Narrow Results

In this paper, we use our recently generalized black hole entropy formula to propose a quantum version of the Friedmann equations. In particular, starting from the differential version of the first law of thermodynamics, we are able to find Planckian (noncommutative) corrections to the Friedmann flat equations. The so modified equations are formally similar to the ones present in Gauss–Bonnet gravity, but in the ordinary 3+1 dimensions. As a consequence of these corrections, by considering negative fluctuations in the internal energy that are allowed by quantum field theory, our equations imply a maximum value both for the energy density $\rho$ and for the Hubble flow H, i.e. the big bang is ruled out. Conversely, by considering positive quantum fluctuations, we found no maximum for $\rho$ and H. Nevertheless, by starting with an early time energy density $\rho \sim 1/t^2$, we obtain a value for the scale factor $a(t)\sim e^{\sqrt{t}}$, implying a finite Planckian universe at t = 0, i.e. the point-like big bang singularity is substituted by a universe of Planckian size at t = 0. Finally, we found possible higher order Planckian terms to our equations together with the related corrections of our generalized Bekenstein–Hawking entropy.

We consider a homogeneous and isotropic Universe, described by the minisuperspace Lagrangian with the scale factor as a generalized coordinate. We show that the energy of a closed Universe is zero. We apply the uncertainty principle to this Lagrangian and propose that the quantum uncertainty of the scale factor causes the primordial fluctuations of the matter density. We use the dynamics of the early Universe in the Einstein–Cartan theory of gravity with spin and torsion, which eliminates the big-bang singularity and replaces it with a nonsingular bounce. Quantum particle production in highly curved spacetime generates a finite period of cosmic inflation that is consistent with the Planck satellite data. From the inflated primordial fluctuations we determine the magnitude of the temperature fluctuations in the cosmic microwave background, as a function of the numbers of the thermal degrees of freedom of elementary particles and the particle production coefficient which is the only unknown parameter.

In this work, we study the effects of Generalized Uncertainty Principle on the evolution of the Universe through Friedmann’s equations. We show that the effects are equivalent to those of the cosmological constant and thus they constitute an additional contribution in the acceleration of the expansion of the Universe.

Active motion is a concept in complex systems theory and was successfully applied to various problems in nonlinear dynamics. Explicit studies for gravitational potentials were missing so far. We interpret the Friedmann equations with cosmological constant as a dynamical system, which can be made "active" in a straightforward way. These active Friedmann equations lead to a cyclic universe, which is shown numerically.

We apply the holographic principle and the equipartition law of energy to the apparent horizon of a Friedmann–Robertson–Walker universe and derive the Friedmann equation describing the dynamics of the universe. We also show that the equipartition law of energy can be interpreted as the first law of thermodynamics at the apparent horizon. The consistency check shows that our derivation is correct for –1 < w < –(1/3), a value that matches the recent cosmological observations.

Because of the dynamical equivalence between the f(R) gravity and the Brans-Dicke theory, the dynamical equation in the f(R) gravity is suggested to be derived from a view point of thermodynamics here. By a conformal transformation, the Brans–Dicke theory in the Jordan frame could be expressed as a minimal coupling scalar field theory in Einstein frame. Using the entropy-area relation , the correct Friedmann equations could be gotten in both frames. Furthermore, we also discuss the corresponding generalized Misner–Sharp energies for theoretical consistence.

We show that by adding a cosmological constant term to the Starobinsky model, it can be solved exactly without using the slow-roll approximation.

In this work, we construct a noncommutative version of the Friedmann equations in the framework of effective loop quantum cosmology, extending and applying the ideas presented in a previous proposal by some of the authors. The model under consideration is a flat FRW spacetime with a free scalar field. First, noncommutativity in the momentum sector is introduced. We establish the noncommutative equations of motion and obtain the corresponding exact solutions. Such solutions indicate that the bounce is preserved, in particular, the energy density is the same as in the standard LQC. We also construct an extension of the modified Friedmann equations arising in effective LQC which incorporates corrections due to noncommutativity, and argue that an effective potential is induced. This, in turn, leads us to investigate the possibility of an inflationary era. Finally, we obtain the Friedmann and the Raychaudhuri equations when implementing noncommutativity in the configuration sector. In this case, no effective potential is induced.

In this study, we investigate the effects of the one- and two-parameters deformed systems on the Friedmann equations of the Friedmann–Robertson–Walker (FRW) universe by using the entropic gravity approach in the framework of the early universe era. We give simplified forms for the deformed Unruh temperature and Einstein field equations for three different deformed systems. Based on these compact equations, we derive the Friedmann equations with the effective gravitational and cosmological terms.

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting $f(\bar{R},\bar{T})$ gravity within the framework of a nonstandard theory, called K-essence theory, where $\bar{R}$ represents the Ricci scalar and $\bar{T}$ denotes the trace of the energy–momentum tensor associated with the K-essence geometry. The Dirac–Born–Infeld (DBI) nonstandard Lagrangian has been employed to generate the emergent gravity metric $({\bar{G}}_{\mu \nu })$ associated with the K-essence. This metric is distinct from the usual gravitational metric $(g_{\mu \nu })$. It has been shown that under a flat Friedmann–Lemaître–Robertson–Walker (FLRW) background gravitational metric, the modified field equations and the Friedmann equations of the $f(\bar{R},\bar{T})$ gravity are distinct from the usual ones. In order to get the equation of state (EoS) parameter $\omega$, we have solved the Friedmann equations by taking into account the function $f(\bar{R},\bar{T})\equiv f(\bar{R})+\lambda \bar{T}$, where $\lambda$ represents a parameter within the model. We have found a relationship between $\omega$ and time for different kinds of $f(\bar{R})$ by treating the kinetic energy of the K-essence scalar field (${\dot{\varphi }}^2$) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on ${\dot{\varphi }}^2$. By presenting graphical representations of the EoS parameter with time, we show that our model is consistent with the data of SNIa$+$BAO$+$$H(z)$ within a certain temporal interval.

We reconstruct $F({𝒢})$ gravity theory with an exponential scale factor to realize the bouncing behavior in the early universe and examine the asymptotic behavior of late-time solutions in this model. We propose an approach for the construction of asymptotic expansions of solutions of the Friedmann equations on the basis of Puiseux series.