Cosmological constraints on two vacuum decay models

Abstract We constrain two vacuum decay models ( $$\varLambda (t)$$ <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> CDM) utilizing the baryon acoustic oscillations (BAO) data released by the Dark Energy Spectroscopic Instrument (DESI), distance prior from the cosmic microwave background (CMB) observed by the Planck satellite, Hubble rate data obtained via the cosmic chronometers (CC) method and type Ia supernova (SNIa) data. The interaction terms between dark matter and dark energy are defined as $$Q=3\varepsilon H\rho _{\varLambda }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>ε</mml:mi> <mml:mi>H</mml:mi> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>Λ</mml:mi> </mml:msub> </mml:mrow> </mml:math> for model I and $$3\varepsilon aH\rho _{\varLambda }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>ε</mml:mi> <mml:mi>a</mml:mi> <mml:mi>H</mml:mi> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>Λ</mml:mi> </mml:msub> </mml:mrow> </mml:math> for model II. We find that the decay parameter is constrained to be $$\varepsilon =0.0094^{+0.0037}_{-0.0033}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>0094</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.0033</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.0037</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> for model I and $$\varepsilon =0.0119\pm {0.0045}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.0119</mml:mn> <mml:mo>±</mml:mo> <mml:mrow> <mml:mn>0.0045</mml:mn> </mml:mrow> </mml:mrow> </mml:math> for model II, respectively, indicating a potential interaction between dark matter and dark energy at the $$2\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> confidence level. The current Hubble parameter values are estimated to be $$H_{0}=70.30\pm {0.67}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>70.30</mml:mn> <mml:mo>±</mml:mo> <mml:mrow> <mml:mn>0.67</mml:mn> </mml:mrow> </mml:mrow> </mml:math> for model I and $$H_{0}=70.28\pm {0.64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>70.28</mml:mn> <mml:mo>±</mml:mo> <mml:mrow> <mml:mn>0.64</mml:mn> </mml:mrow> </mml:mrow> </mml:math> for model II. These values of $$H_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> fall between those derived from the Planck and SH0ES data, suggesting that these two vacuum decay models could provide a potential solution to alleviate the Hubble tension problem.