Suppressing the CMB quadrupole with a bounce from the contracting phase to inflation

Most bouncing models contain a contracting phase from a very large and rarefied state, where dark energy might have had an important role. If this is that case, the presence of dark energy can modify the initial conditions and evolution of cosmological perturbations, changing the known results already obtained in the literature concerning their amplitude and spectrum. In this work, we assume the simplest and most appealing candidate for dark energy, the cosmological constant, and study its influence on the evolution of cosmological perturbations during the contracting phase of a bouncing model, containing also a perfect fluid with constant equation of state parameter w. We show that, due to the vacuum state choice we have to make when a cosmological constant is present, the spectrum of the perturbations are substantially altered. We conclude that, in this case, the presence of a stiff matter fluid in the contracting phase is needed in order to have a scale invariant spectrum of perturbations in the expanding phase.

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HOW DID THE UNIVERSE BEGIN?

International Journal of Modern Physics D ◽

10.1142/s0218271898000486 ◽

1998 ◽

Vol 07 (05) ◽

pp. 727-735 ◽

Cited By ~ 10

Author(s):

M. D. POLLOCK

Keyword(s):

Time Interval ◽

Field Equations ◽

Superstring Theory ◽

Higher Derivative ◽

Planck Time ◽

Contracting Phase ◽

Three Space ◽

Previous Phase ◽

The Universe ◽

Radius Function

The question of the initial configuration of the Universe — did the expanding Friedmann space-time ds2 = dt2 - a2(t)dx2 tend to a singularity when extrapolated back in time, or was there a turning point, indicating a previous phase of contraction? — is re-examined in the context of the heterotic superstring theory of Gross et al. If the adiabatic index tends to the value γ = 1, then the higher-derivative terms ℛ2 in the Lagrangian L dominate the Einstein–Hilbert term R/16πG in the time interval t p ≲ t ≲ 4t p , during which the action is S ≈ 25ℏ, guaranteeing the approximate validity of the classical field equations (if the compactification process is ignored), where [Formula: see text] is the Newton gravitational constant and t p is the Planck time. Under these conditions, Ruzmaĭkina and Ruzmaĭkina have shown, for a flat three-space with K = 0, that the initial singularity can only be avoided at all if there is a spin-zero tachyon, a conclusion modified by Barrow and Ottewill if K = ±1. We have previously shown, however, that the theory is tachyon-free, and have argued that K has to vanish for the existence of a well-defined, quantum-mechanical ground state. Also, if there is no inflation, the radius function is always much too large for the terms in K to exert any effect, a(t) ≳ 5 × 1029t p . While if γ = 2, then ℛ2 never dominates R/16πG. Accordingly, we conjecture that the Universe did not bounce, irrespective of the value of γ, the absence of a prior contracting phase thus being an aspect of causality.

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Nonsingular cosmology from an unstable Higgs field

International Journal of Modern Physics D ◽

10.1142/s0218271817400065 ◽

2017 ◽

Vol 26 (01) ◽

pp. 1740006 ◽

Cited By ~ 2

Author(s):

Robert H. Brandenberger ◽

Yi-Fu Cai ◽

Youping Wan ◽

Xinmin Zhang

Keyword(s):

Higgs Mass ◽

Higgs Field ◽

High Energy ◽

Large Field ◽

Bouncing Cosmology ◽

Very High Energy ◽

Contracting Phase ◽

Early Universe Cosmology ◽

Very High ◽

Higgs Scalar

The observed value of the Higgs mass indicates an instability of the Higgs scalar at large energy scales, and hence also at large field values. In the context of early universe cosmology, this is often considered to lead to problems. Here, we point out that we can use the instability of the Higgs field to generate an ekpyrotic phase of contraction. In the context of string theory, it is possible that at very high energy densities, extra states become massless leading to an [Formula: see text]-brane which causes the transition between a contracting phase in the past and the current expanding phase. Thus, the Higgs field may be useable to generate a nonsingular bouncing cosmology in which the anisotropy problem of usual bouncing scenarios is mitigated.

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The Principle of Good Faith in the Palestinian Civil Code Draft and Its Role in Maintaining Economic Contractual Equilibrium at the Pre-Contracting Phase

Journal of Politics and Law ◽

10.5539/jpl.v12n3p113 ◽

2019 ◽

Vol 12 (3) ◽

pp. 113

Author(s):

Osama Ismail Mohammad Amayreh ◽

Izura Masdina Mohamed Zakri ◽

Pardis Moslemzadeh Tehrani ◽

Yousef Mohammad Shandi

Keyword(s):

Civil Code ◽

Good Faith ◽

Tort Liability ◽

Legal Basis ◽

Bad Faith ◽

Legal Provisions ◽

The Subject ◽

Contracting Phase ◽

The Stability ◽

Definition Of

The jurisprudential and judicial legal trend tends to apply the principle of good faith at the pre-contracting phase as one of the most substantial principles governing this phase, since it is inconceivable that the parties are to negotiate in bad faith, and then must implement the contract in good faith, in accordance with the traditional legal rule that “fraud spoils everything it touches”. However, the Palestinian legislature has ignored enacting legal provisions obliging the parties to abide by the principle of good faith in the pre-contracting phase causing a legislative deficiency in the legislative remedies of the subject of good faith in the pre-contracting phase. This paper seeks to prove that replacing a provision that requires good faith in negotiations with the provisions of tort liability causes many legal problems. To prove this, the legal provisions should be analysed which would also include determining the definition of the principle of good faith, and the function of that principle in achieving contractual equilibrium and the legal basis for this principle at the stage of negotiation which should also be analysed. Moreover, a comparative analytical approach with the French civil code is used to illustrate the Palestinian legislative deficiencies and the need to legislate a legal article which obligates the negotiating parties to behave in good faith, as this has become an unavoidable reality that should be dealt with to contribute to the stability of civil and commercial transactions. As such, the legal article should also specify the compensation to be claimed.

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Unavoidable shear from quantum fluctuations in contracting cosmologies

The European Physical Journal C ◽

10.1140/epjc/s10052-021-08932-0 ◽

2021 ◽

Vol 81 (2) ◽

Author(s):

Julien Grain ◽

Vincent Vennin

Keyword(s):

Scalar Field ◽

Equation Of State ◽

Energy Density ◽

State Parameter ◽

Quantum Fluctuations ◽

Shear Instability ◽

Initial Value ◽

Anisotropic Stress ◽

Equation Of State Parameter ◽

Contracting Phase

AbstractContracting cosmologies are known to be flawed with a shear instability, where the contribution from the anisotropic stress to the overall energy density grows as $$a^{-6}$$ a - 6 , with a the scale factor. Classically, whether or not this contribution becomes important before the bounce depends on its initial value, which can always be sufficiently fine tuned to make it irrelevant. However, vacuum quantum fluctuations inevitably provide a non-vanishing source of anisotropic stress. In this work, we compute the minimum amount of shear that is obtained if one assumes that it vanishes initially, but lets quantum fluctuations build it up. In practice, we consider a massless test scalar field, and describe its quantum fluctuations by means of the stochastic “inflation” (though here applied to a contracting phase) formalism. We find that, if the equation-of-state parameter of the contraction satisfies $$w>-1/9$$ w > - 1 / 9 , regardless of when the contracting phase is initiated, the time at which the shear becomes sizeable is always when the Hubble scale approaches the Planck mass (which is also where the bounce is expected to take place). However, if $$w<-1/9$$ w < - 1 / 9 , the shear backreaction becomes important much earlier, at a point that depends on the overall amount of contraction.

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