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Abstract
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The standard cosmological model, known as the 𝛬CDM model, has been successful in many respects, but it has some significant discrepancies, some of which have not been resolved yet. In measuring the Hubble-Lemaître parameter, there is an apparent discrepancy which is known as the Hubble tension, defined as differences in values of this parameter measured by the Type Ia Supernovae (SNeIa) data (a model-independent method) and by the Cosmic Microwave Background (CMB) radiation maps (a model-dependent method). Although many potential solutions have been proposed, the issue still remains unresolved. Recently, it was observed that the Hubble tension can be due to the concept of uncertainty in measuring cosmological parameters at large distance scales through applying the Heisenberg Uncertainty Principle (HUP) in cosmological setups. Extending this pioneering idea, in the present study we plan to incorporate the Extended Uncertainty Principle (EUP) containing a minimal fundamental measurable momentum (or equivalently, a maximal fundamental measurable length) as a candidate setup for describing large-scale effects of Quantum Gravity (QG) to address the Hubble tension and constrain the EUP length scale. In this regard, by finding a relevant formula for the effective photon rest mass in terms of the present-time value of the Hubble-Lemaître parameter, we see that discrepancies in the value of photon rest mass associated with the Hubble-Lemaître parameter values estimated from model-independent and model-dependent methods perhaps is the cause of Hubble tension. We show explicitly that the presence of a non-zero minimal uncertainty in momentum (or non-zero maximal uncertainty in position) measurements as a consequence of the large distance quantum gravity effect addresses the Hubble tension satisfactorily without having to invoke new physics. Moreover, we use the formula for the effective photon rest mass to find some relevant lower bounds on the EUP length scale.
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