Can Dark Matter Induce Cosmological Evolution of the Fundamental Constants of Nature?

We demonstrate that massive fields, such as dark matter, can directly produce a cosmological evolution of the fundamental constants of nature. We show that a scalar or pseudoscalar (axionlike) dark matter field $\varphi$, which forms a coherently oscillating classical field and interacts with standard model particles via quadratic couplings in $\varphi$, produces “slow” cosmological evolution and oscillating variations of the fundamental constants. We derive limits on the quadratic interactions of $\varphi$ with the photon, electron, and light quarks from measurements of the primordial ${}^4\mathrm{He}$ abundance produced during big bang nucleosynthesis and recent atomic dysprosium spectroscopy measurements. These limits improve on existing constraints by up to 15 orders of magnitude. We also derive limits on the previously unconstrained linear and quadratic interactions of $\varphi$ with the massive vector bosons from measurements of the primordial ${}^4\mathrm{He}$ abundance.

Figure 1

From top left to right: Limits on the quadratic interactions of $\varphi$ with the photon, electron, light quarks, and massive vector bosons, as functions of the scalar particle mass $m_{\varphi }$. The region below the blue line corresponds to constraints derived in the present work from consideration of the primordial ${}^4\mathrm{He}$ abundance produced during BBN (the shape of the constraints on different sides of the mass $m_{\varphi }\sim {10}^{-16}\mathrm{eV}$ arises from the different dependence of the scalar field amplitude ${\varphi }_0$ on $m_{\varphi }$ in these two limiting regions: ${\varphi }_0\propto m_{\varphi }^{-1}=>{\mathrm{\Lambda }}_X^{\prime }\propto m_{\varphi }^{-1}$ for $m_{\varphi }\gg {10}^{-16}\mathrm{eV}$, whereas ${\varphi }_0\propto m_{\varphi }^{-1/4}=>{\mathrm{\Lambda }}_X^{\prime }\propto m_{\varphi }^{-1/4}$ for $m_{\varphi }\ll {10}^{-16}\mathrm{eV}$). The region below the yellow line corresponds to constraints derived in the present work from consideration of CMB angular power spectrum measurements. The region below the red line corresponds to constraints derived in the present work using recent atomic dysprosium spectroscopy data of Ref. [63]. The region below the black line corresponds to existing constraints from consideration of supernova energy loss bounds and fifth-force experimental searches [55]. The light quark and massive vector boson interaction parameters are defined as $({\tilde{\mathrm{\Lambda }}}_q^{\prime }{)}^2=|({\mathrm{\Lambda }}_u^{\prime }{)}^2({\mathrm{\Lambda }}_d^{\prime }{)}^2(m_d-m_u)/[({\mathrm{\Lambda }}_u^{\prime }{)}^2{m}_d-({\mathrm{\Lambda }}_d^{\prime }{)}^2{m}_u]|$ and $({\tilde{\mathrm{\Lambda }}}_V^{\prime }{)}^2=|({\mathrm{\Lambda }}_W^{\prime }{)}^2({\mathrm{\Lambda }}_Z^{\prime }{)}^2/[({\mathrm{\Lambda }}_Z^{\prime }{)}^2-1.4({\mathrm{\Lambda }}_W^{\prime }{)}^2]|$, assuming ${\kappa }_d^{\prime }={\kappa }_u^{\prime }$ and ${\kappa }_W^{\prime }={\kappa }_Z^{\prime }$.