Tachyonic (phantom) power-law cosmology

Abstract

Tachyonic scalar field-driven late universe with dust matter content is considered. The cosmic expansion is modeled with power-law and phantom power-law expansion at late time, i.e. z≲0.45. WMAP7 and its combined data are used to constraint the model. The forms of potential and the field solution are different for quintessence and tachyonic cases. Power-law cosmology model (driven by either quintessence or tachyonic field) predicts unmatched equation of state parameter to the observational value, hence the power-law model is excluded for both quintessence and tachyonic field. In the opposite, the phantom power-law model predicts agreeing valued of equation of state parameter with the observational data for both quintessence and tachyonic cases, i.e. $w_{\phi, 0} = -1.49^{+11.64}_{-4.08}$ (WMAP7+BAO+H ₀) and $w_{\phi, 0} = -1.51^{+3.89}_{-6.72}$ (WMAP7). The phantom-power law exponent β must be less than about −6, so that the −2<w _ϕ,0<−1. The phantom power-law tachyonic potential is reconstructed. We found that dimensionless potential slope variable Γ at present is about 1.5. The tachyonic potential reduced to V=V ₀ ϕ ⁻² in the limit Ω _m,0→0.

Appendix: Errors analysis

In calculating of the accumulated errors, we follow the procedure here. If f is valued of answer in the form

$$ f = f(x_1, x_2, \ldots, x_n) $$

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and f ₀ is the value when x _i is set to their measured values, then the value of f _i is defined as

$$ f_i = f(x_1, \ldots, x_i + \sigma_i, \ldots, x_n) $$

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This value of f is the value with effect of error in variable x _i , that is σ _i . One can find square of the accumulated error from

$$ \sigma^2_{f} = \sum_i^n (f_i - f_0)^2 $$

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Hence giving the error of f from accumulating effect from errors of x _i .