Narrow Results

In this study, we examine two models of the scalar field, that is, a normal scalar field and a tachyon scalar field in $F(R,T,X,\varphi )$ gravity to describe cosmic acceleration of the universe, where $R$, $T$ and $X$ are Ricci curvature scalar, trace of energy–momentum tensor and kinetic energy of scalar field $\varphi$, respectively. Using the minimal-coupling Lagrangian $F(R,T,X,\varphi )=f(R)+\beta T^n+f(X,\varphi )$, for both the scalar models we obtain a viable cosmological system, where $\beta$ and $n$ are real constants. While a normal scalar field gives a system describing expansion from the deceleration to the late-time acceleration, tachyon field together with $R^{\sigma }$ in the system produces a quintessential expansion which is very close to de Sitter point, where we find a new condition $1<\sigma <1.005$ for inflation.

In this work, we study the interaction between the dark matter (DM) component and the dark energy (DE) component using the Tsallis holographic dark energy (THDE) density expression for a Bianchi type-II space–time within the framework of general relativity (GR). To obtain the exact solutions of Einstein’s field equations, we use two constraints: (i) the expansion scalar $(𝜃)$ of the Universe is proportional to the component ${\sigma }_1^1$ of the shear tensor $\left({\sigma }_i^i\right)$, i.e. $𝜃\propto {\sigma }_1^1$ and (ii) we assume that the scale factor follows the Hybrid Expansion Law (HEL). We have discussed some geometrical and physical parameters of our model such as the deceleration parameter (DP) and the equation of state (EoS) parameter. In these parameters, we plot their behavior in terms of redshift $z$. We observe that the DP evolves from the early decelerating phase to the current accelerating phase with a current value consistent with the observation data. The EoS parameter evolves from a state of a stiff-matter fluid-dominated era $({\omega }_T=1)$ for high redshift $z$ to a $\mathrm{\Lambda }$CDM era $({\omega }_T=-1)$ in the later times. Also, we have established a correspondence between the THDE model and the tachyon scalar field dark energy model. We have reconstructed the potential and the tachyon scalar field, which describes the current accelerated expansion of the Universe. Finally, using 51 values of observed Hubble measurement and the technique $R^2$-test, we found the best fit value for the model parameters $\alpha$, $\beta$ and $H_0$ (current value of the Hubble parameter). These results are consistent with the new measurements of $H_0$.³⁷

We explore the swampland conjectures of quintessence and tachyon scalar field models in $f(T)$ and Einstein gravities, respectively. In $f(T)$ gravity, we consider cold and warm (by assuming generalized dissipative coefficient) inflationary scenarios and develop constraints on de-Sitter conjectures through Bekenstein entropy relation. In usual inflation, the de-Sitter conjecture constraint becomes constant (in terms of models constant parameters) which can be easily analyzed for its validity (i.e., $\frac{\left|V^{\prime }\right|}{V}\le O(1)$). However, in warm inflation, we analyze the de-Sitter conjecture constraint through $\frac{{\tau }^{\prime }V}{\tau V^{\prime }}$, i.e., if $\frac{{\tau }^{\prime }V}{\tau V^{\prime }}<1$ then $\frac{\left|V^{\prime }\right|}{V}\le O(1)$ and hence we can obtain the required result. For evaluating this condition, we choose three well-known potentials such as monomial chaotic, hilltop and generalized exponential. It is observed that the condition $\frac{{\tau }^{\prime }V}{\tau V^{\prime }}<1$ satisfied for all three potentials in both regimes of dissipative coefficient for specific choice of constants. We also obtain satisfactory results of de-Sitter conjecture for tachyon and polytropic (with quintessence scalar field) in general relativity. We investigate the consistency of assumed potentials through inflationary parameters $n_s$ and $r$ comparing with Planck’s observational data 2018 and found them compatible with the recent observations.

We discuss the warm inflation in the presence of shaft potential $\left(V(\varphi )=\frac{M_p^4{\varphi }^{2n-2}}{{({\varphi }^n+g^n)}^{2-\frac{2}{n}}}\right)$, tachyon scalar field and the generalized form of dissipative coefficient $\mathrm{\Gamma }=a_0\frac{T^q}{{\varphi }^{q-1}}$. In this respect, we investigate the inflationary parameters (slow-roll parameters, number of e-folds, scalar-tensor power spectra, spectral indices, tensor-to-scalar ratio and running of scalar spectral index) in both strong and weak dissipative regimes. It is interesting to mention that our inflationary parametric results (tensor-scalar ratio, spectral index and running of spectral) are consistent with the recent observational data such as BICEP$2$, WMAP$9$ and latest Planck data.