Cosmological Implications of the Extended Uncertainty Principle: Energy Conditions, Stability, and Late Time Acceleration

TL;DR

This work shows that infrared modifications from the Extended Uncertainty Principle can be embedded into horizon thermodynamics to produce modified Friedmann dynamics with an effective EUP energy density. For a negative deformation parameter η, the model yields a late-time transition to acceleration and allows w(z) to cross the phantom divide without extra fields. Mapping to the CPL framework demonstrates compatibility with Planck, BAO, and supernova data, particularly for η ~ 10^{-27}. The model satisfies NEC, WEC, and DEC while violating SEC, and exhibits a stable phase-space evolution toward a de Sitter attractor with a positive, finite sound speed, indicating dynamical and thermodynamic stability. Overall, EUP-induced IR corrections offer a viable, quantum gravity–motivated alternative to dark energy for explaining late-time cosmic acceleration.

Abstract

We study the cosmological consequences of the Extended Uncertainty Principle (EUP) by deriving modified Friedmann equations through thermodynamic arguments. The evolution of the effective equation of state induced by EUP corrections is analyzed and characterized using the Chevallier-Polarski-Linder (CPL) parametrization. We then examine the fulfillment of classical energy conditions, including the null, weak, strong, and dominant conditions. The dynamical and thermodynamic stability of the model is investigated, showing that the EUP cosmology admits a late-time de Sitter attractor. Finally, we evaluate the effective speed of sound associated with the model and discuss implications for perturbative stability. Our findings indicate that EUP-induced corrections can produce a consistent late-time acceleration without requiring a cosmological constant.

Figures (10)

• Figure 1: Standard and Extended Uncertainty Principle for different values of $\eta$ with specified minimal momentum points. For clarity of illustration, we have used larger values of $\eta$. The actual model employs $\eta\sim-10^{-27}$, consistent with the constraints used in our cosmological analysis in Roushan2024.
• Figure 2: Energy density versus redshift (left panel) and pressure versus redshift (right panel) for different values of $\eta$ to have late-time cosmic speed-up..
• Figure 3: Equation of state parameter as a function of scale factor $a$.
• Figure 4: Distributions of the $(\hat{w}_0\equiv w(a=1)$,$\hat{w}_a \equiv -\frac{dw}{da}(a=1))$ parameters for different data combinations contains planck in the EUP background. Colored markers indicate theoretical values corresponding to different choices of the deformation parameter $\eta$, ranging of the order of $10^{-27}$. The right panel provides a zoomed-in view of the diagram to show the distribution in greater detail.
• Figure 5: Distributions of the $(w_0$, $w_a)$ parameters for different data combinations containing Planck, in the EUP background. Colored markers represent the CPL-equivalent values fitted from the EUP model for different choices of the deformation parameter $\eta$, ranging of the order of $10^{-27}$. The contours correspond to the observational 68% and 95% confidence levels from Planck 2018, BAO, and SN data. The right panel provides a zoomed-in view of the diagram to show the parameter space in greater detail.