No Arabic abstract
We study the role that a cosmic triad in the generalized $SU(2)$ Proca theory, specifically in one of the pieces of the Lagrangian that involves the symmetric version $S_{mu u}$ of the gauge field strength tensor $F_{mu u}$, has on dark energy and primordial inflation. Regarding dark energy, the triad behaves asymptotically as a couple of radiation perfect fluids whose energy densities are negative for the $S$ term but positive for the Yang-Mills term. This leads to an interesting dynamical fine-tuning mechanism that gives rise to a combined equation of state parameter $omega simeq -1$ and, therefore, to an eternal period of accelerated isotropic expansion for an ample spectrum of initial conditions. Regarding primordial inflation, one of the critical points of the associated dynamical system can describe a prolonged period of isotropic slow-roll inflation sustained by the $S$ term. This period ends up when the Yang-Mills term dominates the energy density leading to the radiation dominated epoch. Unfortunately, in contrast to the dark energy case, the primordial inflation scenario is strongly sensitive to the coupling constants and initial conditions. The whole model, including the other pieces of the Lagrangian that involve $S_{mu u}$, might evade the recent strong constraints coming from the gravitational wave signal GW170817 and its electromagnetic counterpart GRB 170817A.
We explore the bound of the trans-Planckian censorship conjecture on an inflation model with multiple stages. We show that if the first inflationary stage is responsible for the primordial perturbations in the cosmic microwave background window, the $e$-folding number of each subsequent stage will be bounded by the energy scale of the first stage. This seems to imply that the lifetime of the current era of accelerated expansion (regarded as one of the multiple inflationary stages) might be a probe for distinguishing inflation from its alternatives. We also present a multistage inflation model in a landscape consisting of anti-de Sitter vacua separated by potential barriers.
The interaction between two initially causally disconnected regions of the universe is studied using analogies of non-commutative quantum mechanics and deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) metrics with scale factors $a$ and $b$ and cosmological constants $Lambda_a$ and $Lambda_b$, respectively. The causality is turned on by positing a non-trivial Poisson bracket $[ {cal P}_{alpha}, {cal P}_{beta} ] =epsilon_{alpha beta}frac{kappa}{G}$, where $G$ is Newtons gravitational constant and $kappa $ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of $kappa$. In this model the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for $kappa ll1 $ is also studied.
Non-canonical scalar fields with the Lagrangian ${cal L} = X^alpha - V(phi)$, possess the attractive property that the speed of sound, $c_s^{2} = (2,alpha - 1)^{-1}$, can be exceedingly small for large values of $alpha$. This allows a non-canonical field to cluster and behave like warm/cold dark matter on small scales. We demonstrate that simple potentials including $V = V_0coth^2{phi}$ and a Starobinsky-type potential can unify dark matter and dark energy. Cascading dark energy, in which the potential cascades to lower values in a series of discrete steps, can also work as a unified model. In all of these models the kinetic term $X^alpha$ plays the role of dark matter, while the potential term $V(phi)$ plays the role of dark energy.
The effective field theory (EFT) of cosmological perturbations is a useful framework to deal with the low-energy degrees of freedom present for inflation and dark energy. We review the EFT for modified gravitational theories by starting from the most general action in unitary gauge that involves the lapse function and the three-dimensional geometric scalar quantities appearing in the Arnowitt-Deser-Misner (ADM) formalism. Expanding the action up to quadratic order in the perturbations and imposing conditions for the elimination of spatial derivatives higher than second order, we obtain the Lagrangian of curvature perturbations and gravitational waves with a single scalar degree of freedom. The resulting second-order Lagrangian is exploited for computing the scalar and tensor power spectra generated during inflation. We also show that the most general scalar-tensor theory with second-order equations of motion-Horndeski theory-belongs to the action of our general EFT framework and that the background equations of motion in Horndeski theory can be conveniently expressed in terms of three EFT parameters. Finally we study the equations of matter density perturbations and the effective gravitational coupling for dark energy models based on Horndeski theory, to confront the models with the observations of large-scale structures and weak lensing.
We study the intermediate inflation in a non-canonical scalar field framework with a power-like Lagrangian. We show that in contrast with the standard canonical intermediate inflation, our non-canonical model is compatible with the observational results of Planck 2015. Also, we estimate the equilateral non-Gaussianity parameter which is in well agreement with the prediction of Planck 2015. Then, we obtain an approximation for the energy scale at the initial time of inflation and show that it can be of order of the Planck energy scale, i.e. ${M_P} sim {10^{18}},{rm{GeV}}$. We will see that after a short period of time, inflation enters in the slow-roll regime that its energy scale is of order ${M_P}/100 sim ;{10^{16}}{rm{GeV}}$ and the horizon exit takes place in this energy scale. We also examine an idea in our non-canonical model to overcome the central drawback of intermediate inflation which is the fact that inflation never ends. We solve this problem without disturbing significantly the nature of the intermediate inflation until the time of horizon exit.