Conjecture on Cosmological Redshift: Action Instead of Velocity, No Need for Dark Energy

At cosmos scale, parameter “Action” would replace parameter “Velocity”. Photon property “ x=ct ” is the core of special relativity. Here, it is proposed to use other photon property “ E=hν ”. By analogy with Lorentz princeps transformation ( x,ct ) a so-called “Lorentz-Action” transformation ( E,hν ) is considered. ( E ¯ h ν ¯ )= γ ( A/h ) ( 1 −A/h −A/h 1 )( E hν ) . Such a transformation keeps Planck constant “h” invariant and for a photon gives: ν ¯ ν = ( 1−A/h 1+A/h ) 1/2 ⇔ A h = 1− ( ν ¯ /ν ) 2 1+ ( ν ¯ /ν ) 2 . Which is similar to relativistic longitudinal redshift: ν ¯ ν = ( 1−V/c 1+V/c ) 1/2 ⇔ V c = 1− ( ν ¯ /ν ) 2 1+ ( ν ¯ /ν ) 2 . Thus, present results on V/c would apply to A/h. A/h would increase with time, which is consistent with the concept of action. By giving up the concept of velocity at cosmos scale, one gives up the concept of accelerating expansion of universe. Thus, there would be no need for dark energy.