Cosmological implications of a minimal length hypothesis

2006 ◽  
Vol 84 (6-7) ◽  
pp. 481-491
Author(s):  
A Ashoorioon ◽  
R B Mann
Keyword(s):  
Spectral Index ◽  
Strong Support ◽  
Planck Scale ◽  
Minimal Length ◽  
Inflationary Cosmology ◽  
Quantum Field ◽  
Standard Quantum ◽  
Consistency Relation ◽  
98.80 Cq ◽  
Theory Result

One of the firm predictions of inflationary cosmology is the consistency relation between scalar and tensor spectra. It has been argued that such a relation — if experimentally confirmed — would offer strong support for the idea of inflation. We examine the possibility that trans-Planckian physics violates the consistency relation in the framework of inflation with a cutoff proposed in astro-ph/0009209. We find that despite the ambiguity that exists in choosing the action, Planck-scale physics modifies the consistency relation considerably. It also leads to the running of the spectral index. For modes that are larger than our current horizon, the tensor spectral index is positive. For a window of k values with amplitudes of the same order as the modes that are the precursors to structure formation, the behavior of the tensor spectral index is oscillatory about the standard Quantum field theory result, taking both positive and negative values. There is a hope that in the light of future experiments, this scenario of short distance physics, can be verified.PACS Nos.: 98.80.Cq , 98.80.-k, 98.80.Qc

scholarly journals Trace dynamics and division algebras: towards quantum gravity and unification

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
Lie Group ◽  
Planck Scale ◽  
The Self ◽  
Division Algebras ◽  
Quantum Field ◽  
Octonion Algebra ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Massless Spin ◽  
Correct Understanding

AbstractWe have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade (fermionic) and even-grade (bosonic) Grassmann matrices. Evolution takes place in Connes time. At energies much lower than Planck scale, trace dynamics reduces to quantum field theory. In the present paper, we explain that the correct understanding of spin requires us to formulate the theory in 8-D octonionic space. The automorphisms of the octonion algebra, which belong to the smallest exceptional Lie group G2, replace space-time diffeomorphisms and internal gauge transformations, bringing them under a common unified fold. Building on earlier work by other researchers on division algebras, we propose the Lorentz-weak unification at the Planck scale, the symmetry group being the stabiliser group of the quaternions inside the octonions. This is one of the two maximal sub-groups of G2, the other one being SU(3), the element preserver group of octonions. This latter group, coupled with U(1)em, describes the electrocolour symmetry, as shown earlier by Furey. We predict a new massless spin one boson (the ‘Lorentz’ boson) which should be looked for in experiments. Our Lagrangian correctly describes three fermion generations, through three copies of the group G2, embedded in the exceptional Lie group F4. This is the unification group for the four fundamental interactions, and it also happens to be the automorphism group of the exceptional Jordan algebra. Gravitation is shown to be an emergent classical phenomenon. Although at the Planck scale, there is present a quantised version of the Lorentz symmetry, mediated by the Lorentz boson, we argue that at sub-Planck scales, the self-adjoint part of the octonionic trace dynamics bears a relationship with string theory in 11 dimensions.

Lecture on SUSY Gauge Theories and Integrable Systems

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3093-3124
Author(s):  
A. Marshakov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Integrable Systems ◽  
Gauge Theories ◽  
Toda Chain ◽  
Quantum Field ◽  
Standard Quantum ◽  
Integrable Equations ◽  
Complex Curves ◽  
Periodic Toda Chain

I consider main features of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential. The example of periodic Toda chain solutions is considered in detail. Recently found exact nonperturbative solutions to [Formula: see text] SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to the integrable systems are discussed.

scholarly journals Inflationary cosmology in unimodular F(T) gravity

2017 ◽  
Vol 32 (21) ◽  
pp. 1750114 ◽  
Author(s):  
Kazuharu Bamba ◽  
Sergei D. Odintsov ◽  
Emmanuel N. Saridakis
Keyword(s):  
Spectral Index ◽  
Teleparallel Gravity ◽  
Specific Model ◽  
Inflationary Cosmology ◽  
Model Parameters ◽  
De Sitter ◽  
Reconstruction Procedure ◽  
Additional Advantage ◽  
Slow Roll ◽  
Good Agreement

We investigate the inflationary realization in the context of unimodular F(T) gravity, which is based on the F(T) modification of teleparallel gravity, in which one imposes the unimodular condition through the use of Lagrange multipliers. We develop the general reconstruction procedure of the F(T) form that can give rise to a given scale-factor evolution, and then we apply it in the inflationary regime. We extract the Hubble slow-roll parameters that allow us to calculate various inflation-related observables, such as the scalar spectral index and its running, the tensor-to-scalar ratio, and the tensor spectral index. Then, we examine the particular cases of de Sitter and power-law inflation, of Starobinsky inflation, as well as inflation in a specific model of unimodular F(T) gravity. As we show, in all cases the predictions of our scenarios are in a very good agreement with Planck observational data. Finally, inflation in unimodular F(T) gravity has the additional advantage that it always allows for a graceful exit for specific regions of the model parameters.

scholarly journals Looking beyond inflationary cosmology

2006 ◽  
Vol 84 (6-7) ◽  
pp. 437-446
Author(s):  
R H Brandenberger
Keyword(s):  
String Theory ◽  
Scalar Fields ◽  
Inflationary Cosmology ◽  
Inflationary Universe ◽  
Basic Principles ◽  
String Gas Cosmology ◽  
98.80 Cq ◽  
Conceptual Problems

In spite of the phenomenological successes of the inflationary universe scenario, the current realizations of inflation making use of scalar fields lead to serious conceptual problems that are reviewed in this lecture. String theory may provide an avenue towards addressing these problems. One particular approach to combining string theory and cosmology is String Gas Cosmology. The basic principles of this approach are summarized.PACS No.: 98.80.Cq}

scholarly journals Heuristic derivation of Casimir effect in minimal length theories

2020 ◽  
Vol 29 (02) ◽  
pp. 2050011 ◽  
Author(s):  
Massimo Blasone ◽  
Gaetano Lambiase ◽  
Giuseppe Gaetano Luciano ◽  
Luciano Petruzziello ◽  
Fabio Scardigli
Keyword(s):  
Field Theory ◽  
Parallel Plate ◽  
Casimir Effect ◽  
Generalized Uncertainty Principle ◽  
Casimir Energy ◽  
Minimal Length ◽  
Quadratic Term ◽  
Quantum Field ◽  
The One ◽  
Plate Geometry

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory (QFT). Experimental developments are finally discussed.

scholarly journals The evidence for a spatially flat Universe

2020 ◽  
Vol 496 (1) ◽  
pp. L91-L95 ◽  
Author(s):  
George Efstathiou ◽  
Steven Gratton
Keyword(s):  
High Precision ◽  
Strong Support ◽  
Inflationary Cosmology ◽  
Density Parameter ◽  
Acoustic Oscillations ◽  
Astrophysical Data ◽  
Flat Universe ◽  
Polarization Spectra ◽  
The Universe ◽  
Good Agreement

ABSTRACT We use a new and statistically powerful Planck likelihood to show that the Planck temperature and polarization spectra are consistent with a spatially flat Universe, in contrast to recent claims in the literature. When combined with other astrophysical data, particularly geometrical measurements of baryon acoustic oscillations, our likelihood constrains the Universe to be spatially flat to extremely high precision. We deduce a curvature density parameter ΩK = 0.0004 ± 0.0018 in good agreement with the 2018 results of the Planck team. In the context of inflationary cosmology, the observations offer strong support for models of inflation with a large number of e-foldings and disfavour models of incomplete inflation.

scholarly journals Aspects of brane-antibrane inflation

2006 ◽  
Vol 84 (6-7) ◽  
pp. 447-452 ◽  
Author(s):  
James M Cline
Keyword(s):  
Cosmic Microwave Background ◽  
Spectral Index ◽  
Fine Tuning ◽  
Good Chance ◽  
Microwave Background ◽  
Dynamical Mechanism ◽  
98.80 Cq

I describe a dynamical mechanism for solving the fine-tuning problem of brane-antibrane inflation. By inflating with stacks of branes and antibranes, the branes can naturally be trapped at a metastable minimum of the potential. As branes tunnel out of this minimum, the shape of the potential changes to make the minimum shallower. Eventually the minimum disappears and the remaining branes roll slowly because the potential is nearly flat. I show that even with a small number of branes, there is a good chance of getting enough inflation. Running of the spectral index is correlated with the tilt in such a way as to provide a test of the model by future cosmic microwave background experiments.PACS Nos.: 11.25.Wx, 98.80.Cq

scholarly journals Bohmian mechanics for instrumentalists

2019 ◽  
Vol 17 (08) ◽  
pp. 1950029
Author(s):  
Hrvoje Nikolić
Keyword(s):  
Condensed Matter ◽  
Relativistic Quantum ◽  
Bohmian Mechanics ◽  
Quantum Field ◽  
Fundamental Theory ◽  
Relativistic Quantum Field Theory ◽  
Long Distance ◽  
Standard Quantum ◽  
Auxiliary Role ◽  
Apparent Conflict

We formulate Bohmian mechanics (BM) such that the main objects of concern are macroscopic phenomena, while microscopic particle trajectories only play an auxiliary role. Such a formulation makes it easy to understand why BM always makes the same measurable predictions as standard quantum mechanics (QM), irrespective of the details of microscopic trajectories. Relativistic quantum field theory (QFT) is interpreted as an effective long-distance theory that at smaller distances must be replaced by some more fundamental theory. Analogy with condensed-matter physics suggests that this more fundamental theory could have a form of nonrelativistic QM, offering a simple generic resolution of an apparent conflict between BM and relativistic QFT.

scholarly journals Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length

2020 ◽  
Vol 35 (33) ◽  
pp. 2050278
Author(s):  
H. Aounallah ◽  
B. C. Lütfüoğlu ◽  
J. Kříž
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Eigenvalue ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Summation Formula ◽  
Minimal Length ◽  
Two Dimensional ◽  
Relativistic Limit ◽  
Ordinary Quantum

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

SOLITONS EXPERIENCE FOR BLACK HOLE PRODUCTION IN ULTRARELATIVISTIC PARTICLE COLLISIONS

2012 ◽  
Vol 26 (27n28) ◽  
pp. 1243010 ◽  
Author(s):  
I. YA. AREF'EVA
Keyword(s):  
Black Hole ◽  
Scattering Amplitudes ◽  
Planck Scale ◽  
Functional Integral ◽  
Quantum Field ◽  
Mass Energy ◽  
Particle Collisions ◽  
Functional Integral Method ◽  
Geometrical Cross Section ◽  
Current Paradigm

We discuss the analogy between soliton scattering in quantum field theory and black hole/wormholes (BH/WH) production in ultrarelativistic particle collisions in gravity. It is a common wisdom of the current paradigm suggests that BH/WH formation in particles collisions will happen when a center-mass energy of colliding particles is sufficiently above the Planck scale (the transplanckian region) and the BH/WH production can be estimated by the classical geometrical cross section. We compare the background of this paradigm with the functional integral method to scattering amplitudes and, in particular, we stress the analogy of the BH production in collision of ultrarelativistic particle and appearance of breathers poles in the scattering amplitudes in the Sin–Gordon model.

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