The expansion model implied by this question is known as the "coasting universe". 

Triggered mostly by the observed coincidence that the gravitational radius $R_0$ of the universe at current time $t_0$ [equals $c t_0$][1], once in a while research papers appear that [try to fit cosmological observations to this model][2]. However, the observed acceleration of the cosmological expansion renders such exercises futile. (See also: [this question][3].)


  [1]: http://arxiv.org/abs/0711.4810
  [2]: http://arxiv.org/abs/astro-ph/0209209
  [3]: http://physics.stackexchange.com/questions/73516/fulvio-melias-linear-universe