Dark energy and QCD instanton vacuum in a Friedmann-Lemaître-Robertson-Walker universe

The standard model of the universe, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>λ</a:mi> <a:mi>CDM</a:mi> </a:math> , is based on the Friedmann-Lemaître-Robertson-Walker metric with a flat three-dimensional coordinate space and the Friedmann equations Navas . [.]. The cosmological constant <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>λ</c:mi> </c:math> provides the cancellation of the matter field contributions in the flat (Minkowski) space, as was proposed long ago in 1967 by Zeldovich for the first time to our knowledge Zeldovich [ , 316 (1967)]; see also Krasinski and Zeldovich []. The dynamical dark energy appears on the surface of the vacuum energy of matter fields at the flat (Minkowski) space. Within the Standard Model, the gluon Yang-Mills (YM) fields are playing a specific role since the properties of their vacuum, where there is the presence of the gluon condensate, provide the nonperturbative vacuum energy. It is natural to apply the successful instanton liquid model of the QCD vacuum and its lowest excitations. Our aim is to calculate the contribution of gluon YM fields to the dark energy density. We find that the universe metric is generating the QCD vacuum excitation, which gives the contribution to the dark energy density. But this one may hardly play a central role in the dynamics of the universe, since its timescale is too small. We also find the equation-of-state parameters <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>w</e:mi> <e:mn>0</e:mn> </e:msub> <e:mo>=</e:mo> <e:mo>−</e:mo> <e:mn>1</e:mn> <e:mo>,</e:mo> <e:msub> <e:mi>w</e:mi> <e:mi>a</e:mi> </e:msub> <e:mo>=</e:mo> <e:mn>0</e:mn> </e:math> in accordance with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>λ</g:mi> <g:mi>CDM</g:mi> </g:math> , while the newest data, analyzed at Shajib and Frieman [.], give them at least in the range <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo>−</i:mo> <i:mn>0.91</i:mn> <i:mo>&lt;</i:mo> <i:msub> <i:mi>w</i:mi> <i:mn>0</i:mn> </i:msub> <i:mo>&lt;</i:mo> <i:mo>−</i:mo> <i:mn>0.73</i:mn> <i:mo>,</i:mo> <i:mspace linebreak="goodbreak"/> <i:mo>−</i:mo> <i:mn>1.05</i:mn> <i:mo>&lt;</i:mo> <i:msub> <i:mi>w</i:mi> <i:mi>a</i:mi> </i:msub> <i:mo>&lt;</i:mo> <i:mo>−</i:mo> <i:mn>0.65</i:mn> </i:math> . They are requesting a contribution from an ultralight scalar such as an axion, or from YM field topological configurations with the nontrivial holonomy due to the deviation from a pure de Sitter state Van Waerbeke and Zhitnitsky [DESI results and dark energy from QCD topological sectors, .].