Facing significant challenges in acquiring and repurposing unsold homes,some cities are turning empty flats into student dorms,hospitals,retirement housing and resettlement homes.
Haug and Tatum have recently outlined a possible path to solving the Hubble tension within R_(H_(t))=ct cosmology models using a trial-and-error algorithm for redshift scaling,specifically z=(R_(H_(0))/R_(H_(t)))-1 an...Haug and Tatum have recently outlined a possible path to solving the Hubble tension within R_(H_(t))=ct cosmology models using a trial-and-error algorithm for redshift scaling,specifically z=(R_(H_(0))/R_(H_(t)))-1 and z=(R_(H_(0))/R_(H_(t)))^(1/2)-1.Their algorithm demonstrates that one can start with the measured CMB temperature and a rough estimate of H_(0).Based on this approach,they nearly perfectly match the entire distance ladder of observed supernovae by identifying a single value for H_(0).This work replaces a previous numerical approach with a formal,closed-form mathematical solution.Furthermore,we will prove that this solution is valid for a much more general case of any cosmological redshift scaling consistent with:z=(R_(H_(0))/R_(H_(t)))^(x)-1.Haug and Tatum have only considered the most common assumptions of x=1 and x=1/2.Our solution involves simply solving an equation to determine the correct value of H_(0).This is possible because an exact mathematical relation between H_(0)and the CMB temperature has recently been established,in combination with the linearity in an R_(H_(t))=ct model.We also demonstrate that a thermodynamic form of the Friedmann equation is consistent with a wide range of redshift scalings,namely:z=(R_(H_(0))/R_(H_(t)))^(x)-1.展开更多
文摘Facing significant challenges in acquiring and repurposing unsold homes,some cities are turning empty flats into student dorms,hospitals,retirement housing and resettlement homes.
文摘Haug and Tatum have recently outlined a possible path to solving the Hubble tension within R_(H_(t))=ct cosmology models using a trial-and-error algorithm for redshift scaling,specifically z=(R_(H_(0))/R_(H_(t)))-1 and z=(R_(H_(0))/R_(H_(t)))^(1/2)-1.Their algorithm demonstrates that one can start with the measured CMB temperature and a rough estimate of H_(0).Based on this approach,they nearly perfectly match the entire distance ladder of observed supernovae by identifying a single value for H_(0).This work replaces a previous numerical approach with a formal,closed-form mathematical solution.Furthermore,we will prove that this solution is valid for a much more general case of any cosmological redshift scaling consistent with:z=(R_(H_(0))/R_(H_(t)))^(x)-1.Haug and Tatum have only considered the most common assumptions of x=1 and x=1/2.Our solution involves simply solving an equation to determine the correct value of H_(0).This is possible because an exact mathematical relation between H_(0)and the CMB temperature has recently been established,in combination with the linearity in an R_(H_(t))=ct model.We also demonstrate that a thermodynamic form of the Friedmann equation is consistent with a wide range of redshift scalings,namely:z=(R_(H_(0))/R_(H_(t)))^(x)-1.
