Unimodular Theory of Gravity in Light of the Latest Cosmological Data

Abstract

The unimodular theory of gravity is an alternative perspective to traditional Einstein's general relativity and opens new possibilities for exploring its implications in cosmology. In this paper, we investigate the unimodular gravity (UG) with the latest cosmological data from the Pantheon sample of Type Ia supernovae (SN), Baryon Acoustic Oscillations (BAO), and the observational H(z) data from Differential Age method (DA). We consider a model consisting of a generalized cosmological constant with radiation and dark matter. The considered theory respects only unimodular coordinate transformations. We fit our model with low-redshift data from SN and DA and determine the value of parameter $\xi$ of the theory. We find the best-fit value of parameter $\xi =6.23 \pm 0.5$; which deviates from 6, for which the theory becomes the standard general theory of relativity. We further study the Hubble constant problem by combining the SN and DA data with BAO data. We observe deviation in the value of $H_0$ from the standard $\Lambda$CDM model. We obtain $H_0$ as $70.7 \pm 4.1 \ \mbox{Km s}^{-1} \mbox{Mpc} ^{-1}$ and $69.24 \pm 0.90 \ \mbox{Km s}^{-1} \mbox{Mpc} ^{-1}$ from supernovae data and BAO data, respectively in unimodular gravity. Combining the BAO data with SN+DA data set, we obtain $H_0$ as $70.57 \pm 0.56 \ \mbox{Km s}^{-1} \mbox{Mpc} ^{-1}$.