Scenario of Accelerating Universe in Modified Gravity

“…where H th , H obs , and σ H(z i ) denotes the model prediction, observed value of Hubble rate, and standard error at the redshift z i , respectively. The Hubble function numerical values for the appropriate redshifts are shown in [73].…”

“…We have studied the different forms of deceleration parameters of several researchers [67][68][69]. In this paper, we introduce a new form of the deceleration parameter (there is some recent work considering the parameterization of the deceleration parameter [70][71][72][73]) in SB theory in the framework of Bianchi type-V space-time with a new deceleration parameter q = α − β H 2 in SB gravity, where α, β, and H are negative constants, positive constants, and the Hubble parameter, respectively. This paper is organized as follows: Section 2 is devoted to metrics that describe the geometry of the Universe and its field equations.…”

The Finsler Spacetime Condition for (α,β)-Metrics and Their Isometries

“…Among all Finsler structures, the class of (α, β)-metrics, obtained by constructing a geometric length measure for curves from a (pseudo)-Riemannian metric a and a 1-form b, are the easiest to construct and the most used in practice. Notorious examples include Bogoslovsky-Kropina (or m-Kropina) metrics, which represent the framework for VSR and its generalization, very general relativity (VGR) [10][11][12][13][14]-also used for dark energy models [15]-and Randers metrics, used, for instance, in the description of the propagation of light in stationary spacetimes [16][17][18][19], for the motion of an electrically charged particle in an electromagnetic field, in the study of Finsler gravitational waves [20,21], as an extended background for field theories [22] and black holes [23], or in Zermelo's navigation problem [16,24].…”