Can decaying vacuum solve the $$H_0$$ tension?

Abstract In the present work we analyze two different models of interaction between dark energy and dark matter, also known as vacuum decay models or $$\Lambda (t)$$ <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> CDM models. In both models, when the $$H_0$$ <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> parameter is constrained by high-redshift data as the Planck distance priors (CMB) and transversal BAO, its value is compatible with a higher value 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> , in agreement with low-redshift data, as Pantheon+ &amp;SH0ES (PS) and Cosmic Chronometers (CC). For one of the models, only a mild $$\sim 2.1\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>2.1</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> tension is found for $$\Omega _m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> , which at least is an alleviation to the $$\gtrsim 5\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≳</mml:mo> <mml:mn>5</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> $$H_0$$ <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> tension in the context of standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model. We find $$H_0=71.63\pm 0.60$$ <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>71.63</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.60</mml:mn> </mml:mrow> </mml:math> km/s/Mpc for one model and $$H_0=71.67\pm 0.60$$ <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>71.67</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.60</mml:mn> </mml:mrow> </mml:math> km/s/Mpc for the other one, by combining CC+PS+BAO+CMB. We also find the decay parameter to be $$\epsilon =0.0162^{+0.0029}_{-0.0026}$$ <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>0162</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.0026</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.0029</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> for one model and $$\epsilon =0.0209\pm 0.0036$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.0209</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0036</mml:mn> </mml:mrow> </mml:math> for the other one. All constraints are at 68% c.l. From these analyses, a noninteracting model is excluded at least at $$5.8\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>5.8</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> c.l. We shall emphasize, however, that this result comes from an analysis that involves an approximated treatment to CMB, the Planck distance priors, as mentioned above. We have also verified that if the SH0ES prior is not included, the evidence for an interacting model decreases from $$5.8\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>5.8</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> to $$4 \sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> , a result closer to other recent works in the literature. This shows that these types of models are promising in solving or at least alleviating the $$H_0$$ <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> tension problem.