Intermediate inflation on the brane

We explore the observational implications of models of intermediate inflation\ndriven by modified dispersion relations, specifically those representing the\nphenomenon of dimensional reduction in the ultraviolet limit. These models are\ndistinct from the standard ones because they do not require violations of the\nstrong energy condition, and this is reflected in their structure formation\nproperties. We find that they can naturally accommodate deviations from exact\nscale-invariance. They also make clear predictions for the running of the\nspectral index and tensor modes, rendering the models straightforwardly\nfalsifiable. We discuss the observational prospects for these models and the\nimplications these may have for quantum gravity scenarios.\n

Brane inflationary universe model in the context of a Chaplygin gas equation of state is studied. General conditions for this model to be realizable are discussed. In the high-energy limit and by using a chaotic potential we describe in great details the characteristic of this model. The parameters of the model are restricted by using recent astronomical observations.

Brane inflationary universe model in the context of logamediate inflation is studied. As the energy density we consider two different fields, first a standard scalar field, and then a tachyon field. In the high-energy limit we describes the conditions for theses models. The parameters of our models are constrained from the observational data.

The Standard Model Lagrangian has an approximate scale symmetry in the high-energy limit. This observation can be included in the fundamental principle of the ultimate theory of Nature as the requirement of the exact quantum scale invariance. In this setup, all low-energy particle phenomenology can be obtained as a result of the spontaneous breaking of scale symmetry leading to the presence of the extra massless scalar field -- the dilaton. We explore the scenario in which this field is capable of solving the strong CP-problem in QCD in a similar way as in QCD axion models. The dilaton, playing the role of the axion, is coupled to the QCD sector and acquires a mass term due to non-perturbative breaking of scale symmetry. We show that the dilaton can form dark matter after the low-scale inflation. As a proof of concept, we construct a model of Higgs-driven inflation consistently realising the axion-like dilaton dark matter production compatible with the CMB data.

The Everett-type interpretations of quantum mechanics and quantum cosmology proposed independently by Hartle, Geroch, and Wada are discussed. They essentially involve regarding a strong peak in the wave function as a definite prediction. Wave functions in quantum cosmology are usually peaked about correlations between coordinates and momenta, and methods for identifying such correlations are introduced. The first method involves Wigner's function, a quantum-mechanical analogue of the classical phase-space distribution. The properties of this distribution are discussed and it is shown how it can be of use in describing the emergence of classical behavior from quantum systems. The second method involves a suitably chosen canonical transformation. These methods are applied to harmonic-oscillator examples, which are of relevance to scalar field fluctuations in inflationary universe models. These methods are also applied to WKB wave functions in quantum mechanics and quantum cosmology. The manner in which the wave function becomes peaked about sets of classical solutions is elucidated. This is extended to include inhomogeneous perturbations about minisuperspace in quantum cosmology, and the derivation of the semiclassical Einstein equations, ${G}_{\ensuremath{\mu}\ensuremath{\nu}}$=8\ensuremath{\pi}G〈${T}_{\ensuremath{\mu}\ensuremath{\nu}}$〉, from the Wheeler-DeWitt equation is considered. A condition under which they are valid is derived. It is essentially the requirement that the distribution of ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$, as a function of the matter modes, is strongly peaked about its average value. Some situations in which this condition is satisfied are discussed.

A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. Applications include a consistent and unified description of the generation and evolution of fluctuations in inflationary Universe models, and a definition of nonequilibrium entropy for the gravitational field at the linearized level.

I briefly review the main features of inflationary universe models. Inflation provides a mechanism which produces energy density fluctuations on cosmological scales. In the original models it was not possible to obtain the correct magnitude of these fluctuations without fine tuning the particle physics models. I discuss two mechanisms, “chaotic inflation”, and a “dynamical relaxation” process, by which inflation may be realized in models which give the right magnitude of fluctuations.

Evolution equation for the expectation value of a scalar field in spatially flat RW universes

We consider an inflationary universe model in the context of generalized cosmic Chaplygin gas by taking matter field as standard and tachyon scalar fields. We evaluate the corresponding scalar fields and scalar potentials during intermediate and logamediate inflationary regimes by modifying the first Friedmann equation. In each case, we evaluate the number of e-folds, scalar as well as tensor power spectra, scalar spectral index and important observational parameter, i.e., tensor-scalar ratio in terms of inflatons. The graphical behavior of this parameter shows that the model remains incompatible with WMAP7 and Planck observational data in each case.

We study the production of large-scale (\ensuremath{\sim}Mpc) magnetic fields in inflationary Universe models. The magnetic fields produced are uninterestingly small unless the conformal invariance of the electromagnetic field is broken. Once the conformal invariance is broken, a mechanism akin to ``superadiabatic amplification'' can operate and lead to sizable primeval magnetic fields. We consider three ways of breaking the conformal invariance: through gravitational couplings of the photon; through the coupling of the photon to a charged massless, nonconformally invariant scalar field; and through the anomalous coupling of the photon to axions. The primeval magnetic fields which result can have astrophysically interesting strengths, but are very model dependent.

Dynamics of warm inflation with gauge fields in Bianchi type I universe model

We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experiments do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.

In light of the results from the WMAP three-year sky survey, we study an inflationary model based on a single-field polynomial potential, with up to quartic terms in the inflaton field. Our analysis is performed in the context of the Randall-Sundrum II braneworld theory, and we consider both the high-energy and low-energy (i.e. the standard cosmology case) limits of the theory. We examine the parameter space of the model, which leads to both large-field and small-field inflationary type solutions. We conclude that small field inflation, for a potential with a negative mass square term, is in general favored by current bounds on the tensor-to-scalar perturbation ratio rs.

I briefly review the main features of inflationary universe models. Inflation provides a mechanism which produces energy density fluctuations on cosmological scales. In the original models it was not possible to obtain the correct magnitude of these fluctuations without fine tuning the particle physics models. I discuss a modified model, “chaotic inflation”, in which the fine tuning problem is less severe. I also mention other approaches to early universe cosmology.

A quantum inflationary universe model is proposed, in which the expansion factor S(t) is treated as a q-number, and the cosmological constant Λ is identified with the energy density of Higgs field. Moreover, the initial quantum state is assumed to be a Gauss wave pocket. In such framework, < S3/2 > follows the classical de-Sitter expansive law. The relative quantum uncertainty of Hubble size lH(t) = (Ṡ/S)-1 was computed: ΔlH(t)/ < lH(t) > similar Z-6, where Z is the inflationary factor of universe. This result is basically different from that of Padmanabhan; the discrepency was explained. We conclude that the quantum Hubble size is practically a classical quantity.