Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term

The European Physical Journal C, Mar 2017

We study the parameterized post-Newtonian approximation in teleparallel model of gravity with a scalar field. The scalar field is non-minimally coupled to the scalar torsion as well as to the boundary term introduced in Bahamonde and Wright (Phys Rev D 92:084034 arXiv:​1508.​06580v4 [gr-qc], 2015). We show that, in contrast to the case where the scalar field is only coupled to the scalar torsion, the presence of the new coupling affects the parameterized post-Newtonian parameters. These parameters for different situations are obtained and discussed.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-017-4760-6.pdf

Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term

Eur. Phys. J. C Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term H. Mohseni Sadjadi 0 0 Department of Physics, University of Tehran , Tehran , Iran We study the parameterized post-Newtonian approximation in teleparallel model of gravity with a scalar field. The scalar field is non-minimally coupled to the scalar torsion as well as to the boundary term introduced in Bahamonde and Wright (Phys Rev D 92:084034 arXiv:1508.06580v4 [gr-qc], 2015). We show that, in contrast to the case where the scalar field is only coupled to the scalar torsion, the presence of the new coupling affects the parameterized post-Newtonian parameters. These parameters for different situations are obtained and discussed. - In a teleparallel model of gravity, instead of the torsionless Levi-Civita connections, curvatureless Weitzenböck connections are used [2–4]. A teleparallel equivalent of general relativity was first introduced in [5] as an attempt for unification of electromagnetism and gravity. This theory is considered as an alternative theory of usual general relativity and has been recently employed to study the late time acceleration of the Universe [6–8]. This can be accomplished by considering modified f (T ) models [9–24], where T is the torsion scalar, or by introducing exotic field such as quintessence. Assuming a non-minimal coupling between the scalar field and the torsion opens new windows in studying the cosmological evolution [25–31], and can be viewed as a promising scenario for late time acceleration and super-acceleration [32]. A non-minimally coupled scalar field, like the scalar– tensor model, may alter the Newtonian potential. So it is necessary to check if the model can pass local gravitational tests such as solar system observations. This can be done in the context of the parameterized post-Newtonian formalism [35–40]. In [33, 34] it was shown that when the scalar field is only coupled to the scalar torsion, there is no deviation from general relativity in the parameterized post-Newtonian (PPN) parameters and the theory is consistent with gravitational tests and solar system observations. Recently a new coupling between the scalar field and a boundary term B, corresponding to the torsion divergence B ∝ ∇μT μ, was introduced in [1], where the cosmological consequences of such a coupling for some simple power law scalar field potential and the stability of the model were discussed. There it was found that the system evolves to an attractor solution, corresponding to late time acceleration, without any fine tuning of the parameters. In this framework, the phantom divide line crossing is also possible. Thermodynamics aspects of this model were studied in [41]. This model includes two important subclasses, i.e. quintessence non-minimally coupled to the Ricci scalar and quintessence non-minimally coupled to the scalar torsion. Another important feature of this model is its ability to describe the present cosmic acceleration in the framework of Z2 symmetry breaking by alleviating the coincidence problem [42]. In this paper, we aim to investigate whether this new boundary coupling may affect the Newtonian potential and PPN parameters: γ (r ) and β(r ). The scheme of the paper is as follows: In the second section we introduce the model and obtain the equations of motion. In the third section, we obtain the weak field expansion of the equations in the PPN formalism and obtain and discuss their solutions for spherically symmetric metric. We show that the PPN parameters may show deviation from general relativity. We consider different special cases and derive explicit solutions for the PPN parameters in terms of the model parameters and confront them with observational data. We use units with h¯ = c = 1 and choose the signature (−, +, +, +) for the metric. 2 The model and the field equations In our study we use vierbeins ea = ea μ∂μ, whose duals, ea μ, are defined through ea μea ν = δμν. The metric tensor is given by gμν = ηabea μebν , η = diag(−1, 1, 1, 1). e = det(ea μ) = det √−g. Greek indices (indicating coordinate bases) like the first Latin indices (indicating orthonormal bases) a, b, c, ... belong to {0, 1, 2, 3}, while i, j, k, ... ∈ {1, 2, 3}. Our model is specified by the action [1] S = where k2 = 8π G N , and G N is the Newtonian gravitational constant. The torsion scalar is defined by T = Sρ μν Tρ μν = 41 T ρ μν Tρ μν + 21 T ρ μν T νμρ −T ρ μρ T νμν , 3 Post-Newtonian formalism To investigate the post-Newtonian approximation [35–40] of the model, the perturbation is specified by the velocity of the source matter |v| such that e.g. O(n) ∼ |v|n. The matter source is assumed to be a perfect fluid obeying the postNewtonian hydrodynamics: where ρ is energy density, p is the pressure and is the specific internal energy. uμ is the four-vector velocity of the fluid. The velocity of the source matter is vi = uu0i . The orders of smallness of the energ (...truncated)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-017-4760-6.pdf

H. Mohseni Sadjadi. Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term, The European Physical Journal C, 2017, pp. 191, Volume 77, Issue 3, DOI: 10.1140/epjc/s10052-017-4760-6