Scalar fields in the de Sitter spacetime

We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the two-point function is calculated up to two loops. Comparing our results with the Hartree-Fock approximation and with the stochastic approach shows that the former resums only the cactus type diagrams, whereas the latter contains the sunset diagram as well and produces the correct result. We compare our results with the preceding results obtained for the massless scalar field

Higgs Starobinsky inflation

In this paper we point out that Starobinky inflation could be induced by quantum effects due to a large non-minimal coupling of the Higgs boson to the Ricci scalar. The Higgs Starobinsky mechanism provides a solution to issues attached to large Higgs field values in the early universe which in a metastable universe would not be a viable option. We verify explicitly that these large quantum corrections do not destabilize Starobinsky's potential

Modeling the quantum evolution of the universe through classical matter

It is well known that the canonical quantization of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor $(t)$ never vanishes and, as $t\to\infty$, we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS). We then show that this single fluid with an implict EoS is equivalent to two non-interacting fluids, one of them representing stiff matter with negative energy density. In the case of two non-interacting scalar fields, one of them of the phantom type, we find their potential energy. In both cases we find that quantum mechanics changes completely the configuration of matter for small values of time, by adding a fluid or a scalar field with negative energy density. As time passes, the density of negative energy decreases and we recover the ordinary content of the classical universe. The more the initial wave function of the universe is concentrated around the classical big bang singularity, the more it is necessary to add negative energy, since this type of energy will be responsible for the removal of the classical singularity.Comment: updated version as accepted by Gen. Relativ. Gravi

Gravitational Collapse of the Shells with the Smeared Gravitational Source in Noncommutative Geometry

We study the formation of the (noncommutative) Schwarzschild black hole from collapsing shell {of the} generalized matters containing polytropic and Chaplygin gas. We show that this collapsing shell depending on various parameters forms either a black hole or a naked singular shell with the help of the pressure.Furthermore, by considering the smeared gravitational sources, we investigate the noncommutative black holes formation. Though this mild noncommutative correction of matters cannot ultimately resolve the emergence of the naked singularity, we show that in some parameter region the collapsing shell evolves to a noncommutative black hole before becoming a naked singular shell.Comment: 16 pages, LateX, 9 figures, Title changed in this published versio

AIC, BIC, Bayesian evidence against the interacting dark energy model

Recent astronomical observations have indicated that the Universe is in the phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting $\Lambda$CDM model where the interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative---the $\Lambda$CDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: SNIa (Union2.1), $h(z)$, BAO, Alcock--Paczynski test and CMB we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting $\Lambda$CDM model when compared to the $\Lambda$CDM model, while those based on the BIC indicated that there is the strong evidence against it in favor the $\Lambda$CDM model. Given the weak or almost none support for the interacting $\Lambda$CDM model and bearing in mind Occam's razor we are inclined to reject this model.Comment: LaTeX svjour3, 12 pages, 3 figure

Higgs field in cosmology

The accelerated expansion of the early universe is an integral part of modern cosmology and dynamically realized by the mechanism of inflation. The simplest theoretical description of the inflationary paradigm is based on the assumption of an additional propagating scalar degree of freedom which drives inflation - the inflaton. In most models of inflation the fundamental nature of the inflaton remains unexplained. In the model of Higgs inflation, the inflaton is identified with the Standard Model Higgs boson and connects cosmology with elementary particle physics. A characteristic feature of this model is a non-minimal coupling of the Higgs boson to gravity. I review and discuss several phenomenological and fundamental aspects of this model, including the impact of quantum corrections and the renormalization group, the derivation of initial conditions for Higgs inflation in a quantum cosmological framework and the classical and quantum equivalence of different field parametrizations.Comment: 36 pages, 9 figures; references added, typos corrected. Invited contribution to the Heraeus-Seminar "Hundred Years of Gauge Theory", 30 July - 3 August 2018, Physikzentrum Bad Honnef, organized by Silvia De Bianchi and Claus Kiefer. To appear in the proceedings "100 Years of Gauge Theory. Past, present and future perspectives" in the series `Fundamental Theories of Physics' (Springer