Towards a de Sitter quintom-like cosmology from a reduction of a 7-dimensional <i>BF</i> theory

Abstract In this article, we analyze a 7-dimensional BF theory that, upon dimensional reduction, transforms into an effective 4-dimensional action in which a generic metric is involved. A constraint is imposed in such a way that this is the Friedmann-Lemaître-Robertson-Walker metric characterized by a scale factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>a</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi mathvariant="normal">exp</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> with a Hubble constant H 0 = 67.70 [km s −1 Mpc −1 ]. We also compute the barotropic parameter ω ≡ p / ρ from our solutions. Three different scenarios are explored, in which the model transitions from quintessence to phantom regimes, crossing the theoretical phantom divide line. Consequently, the effective action represents a quintom-like scenario. Moreover, we derive some analytic solutions for the scale factor by treating it as a dynamical variable in the effective action. In this case, different outcomes are obtained, where the model can transit from a cosmological constant to a quintessence regime; however, it cannot cross the theoretical phantom divide line. However, this simplistic model successfully captures distinct phases of cosmic expansion.