Inflationary solutions in general scalar tensor theory of gravitation

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.     

Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions, including the exponential expansion solutions of the scalar factor a for the bubble. We show that exponential expansion of the bubble continues with a short period, no matter whether the bubble is closed, flat, or open. The exponential expansion ends spontaneously when the bubble becomes large, that is, the scalar factor a of the bubble approaches a Planck length lp. We show that it is the quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.     

Ab-initio calculations of electric field gradient in Ru compounds and their implication on the nuclear quadrupole moments of $$^{99}\hbox {Ru}$$ and $$^{101}\hbox {Ru}$$101Ru

We study a spatially homogeneous and anisotropic cosmological model in the Einstein gravitational theory with a minimally coupled scalar field. We consider a non-interacting combination of scalar field and perfect fluid as the source of matter components which are separately conserved. The dynamics of cosmic scalar fields with a zero rest mass and an exponential potential are studied, respectively. We find that both assumptions of potential along with the average scale factor as an exponential function of scalar field lead to the logarithmic form of scalar field in each case which further gives power-law form of the average scale factor. Using these forms of the average scale factor, exact solutions of the field equations are obtained to the metric functions which represent a power-law and a hybrid expansion, respectively. We find that the zero-rest-mass model expands with decelerated rate and behaves like a stiff matter. In the case of exponential potential function, the model decelerates, accelerates or shows the transition depending on the parameters. The isotropization is observed at late-time evolution of the Universe in the exponential potential model.     

Hybrid natural low scale inflation

We discuss the phenomenological implications of Hybrid Natural Inflation models in which the inflaton is a pseudo-Goldstone boson but inflation is terminated by a second scalar field. A feature of the scheme is that the scale of breaking of the Goldstone symmetry can be lower than the Planck scale and so gravitational corrections are under control. We show that, for supersymmetric models, the scale of inflation can be chosen anywhere between the Lyth upper bound and a value close to the electroweak breaking scale. The observed density perturbations and spectral index are readily obtained by the choice of the free parameters. The tensor to scalar ratio and the spectral tilt are extremely small.     

On quintessential cosmological models and exponential potentials

We first study dark energy models with a minimally-coupled scalar field and generalized exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable. We analyze their analytical solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how quintessential scalar fields with exponential potentials can be connected to the inflationary phase, building up a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have been made by including also radiation into the model.     

Scale invariance and inflation

A scale invariant model for early universe inflationary cosmology is developed. In order to realize dilatation invariance and spontaneous symmetry breaking we introduce two scalar fields, a dilaton and an inflaton. The scale invariant theory encompasses the Brans-Dicke and induced-gravity models as limiting cases. The model is solved numerically for a wide class of initial conditions. We find that the inflationary epoch is generically characterized by a two phase evolution of the universe: A single or double exponential era and a power-law expansion. Onset of gravity triggers double exponential evolution of the scale factor. We further examine inflation in the Brans-Dicke theory and find that scale invariance is restored in the course of spontaneous symmetry breaking.     

Background Dynamics of Pre-inflationary Scenario in Brans-Dicke Loop Quantum Cosmology

Recently the background independent nonperturbative quantization has been extended to various theories of gravity and the corresponding quantum effective cosmology has been derived, which provides us with necessary avenue to explore the pre-inflationary dynamics. Brans-Dicke (BD) loop quantum cosmology (LQC) is one of such theories whose effective background dynamics is considered in this article. Starting with a quantum bounce, we explore the pre-inflationary dynamics of a universe sourced by a scalar field with the Starobinsky potential in BD-LQC. Our study is based on the idea that though Einstein's and Jordan's frames are classically equivalent up to a conformal transformation in BD theory, this is no longer true after quantization. Taking the Jordan frame as the physical one we explore in detail the bouncing scenario which is followed by a phase of a slow roll inflation. The three phases of the evolution of the universe, namely, bouncing, transition from quantum bounce to classical universe, and the slow roll inflation, are noted for an initially kinetic energy dominated bounce. In addition, to be consistent with observations, we also identify the allowed phase space of initial conditions that would produce at least 60 e-folds of expansion during the slow roll inflation.     

Probability of inflation in loop quantum cosmology

Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue (Hollands and Wald in Gen Relativ Gravit, 34:2043, 2002; Kofman et al. in J High Energy Phys 10:057, 2002); (Gibbons and Turok in Phys Rev D 77:063516, 2008). In particular, for a quadratic potential, Kofman et al. (J High Energy Phys 10:057, 2002) have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok (Phys Rev D 77:063516, 2008) have argued that this probability is suppressed by a factor of ~10⁻⁸⁵. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure necessary to specify a satisfactory measure. The second goal of the paper is to present a detailed analysis of the inflationary dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions, we address a sharper question than those investigated in Kofman et al. (J High Energy Phys 10:057, 2002), Gibbons and Turok (Phys Rev D 77:063516, 2008), Ashtekar and Sloan (Phys Lett B 694:108, 2010): What is the probability of a sufficiently long slow roll inflation which is compatible with the seven year WMAP data? We show that the probability is very close to 1. The material is so organized that cosmologists who may be more interested in the inflationary dynamics in LQC than in the subtleties associated with measures can skip that material without loss of continuity.     

Impact of generalized dissipative coefficient on warm inflationary dynamics in the light of latest Planck data

The warm inflation scenario in view of the modified Chaplygin gas is studied. We consider the inflationary expansion to be driven by a standard scalar field whose decay ratio \(\Gamma \) has a generic power-law dependence with the scalar field \(\phi \) and the temperature of the thermal bath T. By assuming an exponential power-law dependence in the cosmic time for the scale factor a(t), corresponding to the intermediate inflation model, we solve the background and perturbative dynamics considering our model to evolve according to (1) weak dissipative regime and (2) strong dissipative regime. Specifically, we find explicit expressions for the dissipative coefficient, scalar potential, and the relevant inflationary observables like the scalar power spectrum, scalar spectral index, and tensor-to-scalar ratio. The free parameters characterizing our model are constrained by considering the essential condition for warm inflation, the conditions for the model evolves according to weak or strong dissipative regime, and the 2015 Planck results through the \(n_s\)–r plane.     

Inflation in cosmological models with a non-minimally coupled, massless scalar field

A homogeneous, spatially flat cosmological model induced by a massless scalar field is investigated. The parameter ξ of coupling of the field with the curvature can take any value. It is shown that the range of values of ξ is divided into three regions, ξ<0, 0<ξ<1/6, and ξ>1/6, each of which is characterized by the behavior of the scale factor in it. The points ξ=0 and ξ=1/6 are singular. Stages with exponential and power-law inflation are found in the ranges 0<ξ<1/6 and ξ>1/6. An exponential inflationary stage with acceptable cosmological consequences can occur for small positive ξ. Kazan’ State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 53–57, March, 1997.     

Tachyon field in cosmology

We study cosmological effects of homogeneous tachyon field as dark energy. We concentrate on two different scalar field potentials, the inverse square potential and the exponential potential. These models have a unique feature that the matter density parameter and the density parameter for tachyons remain comparable for a large range in red-shift. It is shown that there exists a range of parameters for which the universe undergoes an accelerated expansion and the evolution is consistent with structure formation requirements. For a viable model we require fine tuning of parameters comparable to that in ACDM or in quintessence models. For the exponential potential, the accelerated phase is followed by a phase witha(t) α t ^2/3 thus eliminating a future horizon.     

Assisted Inflation in Bianchi VI0 Cosmologies

Exact models for Bianchi VI₀ spacetimes with multiple scalar fields with exponential potentials have been derived and analysed. It has been shown that these solutions, when they exist, attract neighbouring solutions in the two cases corresponding to interacting and non-interacting fields. Unlike the results obtained in a previous work dealing with the late-time inflationary behaviour of Bianchi VI₀ cosmologies, the knowledge of exact solutions has made possible to study in detail the occurrence of inflation before the asymptotic regime. As happened in preceding works, here as well inflation is more likely to happen with a higher number of non-interacting fields or a lower number of interacting scalar fields.     

Integrable Scalar Cosmologies I. Foundations and links with String Theory

We build a number of integrable one-scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non-integrable ones. These include the impossibility for the scalar to emerge from the initial singularity descending along asymptotically exponential potentials with logarithmic slopes exceeding a critical value (“climbing phenomenon”) and the inevitable collapse in a Big Crunch whenever the scalar tries to settle at negative extrema of the potential. We also elaborate on the links between these types of potentials and “brane supersymmetry breaking”, a mechanism that ties together string scale and scale of supersymmetry breaking in a class of orientifold models.     

Primordial fluctuations and non-Gaussianities in multifield Dirac-Born-Infeld inflation

We study Dirac-Born-Infeld inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We show that this could strongly affect the observable curvature power spectrum as well as the amplitude of non-Gaussianities, although their shape remains as in the single-field Dirac-Born-Infeld case.     

Loop quantum cosmology and slow roll inflation

In loop quantum cosmology (LQC) the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. Rather than growing unboundedly in the past, the Hubble parameter vanishes at the bounce and attains a finite universal maximum   at the end of super-inflation. These novel features lead to an unforeseen implication: in presence of suitable potentials all LQC dynamical trajectories are funneled to conditions which virtually guarantee slow roll inflation with more than 68 e-foldings, without any input from the pre-big bang regime. This is in striking contrast to certain results in general relativity, where it is argued that the a priori probability of obtaining a slow roll with 68 or more e-foldings is suppressed by a factor e−204$e^{-204}$.     

Local observation in eternal inflation

We consider landscape models that admit several regions where the conditions for eternal inflation hold. It is shown that one can use the no-boundary wave function to calculate small departures from homogeneity within our past light cone despite the possibility of much larger fluctuations on super horizon scales. The dominant contribution comes from the history exiting eternal inflation at the lowest value of the potential. In a class of landscape models this predicts a tensor to scalar ratio of about 10%. In this way the no-boundary wave function defines a measure for the prediction of local cosmological observations.     

Constraints on inflationary solutions in the presence of shear and bulk viscosity

Inflationary models and their claim to solve many of the outstanding problems in cosmology have been the subject of a great deal of debate over the last few years. A major sticking point has been the lack of both good observational and theoretical arguments to single out one particular model out of the many that solve these problems. Here we examine the degree of restrictiveness on the dynamical relationship between the cosmological scale factor and the inflation driving self-interaction potential of a minimally coupled scalar field, imposed by the condition that the scalar field is required to be real during a classical regime (the reality condition). We systematically look at the effects of this constraint on many of the inflationary models found in the literature within the FLRW framework, and also look at what happens when physically motivated perturbations such as shear and bulk viscosity are introduced. We find that in many cases, either the models are totally excluded or the reality condition gives rise to constraints on the scale factor and on the various parameters of the model.     

Inflation via logarithmic entropy-corrected holographic dark energy model

We study the inflation in terms of the logarithmic entropy-corrected holographic dark energy (LECHDE) model with future event horizon, particle horizon, and Hubble horizon cut-offs, and we compare the results with those obtained in the study of inflation by the holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in the HDE model. Moreover, the consistency with the observational data in the LECHDE model of inflation constrains the reheating temperature and Hubble parameter by one parameter of holographic dark energy and two new parameters of logarithmic corrections.     

Unitarity bounds on low scale quantum gravity

We study the unitarity of models with low scale quantum gravity both in four dimensions and in models with a large extra-dimensional volume. We find that models with low scale quantum gravity have problems with unitarity below the scale at which gravity becomes strong. An important consequence of our work is that their first signal at the Large Hadron Collider would not be of a gravitational nature such as graviton emission or small black holes, but rather would be linked to the mechanism which fixes the unitarity problem. We also study models with scalar fields with non-minimal couplings to the Ricci scalar. We consider the strength of gravity in these models and study the consequences for inflation models with non-minimally coupled scalar fields. We show that a single scalar field with a large non-minimal coupling can lower the Planck mass in the TeV region. In that model, it is possible to lower the scale at which gravity becomes strong down to 14 TeV without violating unitarity below that scale.     

Charged Randall-Sundrum Braneworld Type II with Higher Order Curvature Corrections from Superstring Arguments and Dominated by Quintessence

We discuss a new class of RSII braneworld cosmology exhibiting accelerated expansion and dominated by quintessence. It is explicitly demonstrated that the universe expansion history （transition from inflation to deceleration epoch to acceleration and effective quintessence era） may naturally occur in such unified theory for some classes of inverse scalar potentials. Besides a decaying effective cosmological constant, the model incorporates an increasing black hole mass, an increasing Maxwellian electrical charge with cosmic time and a time-dependent brahe tension. The cosmological model exhibits several features of cosmological and astrophysical interest for both the early and late universe consistent with recent observations, in particular the ones concerned with the gravitational constants, black holes masses and charges and variation of the gauge coupling parameters with cosmic time. One interesting mark of the constructed model concerns the fact that a black hole mass surrounded by quintessence energy may increase with time even if the horizon disappears.