| Ամփոփում: | We propose a new class of cosmological unified dark sector models called “<i>Generalized Logotropic Models</i>”. They depend on a free parameter <i>n</i>. The original logotropic model is a special case of our generalized model corresponding to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model is recovered for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. In our scenario, the Universe is filled with a single fluid, a generalized logotropic dark fluid (GLDF), whose pressure <i>P</i> includes higher order logarithmic terms of the rest-mass density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ρ</mi><mi>m</mi></msub></semantics></math></inline-formula>. The total energy density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> is the sum of the rest-mass energy density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ρ</mi><mi>m</mi></msub><msup><mi>c</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> and the internal energy density <i>u</i> which play the roles of dark matter energy density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϵ</mi><mi>m</mi></msub></semantics></math></inline-formula> and dark energy density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϵ</mi><mrow><mi>d</mi><mi>e</mi></mrow></msub></semantics></math></inline-formula>, respectively. We investigate the cosmological behavior of the generalized logotropic models by focusing on the evolution of the energy density, scale factor, equation of state parameter, deceleration parameter and squared speed of sound. Low values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≤</mo><mn>3</mn></mrow></semantics></math></inline-formula> are favored. We also study the asymptotic behavior of the generalized logotropic models. In particular, we show that the model presents a phantom behavior and has three distinct ways of evolution depending on the value of <i>n</i>. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>n</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>, it leads to a little rip and for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula> to a big rip. We predict the value of the big rip time as a function of <i>n</i> without any free (undetermined) parameter.
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