Signature flips in time-varying $$\Lambda (t)$$ cosmological models with observational data
Annotatsiya
Abstract In this study, we investigate signature flips within the framework of cosmological models featuring a time-varying vacuum energy term $$\Lambda (t)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Specifically, we consider the power-law form of $$\Lambda =\alpha H^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math> , where $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and n are constants. To constrain the model parameters, we use the MCMC technique, allowing for effective exploration of the model’s parameters. We apply this approach to analyze 31 points of observational Hubble Data (OHD), 1048 points from the Pantheon data, and additional CMB data. We consider three scenarios: when n is a free parameter (Case I), when $$n=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> (Case II), and when $$n=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> (Case III). In our analysis across all three cases, we observe that our model portrays the universe’s evolution from a matter-dominated decelerated epoch to an accelerated epoch, as indicated by the corresponding deceleration parameter. In addition, we investigate the physical behavior of total energy density, total EoS parameter, and jerk parameter. Our findings consistently indicate that all cosmological parameters predict an accelerated expansion phase of the universe for all three cases ( $$q_0<0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , $$\omega _0<-\frac{1}{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo><</mml:mo> <mml:mo>-</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>3</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> , $$j_0>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>j</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). Furthermore, our analysis reveals that the Om ( z ) diagnostics for Cases I and III align with the quintessence region, while Case II corresponds to the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model.