International Journal of Modern Physics D

In this paper, our interest lies in investigating the possibilities of reconstructing analytical solutions for some familiar bouncing models in the flat Friedmann–Lemaître–Robertson–Walker (FLRW) geometry. We inspect the various gravitational Lagrangians, which are efficient enough for reproducing analytical solutions for symmetric, oscillatory, power law and bounce from loop quantum cosmology settings. Equation of state parameter, energy conditions, stability analysis have been performed for each model to examine its validity. The outcomes determine that the $f(T,{𝒯})$ modified theory is the competitive candidate of extended theories on the cosmological scale.

Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field $(X,-X)$, which exists in all Lorentzian spacetimes, to construct a connection-independent symmetric tensor that represents the energy–momentum of the gravitational field. It solves the problem of the nonlocalization of gravitational energy–momentum in GR, preserves the ontology of the Einstein equation, and maintains the equivalence principle. The line element field provides MGR with the extra freedom required to describe dark energy and dark matter. An extended Schwarzschild solution for the matter-free Einstein equation of MGR is developed, from which the Tully–Fisher relation is derived, and the gravitational energy density is calculated. The mass of the invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to the result obtained from GR using a dark matter profile. Although dark matter in MGR is described geometrically, it has an equivalent representation as a particle with the property of a vector boson or a pair of fermions; the geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric and the spin-1 Klein–Gordon wave equation. The three classic tests of GR provide a comparison of the theories in the solar system and several parts of the cosmos. MGR provides the flexibility to describe inflation after the Big Bang and galactic anisotropies.

Here, we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed. Sometimes this leads to an unwanted doubling of the results. In this paper, we illustrate this issue with the example of two apparently different gravitational theories: (i) the (minimally coupled) Einstein-massless-scalar (EMS) system and (ii) the Sáez–Ballester theory (SBT). We demonstrate that the latter is not a scalar–tensor theory of gravity, as widely acknowledged. Moreover, SBT is identified with the EMS theory. As illustrations of this identification we show that several known solutions of SBT are also solutions of the EMS system and vice versa. Cosmological arguments are also considered. In particular, a dynamical systems-based demonstration of the dynamical equivalence between these theories is given. The study of the asymptotic dynamics of the Sáez–Ballester-based cosmological model shows that there are no equilibrium points which could be associated with accelerated expansion, unless one includes a cosmological constant term or a self-interacting scalar field. This is a well-known result for cosmological models which are based on the Einstein-self-interacting-scalar theory, also known as quintessence.

In this paper, we worked in the framework of an inflationary $f(R,T)$ theory in the presence of a canonical scalar field. More specifically, the $f(R,T)=\gamma R+2\kappa \alpha T$ gravity. The values of the dimensionless parameters $\alpha$ and $\gamma$ are taken to be $\alpha \ge 0$ and $0<\gamma \le 1$. The motivation for this study was the striking similarities between the slow-roll parameters of the inflationary model used in this work and the ones obtained by the rescaled Einstein–Hilbert gravity inflation $f(R)=\alpha R$. We examined a variety of potentials to determine if they agree with the current Planck Constraints. In addition, we checked whether these models satisfy the Swampland Criteria and we specified the exact region of the parameter space that produces viable results for each model. As we mention in Sec. 4, the inflationary $f(R,T)$ theory used in this work cannot produce a positive $n_T$ which implies that the stochastic gravitational wave background will not be detectable.

We study dynamical dark energy (DE) models within Einstein’s theory by means of matter perturbations and the growth index $\gamma$. Within four-dimensional General Relativity, we assume that DE does not cluster, and we adopt a linear ansatz for the growth index to investigate its impact on the deceleration parameter, $q$, and on the DE equation-of-state parameter, $w$. Following this approach, we identify a relationship between $q_0$ (today’s value of $q$) and $\gamma$, which to the best of our knowledge is new. For $w(z)$, we find that in most of the cases considered it crosses the $-1$ line (quintom) ending at a present day value $w_0>-1$. Furthermore, we show that an analytic expression for $w(z)$ may be obtained in the form of order (4,4) (or higher) Padé parametrizations.

In this paper, the modified $F(R)$ gravity theory with the function $F(R)=-(1/\beta )ln(1-\beta R)$ is studied. The action at small coupling $\beta$ becomes Einstein–Hilbert action. The bound on the parameter $\beta$ from local tests is $\beta \le 2\times 10^{-6}$ cm². We find the constant curvature solutions and it was shown that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. The potential and the mass of the scalar field (scalaron) are obtained in Einstein’s frame. The slow-roll cosmological parameters are studied and e-folds number is evaluated. The critical points of autonomous equations are analyzed. The function $m(r)$ that describes the deviation from the $\mathrm{\Lambda }$CDM model is calculated.

In this paper, we investigate the influence of tidal Love numbers on the equation-of-state (EoS) governing the interior matter distribution of a compact star within the framework of classical general relativity. By invoking a linear EoS for a spherically symmetric anisotropic matter configuration, we solve the Einstein field equations for an arbitrary EoS parameter. We subject our model to rigorous regularity, causality, and stability tests. In particular, we show that our model gives a very good approximation of the pulsar 4U 1608–52. We further demonstrate the intrinsic connection between the EoS parameter which describes the nature of the matter making up the stellar fluid and the tidal Love numbers.

One of the most significant discoveries in modern cosmology is that the universe is currently in a phase of accelerated expansion after a switch from a decelerated expansion. The redshift corresponding to this epoch is commonly referred to as the transition redshift $z_t$. In this work, we put constraints on the transition redshift with both model-independent and model-dependent approaches. We consider the recently compiled database of 32 Hubble parameter measurements and the Pantheon sample of Type Ia Supernovae (SNe). In order to include the possible systematic effects in this analysis, we use the full covariance matrix of systematic uncertainties for the Hubble parameter measurements. We plot a Hubble Phase Space Portrait (HPSP) between $Ḣ(z)$ and $H(z)$ in a model-independent way. From this HPSP diagram, we estimate the transition redshift as well as the current value of the equation of state parameter ${\omega }_0$ in a model-independent way. By considering H(z) measurements, we find the best fit value of $z_t=0.591_{-0.332}^{+0.332}$ and ${\omega }_0=-0.677_{-0.238}^{+0.238}$. We obtain the best fit value of $z_t=0.849_{-0.117}^{+0.117}$ and ${\omega }_0=-0.870_{-0.013}^{+0.013}$ using the Pantheon database. Further, we also use a model-dependent approach to determine $z_t$. Here, we consider a nonflat $\mathrm{\Lambda }$CDM model as a background cosmological model. We reconstruct the cosmic triangle plot among $log({\mathrm{\Omega }}_{m0})$, $-log(2{\mathrm{\Omega }}_{\mathrm{\Lambda }0})$ and $3log(1+z_t),$ where the constraints of each parameter are determined by the location in this triangle plot. By using ${\mathrm{\Omega }}_{m0}$ and ${\mathrm{\Omega }}_{\mathrm{\Lambda }0}$ values, we find the best value of the transition redshift $z_t=0.619_{-0.758}^{+0.580}$, which is in good agreement with the Planck 2018 results at $1\sigma$ confidence level. We also simulate the observed Hubble parameter measurements in the redshift range $0<z<2$ and perform the same analysis to estimate the transition redshift.