Assessing Cosmological Evidence for Nonminimal Coupling

The recent observational evidence of deviations from the Lambda cold dark matter model points toward the presence of evolving dark energy. The simplest possibility consists of a cosmological scalar field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>φ</a:mi></a:math>, dubbed “quintessence,” driving the accelerated expansion. We assess the evidence for the existence of such a scalar field. We find that, if the accelerated expansion is driven by quintessence, the data favor a potential energy <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>V</c:mi><c:mo stretchy="false">(</c:mo><c:mi>φ</c:mi><c:mo stretchy="false">)</c:mo></c:math> that is concave, i.e., <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msup><g:mrow><g:mi>m</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msup><g:mo>=</g:mo><g:msup><g:mrow><g:mi>d</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msup><g:mi>V</g:mi><g:mo>/</g:mo><g:mi>d</g:mi><g:msup><g:mrow><g:mi>φ</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msup><g:mo><</g:mo><g:mn>0</g:mn></g:mrow></g:math>. Furthermore, and more significantly, the data strongly favor a scalar field that is nonminimally coupled to gravity [Bayes factor <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>log</i:mi><i:mo stretchy="false">(</i:mo><i:mi>B</i:mi><i:mo stretchy="false">)</i:mo><i:mo>=</i:mo><i:mn>7.34</i:mn><i:mo>±</i:mo><i:mn>0.6</i:mn></i:mrow></i:math>], leading to time variations in the gravitational constant on cosmological scales, and the existence of fifth forces on smaller scales. The fact that we do not observe such fifth forces implies that new physics must come into play on noncosmological scales that quintessence is an unlikely explanation for the observed cosmic acceleration.