Quantum dark energy from neutrino loops: model, stability and oscillation imprints

Abstract We propose a simple, renormalizable scenario in which all of dark energy arises from a one-loop Coleman–Weinberg potential induced by a scalar field Yukawa-coupled exclusively to Standard-Model neutrinos. Classically, $$V_{\min }=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mo>min</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , but neutrino loops lift the vacuum by $$\rho _{\text {DE}}=\frac{y^{2}m_{\nu }^{6}}{512\pi ^{4}m_{\phi }^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>DE</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mi>y</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mn>6</mml:mn> </mml:msubsup> </mml:mrow> <mml:mrow> <mml:mn>512</mml:mn> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> , matching the observed dark energy scale for $$y\approx 0.28m_{\phi }/$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>y</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>0.28</mml:mn> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> <mml:mo>/</mml:mo> </mml:mrow> </mml:math> eV and $$m_{\nu }\sim 0.1\,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>ν</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.1</mml:mn> <mml:mspace/> </mml:mrow> </mml:math> eV. We detail cosmological tracking, demonstrate stability against neutrino clumping, and show that rapid scalar oscillations leave no detectable imprint on current neutrino-oscillation experiments—though they provide a clear target for future high-precision probes. Compared to other mass varying neutrino models, our framework employs only a renormalizable quadratic potential, avoids unnatural hierarchies, and makes concrete, testable predictions.