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Register a new userNon-canonical scalar field in low anisotropy universe with intermediate inflation
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Added by
Haidar Sheikhahmadi
Publication date
2018
fields
Physics
and research's language is
English
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The behaviour of a non-canonical scalar field within an anisotropic Bianchi type I, spatially homogeneous, Universe in the framework of the intermediate inflation will be studied. It will be examined on the condition that both the anisotropy and non-canonical sources come together and is there any improvement in compatibility with the observational data originated from plank $2015$?. Based on this investigation it can be observed that automatically a steep potential which can manage inflation in a better way will be obtained. Additionally, as a common procedure for an inflationary study, we shall try to calculate the related inflationary observables such as the amplitude of the scalar perturbations, scalar and tensor spectral indices, tensor-to-scalar ratio, the running spectral index, and the number of e-folds. As an exciting part of our results, we will find that our model has a good consistency compared to data risen by CMB and different Planck results. To justify our claims, the well known canonical inflationary scenario in an anisotropic Bianchi type I Universe also will be evaluated.
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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.
We generally investigate the scalar field model with the lagrangian $L=F(X)-V(phi)$, which we call it {it General Non-Canonical Scalar Field Model}. We find that it is a special square potential(with a negative minimum) that drives the linear field solution($phi=phi_0t$) while in K-essence model(with the lagrangian $L=-V(phi)F(X)$) the potential should be taken as an inverse square form. Hence their cosmological evolution are totally different. We further find that this linear field solutions are highly degenerate, and their cosmological evolutions are actually equivalent to the divergent model where its sound speed diverges. We also study the stability of the linear field solution. With a simple form of $F(X)=1-sqrt{1-2X}$ we indicate that our model may be considered as a unified model of dark matter and dark energy. Finally we study the case when the baryotropic index $gamma$ is constant. It shows that, unlike the K-essence, the detailed form of F(X) depends on the potential $V(phi)$. We analyze the stability of this constant $gamma_0$ solution and find that they are stable for $gamma_0leq1$. Finally we simply consider the constant c_s^2 case and get an exact solution for F(X)
We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter $epsilon(phi)$ and its derivatives $epsilon^{prime }(phi)$ and $epsilon^{primeprime }(phi)$, thereby extracting general conditions on the tensor-to-scalar ratio $r$ and the running $n_{sk}$ at $phi_{H}$ where the perturbations are produced, some $50$ $-$ $60$ $e$-folds before the end of inflation. We find quite generally that for models where $epsilon(phi)$ develops a maximum, a relatively large $r$ is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter $xi_2(phi)$. To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic $epsilon(phi)$ decreasing during most part of inflation. Since at $phi_{H}$ the slow-roll parameter $epsilon(phi)$ is increasing, we thus require that $epsilon(phi)$ develops a maximum for $phi > phi_{H}$ after which $epsilon(phi)$ decrease to small values where most $e$-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion $Deltaphi_eequiv |phi_H-phi_e |$ is obtained with a sufficiently thin profile for $epsilon(phi)$ which, however, should not conflict with the second slow-roll parameter $eta(phi)$. As a consequence of this analysis we find bounds for $Delta phi_e$, $r_H$ and for the scalar spectral index $n_{sH}$. Finally we provide examples where these considerations are explicitly realised.
Assuming that a scalar field controls the inflationary era, we examine the combined effects of string and $f(R)$ gravity corrections on the inflationary dynamics of canonical scalar field inflation, imposing the constraint that the speed of the primordial gravitational waves is equal to that of lights. Particularly, we study the inflationary dynamics of an Einstein-Gauss-Bonnet gravity in the presence of $alpha R^2$ corrections, where $alpha$ is a free coupling parameter. As it was the case in the pure Einstein-Gauss-Bonnet gravity, the realization that the gravitational waves propagate through spacetime with the velocity of light, imposes the constraint that the Gauss-Bonnet coupling function $xi(phi)$ obeys the differential equation $ddotxi=Hdotxi$, where $H$ is the Hubble rate. Subsequently, a relation for the time derivative of the scalar field is extracted which implies that the scalar functions of the model, which are the Gauss-Bonnet coupling and the scalar potential, are interconnected and simply designating one of them specifies the other immediately. In this framework, it is useful to freely designate $xi(phi)$ and extract the corresponding scalar potential from the equations of motion but the opposite is still feasible. We demonstrate that the model can produce a viable inflationary phenomenology and for a wide range of the free parameters. Also, a mentionable issue is that when the coupling parameter $alpha$ of the $R^2$ correction term is $alpha<10^{-3}$ in Planck Units, the $R^2$ term is practically negligible and one obtains the same equations of motion as in the pure Einstein-Gauss-Bonnet theory, however the dynamics still change, since now the time derivative of $frac{partial f}{partial R}$ is nonzero.
We propose a model of cosmological evolution of the early and late Universe which is consistent with observational data and naturally explains the origin of inflation and dark energy. We show that the de Sitter accelerated expansion of the FLRW space with no matter fields (hereinafter, empty space) is its natural state, and the model does not require either a scalar field or cosmological constant or any other hypotheses. This is due to the fact that the de Sitter state is an exact solution of the rigorous mathematically consistent equations of one-loop quantum gravity for the empty FLRW space that are finite off the mass shell. Space without matter fields is not empty, as it always has the natural quantum fluctuations of the metric, i.e. gravitons. Therefore, the empty (in this sense) space is filled with gravitons, which have the backreaction effect on its evolution over time forming a self-consistent de Sitter instanton leading to the exponentially accelerated expansion of the Universe. At the start and the end of cosmological evolution, the Universe is assumed to be empty, which explains the origin of inflation and dark energy. This scenario leads to the prediction that the signs of the parameter 1+w should be opposite in both cases, and this fact is consistent with observations. The fluctuations of the number of gravitons lead to fluctuations of their energy density which in turn leads to the observed CMB temperature anisotropy of the order of 10^-5 and CMB polarization. In the frame of this scenario, it is not a hypothetical scalar field that generates inflation and relic gravitational waves but on the contrary, the gravitational waves (gravitons) generate dark energy, inflation, CMB anisotropy and polarization.
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