Optical and X-ray GRB Fundamental Planes as Cosmological Distance Indicators


Gamma-Ray Bursts (GRBs), observed up to $z=9.4$, can be employed as standardized candles, extending the distance ladder beyond Supernovae Type Ia (SNe Ia, $z=2.26$). We standardize GRBs using the 3D fundamental plane relation among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. Combining SNe Ia and GRBs, we constrain the matter content $backslashOmega_backslashtextM= 0.299 backslashpm 0.009$ assuming a flat $backslashLambda$CDM cosmology with and without correcting for selection biases and redshift evolution. Using a similar 3D correlation in optical, we find that our optical GRB sample is as efficacious in the determination of $backslashOmega_backslashtextM$ as the X-ray sample. We trimmed our GRB samples to achieve tighter planes to be used to simulate additional GRBs. We determined how many GRBs are needed to be used as standalone probes to achieve a comparable precision on $backslashOmega_backslashtextM$ to the one obtained by SNe Ia only. $backslash$bf We achieve the error measurements derived using SNe Ia in (Conley et al. 2011) with 142 GRBs in optical considering the errorbars on the variables halved and in Betoule et al. (2014) with 284 optical GRBs, by considering that the error bars on the variables halved. Using a doubled sample (obtained by future machine learning approaches that allow both a lightcurve reconstruction and the estimates of GRBs for which the GRB is unknown) compared to our current one, with errorbars halved we will reach the same precision of (Scolnic et al. 2018) with 390 GRBs which will be uses as efficient standalone probes as SNe Ia by 2054.