Narrow Results

The Friedmann–Lemaître–Robertson–Walker (FLRW) metric used to describe the cosmic spacetime is based on the cosmological principle, which assumes homogeneity and isotropy throughout the Universe. It also adopts free-fall conditions via the selection of a constant lapse function, $g_{tt}=1$, regardless of whether or not the chosen energy–momentum tensor $T^{\alpha \beta }$ produces an accelerated expansion. This is sometimes justified by arguing that one may shift the gauge, if necessary, transforming the time $dt$ to a new coordinate $d{t}^{\prime }\equiv \sqrt{g_{tt}}dt$, thereby re-establishing a unitary value for $g_{t^{\prime }{t}^{\prime }}$. Previously, we have demonstrated that this approach is inconsistent with the Friedmann equations derived using comoving coordinates. In this paper, we advance this discussion significantly by using the Local Flatness Theorem in general relativity to prove that $g_{tt}$ in FLRW is inextricably dependent on the expansion dynamics via the expansion factor $a(t)$, which itself depends on the equation-of-state in $T^{\alpha \beta }$. One is therefore not free to choose $g_{tt}$ arbitrarily without ensuring its consistency with the energy–momentum tensor. We prove that the use of FLRW in cosmology is valid only for zero active mass, i.e. $\rho +3p=0$, where $\rho$ and $p$ are, respectively, the total energy density and pressure in the cosmic fluid.

This study focuses on the cosmological evolution of Barrow holographic dark energy (BHDE) in a flat FLRW-universe. We take into account a time-dependent scale factor $a(t)={[sinh(kt)]}^{\frac{1}{n}}$, where k and n are positive values, to find the solutions to field equations. This scale factor results in a smooth transition of the universe from its previous decelerating stage to its most recent accelerating stage. Using the Granda–Oliveros cut-off, we examine the chronology of the deceleration parameter, equation of state parameter, and density parameter, and we analyze the positive aspects of the BHDE model. Negative pressure values in this model suggest dark energy dominance, resulting in the universe’s acceleration. We use the statefinder parameters ($r,s$) to improve the accuracy of the results of the dark energy model that is similar to the $\mathrm{\Lambda }$-CDM model.

In this paper, an attempt is made to construct a Friedmann–Lemaitre–Robertson–Walker model in $f(R,T)$ gravity with a perfect fluid that yields acceleration at late times. We take $f(R,T)$ as $R+8\pi \mu T$. As in the $\mathrm{\Lambda }$CDM model, we take the matter to consist of two components, viz., ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_{\mu }$ such that ${\mathrm{\Omega }}_m+{\mathrm{\Omega }}_{\mu }=1$. The parameter ${\mathrm{\Omega }}_m$ is the matter density (baryons $+$ dark matter), and ${\mathrm{\Omega }}_{\mu }$ is the density associated with the Ricci scalar $R$ and the trace $T$ of the energy–momentum tensor, which we shall call dominant matter. We find that at present ${\mathrm{\Omega }}_{\mu }$ is dominant over ${\mathrm{\Omega }}_m$, and that the two are in the ratio 3:1–3:2 according to the three data sets: (i) 77 Hubble OHD data set, (ii) 580 SNIa supernova distance modulus data set and (iii) 66 pantheon SNIa data which include high red shift data in the range $0\le z\le 2.36$. We have also calculated the pressures and densities associated with the two matter densities, viz., $p_{\mu }$, ${\rho }_{\mu }$, $p_m$ and ${\rho }_m$, respectively. It is also found that at present, ${\rho }_{\mu }$ is greater than ${\rho }_m$. The negative dominant matter pressure $p_{\mu }$ creates acceleration in the universe. Our deceleration and snap parameters show a change from negative to positive, whereas the jerk parameter is always positive. This means that the universe is at present accelerating and in the past it was decelerating. State finder diagnostics indicate that our model is at present a dark energy quintessence model. The various other physical and geometric properties of the model are also discussed.