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Dark energy and accelerating cosmological evolution in a Universe with a Weylian boundary

Tiberiu Harko, Shahab Shahidi

Abstract

We investigate the influence of boundary terms in gravitational field theories, by considering that in the Einstein-Hilbert action the boundary can be described by a non-metric Weyl-type geometry. The gravitational action and the the field equations, are thus generalized to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. The field equations obtained within this framework generalize the standard Einstein equations by including in their mathematical structure the Weyl vector, and its covariant derivatives. As an applications of the general formalism we investigate the cosmological evolution in a flat FLRW geometry. We obtain the generalized Friedmann equations, which contain extra terms depending on the Weyl vector and its derivatives, arising due to the presence of the Weylian boundary, and which describe an effective, time dependent dark energy. By imposing to the dark energy an equation of state parameter of the Barboza-Alcaniz type, the Friedmann equations can be solved numerically. We compare the predictions of the Weylian boundary gravitational theory with late-time observational data and the predictions of the $Λ$CDM paradigm. Our results show that the Weylian boundary cosmological models give a good description of the observational data, and they can reproduce almost exactly the predictions of the $Λ$CDM paradigm. Hence, the extension of gravitational theories through the addition of Weylian boundary terms, in which dark energy has a purely geometric origin, emerges as a viable alternative to standard general relativity.

Dark energy and accelerating cosmological evolution in a Universe with a Weylian boundary

Abstract

We investigate the influence of boundary terms in gravitational field theories, by considering that in the Einstein-Hilbert action the boundary can be described by a non-metric Weyl-type geometry. The gravitational action and the the field equations, are thus generalized to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. The field equations obtained within this framework generalize the standard Einstein equations by including in their mathematical structure the Weyl vector, and its covariant derivatives. As an applications of the general formalism we investigate the cosmological evolution in a flat FLRW geometry. We obtain the generalized Friedmann equations, which contain extra terms depending on the Weyl vector and its derivatives, arising due to the presence of the Weylian boundary, and which describe an effective, time dependent dark energy. By imposing to the dark energy an equation of state parameter of the Barboza-Alcaniz type, the Friedmann equations can be solved numerically. We compare the predictions of the Weylian boundary gravitational theory with late-time observational data and the predictions of the CDM paradigm. Our results show that the Weylian boundary cosmological models give a good description of the observational data, and they can reproduce almost exactly the predictions of the CDM paradigm. Hence, the extension of gravitational theories through the addition of Weylian boundary terms, in which dark energy has a purely geometric origin, emerges as a viable alternative to standard general relativity.
Paper Structure (19 sections, 76 equations, 9 figures, 4 tables)

This paper contains 19 sections, 76 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Weyl geometry, Einstein-Hilbert action, and boundary terms
  3. Fundamentals of Weyl geometry
  4. The boundary term in general relativity
  5. Gravitational action, and field equations with Weylian boundary terms
  6. Variation of the Weylian boundary terms
  7. Einstein-Hilbert action and gravitational field equations with Weyl type boundary terms
  8. Cosmological applications
  9. The generalized Friedmann equations
  10. Dimensionless representation
  11. Statistical analysis
  12. The cosmographic parameters
  13. The jerk and snap parameters.
  14. Matter and dark energy density parameters
  15. The matter density parameter.
  16. ...and 4 more sections

Figures (9)

  • Figure 1: The corner plot for the values of the parameters $H_0$, $\Omega_{m0}$, $\gamma_0$ and $\gamma_a$ with their $1\sigma$ and $2\sigma$ confidence levels for the Weyl Boundary gravity model.
  • Figure 2: The behavior of the rescaled Hubble parameter $H(z)/(1+z)$ (left panel) and of the deceleration parameter $q(z)$ (right panel) as a function of the redshift $z$ for the Weyl Boundary gravity model for the best fit values of the parameters, as given by table \ref{['bestfit']}. The shaded area denotes the $1\sigma$ error. The dashed line represents the $\Lambda$CDM model.
  • Figure 3: The behavior of the jerk parameter $j(z)$ (left panel) and of the snap parameter $s(z)$ (right panel) as a function of the redshift $z$ for the Weyl Boundary gravity model for the best fit values of the parameters, as given by table \ref{['bestfit']}. The shaded area denotes the $1\sigma$ error. The dashed line represents the $\Lambda$CDM model.
  • Figure 4: The behavior of the jerk parameter $j$ as a function of the deceleration parameter $q$, $j=j(q)$ (left panel), and of the snap parameter as a function of the jerk parameter, $s=s(j)$ (right panel) for the Weyl Boundary gravity model for the best fit values of the parameters as given by table \ref{['bestfit']}. The dashed line represents $\Lambda$CDM model.
  • Figure 5: The behavior of the matter density abundance $\Omega_m$ and $\omega_1$ as functions of the redshift $z$ for the Weyl Boundary gravity model for the best fit values of the parameters as given by table \ref{['bestfit']}. The dashed line represents $\Lambda$CDM model.
  • ...and 4 more figures