Narrow Results

In this paper, we aim to interpret the background gravitational effects appearing in quantum field theory on curved space-time by studying the Brownian motion of quantum states along with the Hamilton–Perelman Ricci flow. It has been shown that the Wiener measure automatically contains the Einstein–Hilbert action and the path-integral formulation of the scalar quantum field theory on curved space-time at the first order of local approximations. This provides a well-defined formulation of the path-integral measure for quantum field theory in the presence of gravity. However, we establish that the emergence of Einstein–Hilbert action is independent of the matter field interactions and is a merely entropic/geometric effect stemming from the nature of the Ricci flow of the universe geometry. We also extract an explicit formula for the cosmological constant in terms of the Ricci flow and Hamilton’s theorem for 3-manifolds. Then, we discuss the cosmological features of the FLRW solution in $\mathrm{\Lambda }$CDM Model via the derived equations of the Ricci flow. We also argue the correlation between our formulations and the entropic aspects of gravity. Finally, we provide some theoretical evidence that proves the second law of thermodynamics is the basic source of gravity and probably a more fundamental concept.

If the spacetime metric has anisotropic spatial curvature, one can still expand the universe as if it were isotropic, provided that the energy–momentum tensor satisfies a certain constraint. This leads to the so-called shear-free (SF) metrics, which have the interesting property of violating the cosmological principle while still preserving the isotropy of the cosmic microwave background (CMB) radiation. In this work, we show that SF cosmologies correspond to an attractor solution in the space of models with anisotropic spatial curvature. Through a rigorous definition of linear perturbation theory in these spacetimes, we show that SF models represent a viable alternative to explain the large-scale evolution of the universe, leading, in particular to a kinematically equivalent Sachs–Wolfe (SW) effect. Alternatively, we discuss some specific signatures that SF models would imprint on the temperature spectrum of CMB.

The recent measurements of the Hubble constant based on the standard $\mathrm{\Lambda }$CDM cosmology reveal an underlying disagreement between the early-Universe estimates and the late-time measurements. Moreover, as these measurements improve, the discrepancy not only persists but becomes even more significant and harder to ignore. The present situation places the standard cosmology in jeopardy and provides a tantalizing hint that the problem results from some new physics beyond the $\mathrm{\Lambda }$CDM model.

It is shown that a nonconventional theory — the Milne model — which introduces a different evolution dynamics for the Universe, alleviates the Hubble tension significantly. Moreover, the model also averts some long-standing problems of the standard cosmology, for instance, the problems related with the cosmological constant, the horizon, the flatness, the Big Bang singularity, the age of the Universe and the nonconservation of energy.

In this paper, we have examined the viability of the Bianchi type-V universe in Brans–Dicke (BD) theory of gravitation. We have discussed the interacting and non-interacting scenarios between dark matter (DM) and dark energy (DE) of the derived universe within the framework of BD theory. CCA technique has been applied to constrain the model parameters using 46 values of observational Hubble data (OHD), Pantheon data (the latest compilation of SNIa with 40 binned in the redshift range $0.014\le z\le 1.62)$ and their combined datasets. We establish an exact solution of the field equations to derive the dynamics of the derived universe and the obtained results are found to agree with the observations. We also noted a distinctive change in the sign of the deceleration parameter from positive to negative, as well as the presence of a transition red-shift exists. Using various observational data points, the evolution trajectories for $(r-s)$ diagnostic planes are shown to understand the geometrical behavior of the Bianchi-V model. Some physical properties of the universe are also discussed. It is also worth noting that the conclusions of the cosmological parameter are consistent with modern observational data.

This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime within the Lambda Cold Dark Matter ($\mathrm{\Lambda }$CDM) model. Using the radial free motion solutions, we provide two methods for characterizing the geodesics and defines a general formula that encapsulates all possible solutions, determined by two initial conditions. We show that the past light cone, event horizon, and particle horizon, can be considered as special cases of this overarching formula. Furthermore, the paper explores the free geodesics within the currently accepted cosmological model based on the recent Planck results, thoroughly examining the various possible geodesic scenarios.

In this study, our primary focus lies in meticulously exploring the intricacies of the universe by employing a flat Friedmann–Lemaître–Robertson–Walker (FLRW) model within the framework of $f(R,G)$ gravity. In our analysis, the $f(R,G)$ function is delineated as the sum of two distinct components, commencing with a quadratic correction of the geometric term denoted by $f(R)$, structured as $f(R)=R+\xi R^2$, alongside a matter term denoted by $f(G)=\lambda G^2$, where $R$ and $G$ symbolize the Ricci scalar and Gauss–Bonnet invariant, respectively. In the pursuit of solutions to the gravitational field equations within the $f(R,G)$ formalism, we embrace a specific expression for the scale factor, represented as $a={sinh}^{\frac{1}{\alpha }}(\beta t)$ [D. Rabha and R. R. Baruah, The dynamics of a hyperbolic solution in $f(R,G)$ gravity, Astron. Comput. 45 (2023) 100761]. In this context, the parameters $\alpha$ and $\beta$ intricately shape the scale factor’s behavior. The model posits the intriguing prospect of perpetual cosmic acceleration when $0<\alpha <1.19$, signifying a continuous expansion of the universe. Conversely, for $\alpha \ge 1.19$, the model proposes a pivotal transition from an early deceleration phase to the present accelerated epoch, a transformative shift in line with our understanding of cosmic evolution. Furthermore, the model demonstrates its credibility by satisfying Jean’s instability condition during the shift from a radiation-dominated era to a matter-dominated era, substantiating the formation of cosmic structures. In our analysis, a central focus is directed toward scrutinizing the equation of state parameter $\omega$ within our model. We delve into a comprehensive examination of the scalar field and meticulously assess the energy conditions surrounding the derived solution. To establish the robustness of our model, we deploy an array of diagnostic tools, including the Jerk, Snap, and Lerk parameters, along with the Om diagnostic, Classical stability of the model, and statefinder diagnostic tools, Observational Constraints on the Model Parameters. The outcomes, intertwined with a detailed analysis of both the results and the inherent intricacies of the model, are diligently clarified and presented.