Toy Model of Quantum Cosmology with Evolving Dark Energy

Qualitatively we assume that, at any stage of cosmic evolution, 1) Space-time curvature follows,GMt�=Rtc2whereMtandRtrepresent the cosmic mass and radius respectively. 2) Planck scaleHubble parameter plays a crucial role in cosmic evolution. 3) Ratio of cosmic mass and volume isequal to the ordinary matter density. With further research, a unified model of ‘quantum cosmology’with evolving dark energy can be developed.Proceeding further, we define the Planck scale Hubble parameter,Hpl�=√c5G~�1:86�1043sec1and apply it to cosmological data fitting and prediction in the form oft�=[1 + ln(HplHt)]whereHtis the running Hubble parameter. At any stage of cosmic evolution: 1) Ratio of ordinarymatter density and critical density is,(ΩOM)t�=(1+pt2)(11+t). 2) Ratio of dark matterdensity and critical density is,(ΩDM)t�=(1+pt2)2(11+t). 3) Ratio of dark energy density andcritical energy density is,(ΩDE)t�=1[(ΩOM)t+ (ΩDM)t]. 4) Ratio of dark matter densityand ordinary matter density is,(ΩDM)t(ΩOM)t�=(1+pt2). 5) Cosmic radius and (ordinary) mass are:Rt�=√2(ΩOM)t(cHt)andMt�=√2(ΩOM)t(c3GHt)respectively. 6) Thermal wavelength andtemperature are :(�max)t�=(1+pt2)√Rt(Rt)plandTt�=2:898�103Km(�max)trespectively where(Rt)pl�=2√G~c3. 7) Observed anisotropy in current CMBR temperature can be understoodwith the relational condition:((ΩOM)0(ΩDM)0)galaxyis greater than or less than(1+p02)1. 8) For(z+ 1)�1100, cosmic scale factor and age are:(1z+1)�[exp(0t2)]1�T0Tt�√H0Htandt�(1+z)32H0�pz+1Ht�(H0:75tH0:250)1respectively whereHt�=Hpl0[2 ln(z+1)]�(1 +z)2H0. 9)Cosmic expansion velocity is,Vt�=√2(ΩOM)tc.