Cosmic Hubble-Hawking Temperature Relation: Quantum Gravity Scaling for Compact Object Accretion and Thermal Emissions

In our Hubble-Hawking models of cosmology, following Hawking’s black hole temperature relation and by considering the geometric mean of the Hubble mass and Planck mass, we have fitted the current Hubble parameter and current cosmic temperature. Methods: Following the same relation, it seems possible to fit inner assertion disk temperatures of compact astrophysical objects, linking quantum gravity to observable thermal emissions via the geometric mean of object mass and Planck mass. Considering a proportionality between black hole thermal energy density and mass-energy density, there is a possibility to derive Hubble-Hawking like thermal relation. Results: For stellar-size black holes of mass 10 solar masses, it predicts a surface temperature of $10^{12}$ K, and for supermassive black holes of mass $10^9$ solar masses, it predicts $10^8$ K. By considering a scale factor associated with the strong coupling constant and the Hubble mass, estimated inner accretion disk temperatures are ($10^6$ – $10^8$ K stellar, $10^5$ – $10^7$ K supermassive) responsible for X-ray/UV output, unlike classical Hawking radiation (~$10^{-8}$ K stellar). Considering two simple coefficients, this extends to neutron stars ($10^6$ – $10^7$ K surfaces) and white dwarfs ($10^4$ –$10^5$ K), unifying high-energy behavior across gravitationally bound systems including eternally collapsing objects. By bridging microphysical constants with empirical multi-wavelength data from Chandra/JWST, the relation offers testable predictions challenging Lambda-CDM and enabling quantum gravity validation in local astrophysics and cosmic evolution. Conclusions: The Hubble-Hawking temperature relation and its proposed simple derivation emerges as a robust, universal framework that successfully unifies quantum gravitational scales with the thermal properties of compact objects across six orders of magnitude in mass, providing superior empirical agreement over classical black hole thermodynamics. This formulation not only resolves longstanding discrepancies between Hawking predictions and observations but also establishes a consistent quantum gravity signature observable through existing X-ray/UV spectroscopy, opening pathways for definitive experimental validation and potentially revolutionizing our understanding of gravitationally collapsed matter from stellar scales to cosmological horizons.