TRANS-PLANCKIAN PHYSICS AND INFLATIONARY COSMOLOGY

String theory enjoys an elevated role among quantum gravity theories, since it seems to be the most consistent UV completion of general relativity and the Standard Model. However, it is hard to verify the existence of this underlying theory on terrestrial accelerators. One way to probe string theory is to study its imprints on the low-energy effective inflationary Lagrangian, which are quantified in terms of high energy correction terms. It is highly likely, thus, to find higher order curvature terms combined with string moduli, that is scalar fields, since both these types of interactions and matter fields appear in string theory. In this work we aim to stress the probability that the inflationary dynamics are controlled by the synergy of scalar fields and higher order curvature terms. Specifically, we shall consider a well motivated quantum corrected canonical scalar field theory, with the quantum corrections being of the R2 type. The reason for choosing minimally coupled scalar theory is basically because if scalar fields are evaluated in their vacuum configuration, they will either be minimally coupled or conformally coupled. Here we choose the former case, and the whole study shall be performed in the string frame (Jordan frame), in contrast to similar studies in the literature where the Einstein frame two scalar theory is considered. We derive the field equations of the quantum-corrected theory at leading order and we present the form the slow-roll indices obtain for the quantum corrected theory. We exemplify our theoretical framework by using the quadratic inflation model, and as we show, the R2 quantum corrected quadratic inflation model produces a viable inflationary phenomenology, in contrast with the simple quadratic inflation model.

Although Edward Witten does an admirable job explaining why the mathematical structure of string theory is quite beautiful (Physics Today, November 2015, page 38), I think he overstates the evidence that “string theory potentially unifies gravity with the other forces of nature.” In particular, it is unclear whether string theory provides a natural explanation for supersymmetry breaking or the observed properties of elementary particles. In addition, string theory has yet to explain how the unphysical predictions of classical general relativity are eliminated; for example, how the unphysical features of the interior Kerr metric—which describes the spacetime inside the event horizon of a rotating black hole—are eliminated in the course of the gravitational collapse of massive rotating objects.It is true that string theory has provided a nice model, the anti–de Sitter/ conformal field theory (AdS/CFT) correspondence, for the nature of spacetime just outside an event horizon, but to date string theory has had nothing definitive to say about the nature of spacetime inside an event horizon. A related problem for string theory (and also for classical general relativity) is that it provides no explanation for what the universe looked like prior to the Big Bang, which is unexpected if string theory really provides an underlying quantum theory of elementary particles and gravity.I completely agree with Witten that two-dimensional CFT is likely to have a critical role in any fundamental theory of spacetime. However, because of the obvious importance of four dimensions in the real world, it seems much more likely that four-dimensional curved twistor spaces11. R. S. Ward, R. O. Wells Jr, Twistor Geometry and Field Theory, Cambridge U. Press (1990). rather than strings play the role of fundamental objects.22. G. Chapline, K. Yamagishi, Phys. Rev. Lett. 66, 3064 (1991). https://doi.org/10.1103/PhysRevLett.66.3064 This, I submit, is an even more beautiful idea than string theory.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. S. Ward, R. O. Wells Jr, Twistor Geometry and Field Theory, Cambridge U. Press (1990). Google ScholarCrossref2. G. Chapline, K. Yamagishi, Phys. Rev. Lett. 66, 3064 (1991). https://doi.org/10.1103/PhysRevLett.66.3064, Google ScholarCrossref, ISI© 2016 American Institute of Physics.

▪ Abstract The evolution of the universe is the ultimate laboratory for studying fundamental physics across energy scales that span approximately 25 orders of magnitude. The standard models of cosmology and particle physics provide the basic understanding of the early and present universe and predict a series of phase transitions that occurred in succession during the universe's expansion and cooling history. We survey these phase transitions, highlighting the equilibrium and nonequilibrium effects as well as their observational and cosmological consequences. We discuss the current theoretical and experimental programs studying phase transitions in QCD and nuclear matter in accelerators. A critical assessment of similarities and differences between the conditions in the early universe and those in ultrarelativistic heavy ion collisions is presented. Cosmological observations and accelerator experiments are converging toward an unprecedented understanding of the early and present universe.

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with $U(2)\times U(2)$ symmetry, in which there is a parameter $\lambda_2$ that controls the strength of the first-order phase transition driven by fluctuations. In the limit of $\lambda_2\to0$, the $U(2)\times U(2)$ theory is reduced to an $O(8)$ scalar theory that exhibits a second-order phase transition in three dimensions. We develop a new insight for the understanding of the fluctuation-induced first-order phase transition as a smooth continuation from the standard RG flow in the $O(8)$ system. In our view from the RG flow diagram on coupling parameter space, the region that favors the first-order transition emerges from the unphysical region to the physical one as $\lambda_2$ increases from zero. We give this interpretation based on the Taylor expansion of the functional RG equations up to the fourth order in terms of the field, which encompasses the $\epsilon$-expansion results. We compare results from the expansion and from the full numerical calculation and find that the fourth-order expansion is only of qualitative use and that the sixth-order expansion improves the quantitative agreement.

Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that are less than satisfactory. Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free, perturbation analysis of interacting models expanded about a suitable pseudofree theory, which differs from a free theory by an O(ℏ2) counterterm. These positive features are realized within a functional integral formulation by a local, nonclassical, counterterm that effectively transforms parameter changes in the action from generating mutually singular measures, which are the basis for divergences, to equivalent measures, thereby removing all divergences. The use of an alternative model about which to perturb is already supported by properties of the classical theory and is allowed by the inherent ambiguity in the quantization process itself. This procedure not only provides acceptable solutions for models for which no acceptable, faithful solution currently exists, e.g. φ4n, for spacetime dimensions n ⩾ 4, but offers a new, divergence-free solution for less-singular models as well, e.g. φ4n, for n = 2, 3. Our analysis implies similar properties for multicomponent scalar models, such as those associated with the Higgs model.

Complexity will be more and more essential in high-energy physics. It is naturally extended into the very early universe. Considering the universe as a quantum chaotic system, the curvature perturbation of the scalar field is identified with the two-mode squeezed state. By solving the Schrödinger equation, one can obtain the numerical solutions of the angle parameter and squeezing parameter. The solution of the squeezing parameter mainly determines the evolution of complexity. Our numeric indicates that the complexity of the modified dispersion relation will have a non-linear pattern after the horizon exits. Meanwhile, its corresponding Lyapunov index is also larger compared with the standard case. During the inflationary period, the complexity will irregularly oscillate and its scrambling time is also shorter compared with the standard case. Since the modified dispersion relation can be dubbed as the consequences of various frameworks of quantum gravity, it could be applicable to these frameworks. Finally, one can expect the framework of quantum gravity will lead to the fruitful evolution of complexity, which guides us in distinguishing various inflationary models.

Observations indicate that the universe is effectively flat, but they do not rule out a closed universe. The role of positive curvature is negligible at late times, but can be crucial in the early universe. In particular, positive curvature allows for cosmologies that originate as Einstein static universes, and then inflate and later reheat to a hot big-bang era. These cosmologies have no singularity, no ‘beginning of time’ and no horizon problem. If the initial radius is chosen to be above the Planck scale, then they also have no quantum gravity era, and are described by classical general relativity throughout their history.

We derive loop equations in a scalar matrix field theory. We discuss their\nsolutions in terms of simplicial string theory -- the theory describing\nembeddings of two--dimensional simplicial complexes into the space--time of the\nmatrix field theory. This relation between the loop equations and the\nsimplicial string theory gives further arguments that favor one of the\nstatements of the paper hep-th/0407018. The statement is that there is an\nequivalence between the partition function of the simplicial string theory and\nthe functional integral in a continuum string theory -- the theory describing\nembeddings of smooth two--dimensional world--sheets into the space--time of the\nmatrix field theory in question.\n

It is well known nowadays that the best candidate for the cosmological model is the inflationary model which describes the rapid expansion of the universe at the early time. This inflationary scenario is assumed to take place at a very high energy scale, at which classical general relativity is no longer valid as the quantum effects become more relevant. String theory is the most promising candidate for describing the nature of physics in this scale. The universal property of this theory is the stringy space-time uncertainty relation. The noncommutative property of space and time is the important consequence of this property. The aim of this thesis is to study the inflationary model in which the effect of noncommutative space-time is taken into account. The Cosmic Microwave Background (CMB) power spectrum is the convenient quantity that one uses to compare the result of the model with observed data. The comparison can be divided into two classes according to their vacua, which are the adiabatic vacuum and the minimized uncertainty vacuum. The result of both vacua is consistent that the noncommutative effect suppresses the spectrum at the low multipole. This result is more compatible with observation than the result of the commutative space-time.

In classical general relativity, singularity theorems are concerned with the existence of an incomplete inextendible nonspacelike geodesic. We prove the incompleteness of a geodesic surface under assumptions on the Gaussian curvature of the geodesic surface and the elasticity of the string.

Current cosmological observations are remarkably consistent with a concordance cosmology including an epoch of inflation in the very early universe. There is a tantalizing possibility that the ultra-high energy physics of the very early universe could be deduced from cosmological observations. In particular, the observed angular power spectrum of the CMB anisotropy is a convolution of the cosmological radiative transport kernel with the power spectrum of primordial perturbations. Exquisite measurements of the angular power spectrum over a wide range of multipoles from WMAP have opened up the possibility to deconvolve the primordial power spectrum for a given set of cosmological parameters. We present an update on our ongoing research program to recover the primordial power spectrum from CMB anisotropy. The robust features in the recovered primordial spectrum could be signatures of the physics behind inflation. Initial work towards mapping out the likelihood, ‘optimized’ over the unknown primordial spectrum, in the space the cosmological parameters reveal interesting results.

This paper describes CosmoLattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoLattice incorporates a series of features that makes it very versatile and powerful: i) it is written in C++ fully exploiting the object oriented programming paradigm, with a modular structure and a clear separation between the physics and the technical details, ii) it is MPI-based and uses a discrete Fourier transform parallelized in multiple spatial dimensions, which makes it specially appropriate for probing scenarios with well-separated scales, running very high resolution simulations, or simply very long ones, iii) it introduces its own symbolic language, defining field variables and operations over them, so that one can introduce differential equations and operators in a manner as close as possible to the continuum, iv) it includes a library of numerical algorithms, ranging from O(δt2) to O(δt10) methods, suitable for simulating global and gauge theories in an expanding grid, including the case of ‘self-consistent’ expansion sourced by the fields themselves. Relevant observables are provided for each algorithm (e.g. energy densities, field spectra, lattice snapshots) and we note that, remarkably, all our algorithms for gauge theories (Abelian or non-Abelian) always respect the Gauss constraint to machine precision. Program summaryProgram Title::CosmoLatticeCPC Library link to program files:https://doi.org/10.17632/44vr5xssc6.1Developer's repository link:http://github.com/cosmolattice/cosmolatticeLicensing provisions: MITProgramming language: C++, MPINature of problem: The phenomenology of high energy physics in the early universe is typically characterized by non-linear dynamics, which cannot be captured accurately with analytical techniques. In order to fully understand the non-linearities developed in a given scenario, one needs to carry out lattice simulations. A number of public packages for lattice simulations have appeared over the years, but most of them are only capable of simulating scalar fields. However, realistic models of particle physics do contain other kind of field species, such as (Abelian or non-Abelian) gauge fields, whose non-linear dynamics can also play a relevant role in the early universe. Tensor modes representing gravitational waves are also naturally expected in many scenarios.Solution method:CosmoLattice represents a modern code for lattice simulations of scalar-gauge field theories in an expanding universe. It allows for the simulation of the evolution of interacting (singlet) scalar fields, charged scalar fields under U(1) and/or SU(2) gauge groups, and the corresponding associated Abelian and/or non-Abelian gauge fields. From version 1.1 onward, CosmoLattice also allows to simulate the production of gravitational waves. Simulations can be done either in a flat space-time background, or in a homogeneous and isotropic (spatially flat) expanding FLRW background. CosmoLattice provides symplectic integrators, with accuracy ranging from O(δt2) up to O(δt10), to simulate the non-linear dynamics of the appropriate fields in comoving three-dimensional lattices. The code is parallelized with MPI, and uses a discrete Fourier Transform parallelized in multiple spatial dimensions, which makes it a very powerful code for probing physical problems with well-separated scales. Moreover, the code has been designed as a ‘platform’ to implement any system of dynamical equations suitable for discretization on a lattice.

We modify the standard Abelian-Higgs model by introducing spatially-dependent couplings for the scalar and vector fields. We investigate static, non-cylindrically symmetric solutions of the resulting field equations and propose a pinch solution which interpolates between degenerate vacua along the string, labelled by $\pm |n|$. This configuration corresponds to a vortex which shrinks to Planck scale before re-emerging as an anti-vortex, resulting in the formation of a bead pair with one bead at either side of the intersection. The solution is then topologically stable. A key assumption is that quantities such as phase and winding number, along with those which depend on them like the magnetic flux, become undefined at the Planck scale so that regions of opposite winding may be joined via a Planck-sized segment of neutral string. Similarities between this solution and the extra-dimensional windings of strings in type IIB string theory are discussed and a correspondence between field theory and string theory parameters is suggested. The spatial-dependence of the field couplings is found to have a natural interpretation in the dual string picture and results from the variation of the winding radius, giving rise to a varying (effective) string coupling. An interesting result is an estimate of the Higgs mass (at critical coupling) in terms of the parameters which define the Klebanov-Strassler geometry and which, in principle, may be constrained by cosmological observations.

We discuss recent results on renormalization-group evolution of several types of theories. First, we consider asymptotically free vectorial gauge theories with various fermion contents and discuss higher-loop calculations of the UV to IR evolution in these theories, including an IR zero of the beta function and the value of the anomalous dimension [Formula: see text] at this point, together with comparisons with lattice measurements. Effects of scheme transformations are discussed. We then present a novel way to determine the value of [Formula: see text] in an [Formula: see text] technicolor model from a particular embedding in an extended technicolor theory. Finally, we analyze the renormalization-group behavior of several non-asymptotically free theories, including a U(1) gauge theory, a non-Abelian gauge theory with many fermions, an [Formula: see text] [Formula: see text] scalar theory, and Yukawa theories.

Nullification in scalar theories with derivative couplings