Narrow Results

It is shown how quantum fluctuations of the radiation during the contraction era of a comes back empty (CBE) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison–Zel’dovich–Peebles sense. It is necessary to be consistent with observations of large scale structure.

In a cyclic entropy model in which the extroverse is jettisoned at turnaround with a Come Back Empty (CBE) assumption, we address the matching of the contaction scale factor $â(t)=f(t_T)a(t)$ to the expansion scale factor $a(t)$, where $f(t_T)$ is the ratio at turnaround of the introverse to the extroverse radii. Such matching is necessary for infinite cyclicity and fixes the CBE period at $\sim$ 2.6 Ty.

Among many models which can describe the bouncing cosmology, a matter bounce scenario that is deformed by a running vacuum model of dark energy (RVM-DE) has been interested. In this research, I show that a class of RVM-CDM (cold dark matter) model can also describe a cyclical cosmology in which the universe undergoes cycles of expansion to the contraction phase and vice versa. To this end, following our previous work, I consider one of the most successful classes of RVM-CDM model in bouncing cosmology, ${\rho }_x=n_0+n_2{H}^2+n_4{H}^4$, in which the power spectral index gets a red tilt and the running of the spectral index may give a negative value by choosing the appropriate value of parameters $(n_0$, $n_2$, $n_4)$, which is consistent with the cosmological observations. It is worthwhile to mention that most matter bounce models do not produce this negative value. However, the main purpose of this paper is to investigate the RVM-CDM model in the turnaround phase. Far from the bounce in a phantom expanding universe, the turnaround conditions are investigated before the occurrence of a sudden big rip. By analyzing the Hubble parameter, equation of state (EoS) parameter, and deceleration parameter around the turnaround, we show that a successful turnaround may occur after an expansion in an interacting case of RVM-CDM by choosing the appropriate value of parameters. A minimum value for the interaction parameter is obtained and also find any relation between other model parameters. Finally, the effect of each parameter on a turnaround is studied, and we see that the transition time from accelerating to decelerating expansion can occur earlier for larger values of interaction parameter. Also, in several graphs, the effect of the second term in DE density, including $H^2$, is studied, and we see that by increasing its coefficient, $n_2$, the transition point leads to lower values.

The present work investigates the implications of incorporating noncommutativity into $f(R)$ gravity. In particular, we explore the proposed framework in a flat Friedmann–Robertson–Lamaître–Walker background. We introduced the noncommutativity between the coordinates and the momenta, in a $2n$-dimensional phase space. Applying the machinery of canonical quantization we obtain the noncommutative version of the Wheeler–DeWitt equation, and using a WKB-type approximation we can get analytical solutions for the model examining two cases for the leading noncommutative coefficient. In the first, solutions for the scale factor present a structure similar to previous solutions reported in the literature. The second one, in contrast to its commutative counterpart, the solutions obtained for the scale factor show that its evolution has the behavior of a non-singular cyclic universe. Also, we present the demeanor of the Hubble parameter and the effective equation of state parameter, where the latter crosses the “$-1$” divide line.

Recent works have shown the important role nonlinear electrodynamics (NLED) can have in two crucial questions of cosmology, concerning particular moments of its evolution for very large and for low-curvature regimes, that is for very condensed phase and at the present period of acceleration. We present here a toy model of a complete cosmological scenario in which the main factor responsible for the geometry is a nonlinear magnetic field which produces a Friedmann–Robertson–Walker homogeneous and isotropic geometry. In this scenario we distinguish four distinct phases: a bouncing period, a radiation era, an acceleration era, and a re-bouncing period. It has already been shown that in NLED a strong magnetic field can overcome the inevitability of a singular region typical of linear Maxwell theory; on the other extreme situation, that is for very weak magnetic field it can accelerate the expansion. The present model goes one step further: after the acceleration phase the universe re-bounces and enters into a collapse era. This behavior is a manifestation of the invariance under the dual map of the scale factor a(t) → 1/a(t), a consequence of the corresponding inverse symmetry of the electromagnetic field (F → 1/F, where F ≡ F^μνF_μν) of the NLED theory presented here. Such sequence collapse–bouncing–expansion–acceleration–re-bouncing–collapse constitutes a basic unitary element for the structure of the universe that can be repeated indefinitely yielding what we call a cyclic magnetic universe.

We address how to construct an infinitely cyclic universe model. A major consideration is to make the entropy cyclic which requires the entropy to be reset to zero in each cycle expansion $\to$ turnaround $\to$ contraction $\to$ bounce $\to$ etc. Here, we reset entropy at the turnaround by selecting the introverse (visible universe) from the extroverse which is generated by the accelerated expansion. In the model, the observed homogeneity is explained by the low entropy at the bounce. The observed flatness arises from the contraction together with the reduction in size between the expanding and contracting universe. The present flatness is predicted to be very precise.

Although General Relativity (GR) is an extremely successful theory, at least for weak gravitational fields, it breaks down at very high energies. For example, extrapolating the expansion of the Universe backwards in time yields an infinite energy density, which is referred to as the initial singularity problem. Quantum Gravity is expected to provide a solution to this open question. In fact, one alternative scenario to the Big Bang, that avoids the singularity, is offered by Loop Quantum Cosmology (LQC), which predicts that the Universe undergoes a collapse to an expansion through a bounce. In this work we use metric f(R) gravity to reproduce the modified Friedmann equations, which have been obtained in the context of modified loop quantum cosmologies (mLQC). Using a order reduction method, we obtain covariant effective actions that lead to a bounce, for specific models of mLQC, considering a massless scalar field.

Cosmological hysteresis has interesting and vivid implications in the scenario of a cyclic bouncy universe. This, purely thermodynamical in nature, is caused by the asymmetry in the equation of state parameter during expansion and contraction phase of the universe, due to the presence of a single scalar field. When applied to variants of modified gravity models this phenomenon leads to the increase in amplitude of the consecutive cycles of the universe, provided we have physical mechanisms to make the universe bounce and turnaround. This also shows that the conditions which creates a universe with an ever increasing expansion, depend on the signature of ∮ pdV and on model parameters.