The principal goal of this paper is to use attempts at reconciling the Swift long gamma-ray bursts ( LGRBs ) with the star formation history ( SFH ) to compare the predictions of \Lambda CDM with those in the R _ { h } = ct Universe .
In the context of the former , we confirm that the latest Swift sample of GRBs reveals an increasing evolution in the GRB rate relative to the star formation rate ( SFR ) at high redshifts .
The observed discrepancy between the GRB rate and the SFR may be eliminated by assuming a modest evolution parameterized as ( 1 + z ) ^ { 0.8 } —perhaps indicating a cosmic evolution in metallicity .
However , we find a higher metallicity cut of Z = 0.52 Z _ { \odot } than was seen in previous studies , which suggested that LGRBs occur preferentially in metal poor environments , i.e. , Z \sim 0.1 - 0.3 Z _ { \odot } .
We use a simple power-law approximation to the high- z ( \ga 3.8 ) SFH , i.e. , R _ { SF } \propto [ ( 1 + z ) / 4.8 ] ^ { \alpha } , to examine how the high- z SFR may be impacted by a possible abundance evolution in the Swift GRB sample .
For an expansion history consistent with \Lambda CDM , we find that the Swift redshift and luminosity distributions can be reproduced with reasonable accuracy if \alpha = -2.41 _ { -2.09 } ^ { +1.87 } .
For the R _ { h } = ct Universe , the GRB rate is slightly different from that in \Lambda CDM , but also requires an extra evolutionary effect , with a metallicity cut of Z = 0.44 Z _ { \odot } .
Assuming that the SFR and GRB rate are related via an evolving metallicity , we find that the GRB data constrain the slope of the high- z SFR in R _ { h } = ct to be \alpha = -3.60 _ { -2.45 } ^ { +2.45 } .
Both cosmologies fit the GRB/SFR data rather well .
However , in a one-on-one comparison using the Aikake Information Criterion , the best-fit R _ { h } = ct model is statistically preferred over the best-fit \Lambda CDM model with a relative probability of \sim 70 \% versus \sim 30 \% .