Emergent Early Dark Energy from Renormalization Group Fluctuations and Walking Dynamics (v1)

We propose a first-principles mechanism for early dark energy (EDE) arising from renormalization group (RG) dynamics and entropy-driven fluctuations in an emergent framework of cosmology. Starting from a stationary fundamental action, we show that coarse-graining induces a stochastic RG flow for a reduced dynamical variable, leading to fluctuation-driven corrections to the beta function. These corrections generate an effective walking regime, characterized by a near-vanishing RG drift over a finite range of scales. We construct an effective action description in which the emergent degree of freedom behaves as a scalar field with a time-dependent mass determined by the effective number of degrees of freedom g* (z). In the early universe, large g* induces a dynamical flattening of the effective potential, enhancing fluctuations and producing a transient EDE component at the percent level. As g* decreases, the system exits the walking regime and asymptotically approaches a Lambda-like behavior. We compute the resulting cosmological evolution and show that the model generates an early dark energy fraction fEDE approximately in the range 1% to 3%, consistent with current constraints from cosmic microwave background data. This leads to a shift in the inferred Hubble constant H0 approximately in the range 69 to 71 kilometers per second per megaparsec, reducing the Hubble tension by approximately a factor of two without spoiling agreement with existing observations. A key prediction of the model is a stochastic component in the expansion history, leading to a small but characteristic smoothing of acoustic peaks in the CMB power spectrum at the level of about 10 to the minus 3. This signature distinguishes the scenario from standard EDE models and is potentially detectable with upcoming experiments. Our results demonstrate that early dark energy can emerge naturally from RG fluctuations and walking dynamics, providing a theoretically grounded and observationally viable contribution to the partial alleviation of the Hubble tension.