ONE-LOOP CALCULATION OF COSMOLOGICAL CONSTANT IN A SCALE INVARIANT THEORY

We compute the cosmological constant in a scale invariant scalar field theory. The gravitational action is also suitably modified to respect scale invariance. Due to scale invariance, the theory does not admit a cosmological constant term. The scale invariance is broken by a recently introduced mechanism called cosmological symmetry breaking. This leads to a nonzero cosmological constant. We compute the one-loop corrections to the cosmological constant and show that it is finite.

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COSMOLOGICAL SYMMETRY BREAKING, PSEUDO-SCALE INVARIANCE, DARK ENERGY AND THE STANDARD MODEL

Modern Physics Letters A ◽

10.1142/s0217732307023754 ◽

2007 ◽

Vol 22 (22) ◽

pp. 1651-1661 ◽

Cited By ~ 13

Author(s):

PANKAJ JAIN ◽

SUBHADIP MITRA

Keyword(s):

Field Theory ◽

Dark Energy ◽

Scalar Field ◽

Symmetry Breaking ◽

Scale Invariance ◽

Quantum Theories ◽

A Value ◽

Wide Range ◽

Time Dependent Solution ◽

The Universe

The energy density of the universe today may be dominated by the vacuum energy of a slowly rolling scalar field. Making a quantum expansion around such a time-dependent solution breaks fundamental symmetries of quantum field theory. We call this mechanism cosmological symmetry breaking and argue that it is different from the standard phenomenon of spontaneous symmetry breaking. We illustrate this with a toy scalar field theory, whose action displays a U(1) symmetry. We identify a symmetry, called pseudo-scale invariance, which sets the cosmological constant exactly equal to zero, both in classical and quantum theories. This symmetry is also broken cosmologically and leads to a nonzero vacuum or dark energy. The slow-roll condition along with the observed value of dark energy leads to a value of the background scalar field of the order of Planck mass. We also consider a U(1) gauge symmetry model. Cosmological symmetry breaking, in this case, leads to a nonzero mass for the vector field. We also show that a cosmologically broken pseudo-scale invariance can generate a wide range of masses.

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Tidal effects in quantum field theory

Journal of High Energy Physics ◽

10.1007/jhep12(2020)024 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Kays Haddad ◽

Andreas Helset

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Scalar Field ◽

Weyl Tensor ◽

Hilbert Series ◽

Quantum Field ◽

Tidal Effects ◽

Gravitational Action ◽

Higher Dimensional ◽

The One

Abstract We apply the Hilbert series to extend the gravitational action for a scalar field to a complete, non-redundant basis of higher-dimensional operators that is quadratic in the scalars and the Weyl tensor. Such an extension of the action fully describes tidal effects arising from operators involving two powers of the curvature. As an application of this new action, we compute all spinless tidal effects at the leading post-Minkowskian order. This computation is greatly simplified by appealing to the heavy limit, where only a severely constrained set of operators can contribute classically at the one-loop level. Finally, we use this amplitude to derive the $$ \mathcal{O}\left({G}^2\right) $$ O G 2 tidal corrections to the Hamiltonian and the scattering angle.

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Scale Invariance, Horizons, and Inflation

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab1102 ◽

2021 ◽

Author(s):

Andre Maeder ◽

Vesselin G Gueorguiev

Keyword(s):

Scalar Field ◽

Scale Invariance ◽

Maxwell Equations ◽

High Redshift ◽

Empty Space ◽

Causal Connection ◽

Cosmological Constant Problem ◽

Scale Invariant ◽

Starting Point ◽

Final Answer

Abstract Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from ϱ = 0 to ϱc, and are forbidden for densities above ϱc. The absence of scale invariance in this case is consistent with considerations about causal connection. Below ϱc, scale invariance appears as an open possibility, which also depends on the occurrence of in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field ϕ in the energy density $\varrho = \frac{1}{2} \dot{\varphi }^2 + V(\varphi )$ of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called “cosmological constant problem”. In the framework of scale invariance, an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ϱc is an open possibility; the final answer may come from high redshift observations, where differences from the ΛCDM models appear.

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Coherent states and spontaneous symmetry breaking in light-front scalar field theory

Nuclear Physics B - Proceedings Supplements ◽

10.1016/j.nuclphysbps.2006.08.061 ◽

2006 ◽

Vol 161 ◽

pp. 223-229 ◽

Cited By ~ 1

Author(s):

J.P. Vary ◽

D. Chakrabarti ◽

A. Harindranath ◽

R. Lloyd ◽

L. Martinovic ◽

...

Keyword(s):

Field Theory ◽

Scalar Field ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Coherent States ◽

Light Front ◽

Scalar Field Theory

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Effective Abelian-Higgs Theory from SU(2) gauge field theory

International Journal of Modern Physics A ◽

10.1142/s0217751x05026807 ◽

2005 ◽

Vol 20 (15) ◽

pp. 3481-3487 ◽

Cited By ~ 1

Author(s):

VLADIMIR DZHUNUSHALIEV ◽

DOUGLAS SINGLETON ◽

DANNY DHOKARH

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Scalar Field ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Mass Term ◽

Gauge Field Theory ◽

Ginzburg Landau ◽

Flux Tubes ◽

Color Confinement

In the present work we show that it is possible to arrive at a Ginzburg-Landau (GL) like equation from pure SU (2) gauge theory. This has a connection to the dual superconducting model for color confinement where color flux tubes permanently bind quarks into color neutral states. The GL Lagrangian with a spontaneous symmetry breaking potential, has such (Nielsen-Olesen) flux tube solutions. The spontaneous symmetry breaking requires a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

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GENERALIZED GRAVITY IN CLIFFORD SPACES, VACUUM ENERGY AND GRAND UNIFICATION

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781100566x ◽

2011 ◽

Vol 08 (06) ◽

pp. 1239-1258 ◽

Cited By ~ 2

Author(s):

CARLOS CASTRO

Keyword(s):

Cosmological Constant ◽

Gauge Field ◽

Constant Term ◽

Gauge Field Theories ◽

Field Equations ◽

Spectral Action ◽

Action Model ◽

The One ◽

Curvature And Torsion ◽

Vacuum Solutions

Polyvector-valued gauge field theories in Clifford spaces are used to construct a novel Cl (3, 2) gauge theory of gravity that furnishes modified curvature and torsion tensors leading to important modifications of the standard gravitational action with a cosmological constant. Vacuum solutions exist which allow a cancelation of the contributions of a very large cosmological constant term and the extra terms present in the modified field equations. Generalized gravitational actions in Clifford-spaces are provided and some of their physical implications are discussed. It is shown how the 16 fermions and their masses in each family can be accommodated within a Cl (4) gauge field theory. In particular, the Higgs fields admit a natural Clifford-space interpretation that differs from the one in the Chamseddine–Connes spectral action model of non-commutative geometry. We finalize with a discussion on the relationship with the Pati–Salam color-flavor model group SU (4)C × SU (4)F and its symmetry breaking patterns. An Appendix is included with useful Clifford algebraic relations.

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Inflation without a trace of lambda

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8428-2 ◽

2020 ◽

Vol 80 (9) ◽

Author(s):

John D. Barrow ◽

Spiros Cotsakis

Keyword(s):

General Relativity ◽

Scalar Field ◽

Cosmological Constant ◽

Conformal Transformation ◽

Vacuum Energy ◽

Einstein Equations ◽

Scale Invariant ◽

Field Source ◽

Scale Theory ◽

Wide Range

AbstractWe generalise Einstein’s formulation of the traceless Einstein equations to f(R) gravity theories. In the case of the vacuum traceless Einstein equations, we show that a non-constant Weyl tensor leads via a conformal transformation to a dimensionally homogeneous (‘no-scale’) theory in the conformal frame with a scalar field source that has an exponential potential. We then formulate the traceless version of f(R) gravity, and we find that a conformal transformation leads to a no-scale theory conformally equivalent to general relativity and a scalar field $$\phi $$ ϕ with a potential given by the scale-invariant form: $$V(\phi )=\frac{D-2}{4D}Re^{-\phi }$$ V ( ϕ ) = D - 2 4 D R e - ϕ , where $$\phi =[2/(D-2)]\ln f^{\prime }(R)$$ ϕ = [ 2 / ( D - 2 ) ] ln f ′ ( R ) . In this theory, the cosmological constant is a mere integration constant, statistically distributed in a multiverse of independent causal domains, the vacuum energy is another unrelated arbitrary constant, and the same is true of the height of the inflationary plateau present in a huge variety of potentials. Unlike in the conformal equivalent of full general relativity, flat potentials are found to be possible in all spacetime dimensions for polynomial lagrangians of all orders. Hence, we are led to a novel interpretation of the cosmological constant vacuum energy problem and have accelerated inflationary expansion in the very early universe with a very small cosmological constant at late times for a wide range of no-scale theories. Fine-tunings required in traceless general relativity or standard non-traceless f(R) theories of gravity are avoided. We show that the predictions of the scale-invariant conformal potential are completely consistent with microwave background observational data concerning the primordial tilt and the tensor-to-scalar ratio.

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SOLITONS IN TWO-DIMENSIONAL ANTI-DE SITTER SPACE

International Journal of Modern Physics A ◽

10.1142/s0217751x10048615 ◽

2010 ◽

Vol 25 (02n03) ◽

pp. 289-299

Author(s):

TONNIS TER VELDHUIS

Keyword(s):

Field Theory ◽

Scalar Field ◽

Soliton Solution ◽

Quantum Correction ◽

Soliton Solutions ◽

Two Dimensional ◽

De Sitter ◽

Fluctuation Spectrum ◽

Background Space ◽

The One

Soliton solutions in a scalar field theory defined on an AdS1+1 background space-time are investigated. An analytic soliton solution is obtained in a polynomial model, and the classical soliton mass is calculated. The fluctuation spectrum around the soliton solution is determined, and the one-loop quantum correction to the soliton mass is computed in the semi-classical approximation.

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Role of Regularization in Quantum Corrections to the Scalar–Tensor Theories of Gravity

Modern Physics Letters A ◽

10.1142/s0217732397000388 ◽

1997 ◽

Vol 12 (06) ◽

pp. 371-380 ◽

Cited By ~ 6

Author(s):

Yasunori Fujii

Keyword(s):

Scalar Field ◽

Invariant Theory ◽

Quantum Corrections ◽

Scale Invariant ◽

Classical Level ◽

Fifth Force ◽

Robust Property ◽

Theories Of Gravity ◽

Matter Fields

We show that regularizing divergent integrals is important when applied to the loop diagrams corresponding to quantum corrections to the coupling of the "gravitational" scalar field due to the interaction among matter fields. We use the method of continuous spacetime dimensions to demonstrate that WEP is a robust property of the Brans–Dicke theory beyond the classical level, hence correcting our previous assertion of the contrary. The same technique can be used to yield the violation of WEP when applied to the scale-invariant theory, thus providing another reason for expecting fifth-force-type phenomena.

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