Modified Uncertainty Principle with Cosmological Constant: More Insights on Dark Energy and Chandrasekhar Limit

Abstract: Numerous studies have shown that generalized uncertainty principle (GUP) removes the Chandrasekhar limit, which can be restored using a negative GUP parameter. This study indicates that observational phantom dark energy also requires an extended uncertainty principle (EUP) parameter with the opposite sign. Altering the signs of the GUP and EUP parameters without a physical rationale is questionable. We demonstrate that incorporating cosmological constant in a modified uncertainty principle (MUP) can address the sign change in GUP and EUP within a unified framework. The main advantage of MUP is that the sign change of the cosmological constant is acceptable and geometrically meaningful. To achieve this, we first derive a modified equation of state from the MUP framework and second test it with observational data for dark matter and dark energy. Importantly, the proposed MUP parameter, which is proportional to the cosmological constant with positive and negative signs, aligns with dark energy observations and restores the Chandrasekhar limit for stars. Finally, we will show that the Chandrasekhar mass limit provides an upper bound of (\leq 10^{-32}{\rm m^{-2}}) for the cosmological constant, consistent with the observational value of (\Lambda_{\rm obs}=10^{-52}{\rm m^{-2}}).