The energy conditions and model selection in the local Universe

Abstract The four principal energy conditions (ECs) in general relativity prohibit negative energies, repulsive gravity and superluminal energy flows. One must invoke exotic matter to violate any one of these, yet $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM does so quite prominently during inflation and in the epoch of dark energy dominance. In this paper, we carry out model selection between the standard model and the $$R_{\textrm{h}}=ct$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mtext>h</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> universe using a combination of H II galaxy and cosmic chronometer measurements in the local Universe, and directly compare the results to the constraints imposed by the ECs. We find that the latter cosmology is not only strongly favored by these data, with a likelihood of $$\sim 92\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>92</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> versus only $$\sim 8\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>8</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> for the former, but that its optimized fit is fully compliant with all four ECs, while $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM’s best fit violates the so-called strong energy condition at $$z\lesssim 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>≲</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> .