Explosive particle production in non-commutative inflation

Perrier, Hideki; Durrer, Ruth; Rinaldi, Massimiliano

doi:10.1007/jhep01(2013)067

Cited by 6 publications

(5 citation statements)

References 31 publications

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“…This is not surprising since the adiabatic subtraction scheme employed here is valid only for k=a ) m. A similar behavior has also been observed in Ref. [3] in the regime where the adiabatic subtraction is not valid. Figure 1 shows that the main contribution to the 2-point function comes from long wave modes.…”

Section: Comment On ''Origin Of Cosmic Magnetic Fields''supporting

confidence: 88%

Comment on “Origin of Cosmic Magnetic Fields”

2013

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In a recent Letter [1] it has been proposed that primordial magnetic fields are generated during a de Sitter inflationary phase, contrarily to what is commonly believed, and that they are the seeds of the galactic and galaxy cluster magnetic fields observed today. The key result is that the two-point function of the magnetic field, once renormalized with adiabatic subtraction, is constant and proportional to H 4 in de Sitter space-time. In this Comment, we show that, although the result is mathematically correct (it is simply a calculation of the conformal anomaly in de Sitter spacetime), it does not have any physical relevance because inflation cannot be modeled by a de Sitter phase without beginning.In a realistic model of inflation, at the beginning of the quasi-exponential expansion, all physically relevant modes are sub-Hubble modes, short wavelength modes ''inside the horizon.'' The very large scale modes which are already outside the horizon initially are not physically relevant. However, these last ones are precisely the modes responsible for the result of [1] and this is the main reason why we believe that the result is unphysical. As we show below, if one introduces some maximal wavelength, max ¼ 2=k min with k min Þ 0, the entire renormalized two-point function vanishes.Let us substantiate our claim. We follow Ref.[1] (see the Letter for details), and introduce the ''physical''spectrum P phys ðk; mÞ ¼ P ðk; mÞ À P ðAÞ ðk; mÞ, where P ðAÞ ðk; mÞ is the adiabatic expansion up to fourth order [2], and m the photon regulator mass. This removes the ultraviolet divergence of the bare 2-point function and leads to the result shown in Fig. 1. One immediately notes that this cannot be the power spectrum of a well-defined correlation function since it becomes negative at k=a $ m. This signifies, in the best case, that the correlation function has singularities. This is not surprising since the adiabatic subtraction scheme employed here is valid only for k=a ) m. A similar behavior has also been observed in Ref. [3] in the regime where the adiabatic subtraction is not valid. Figure 1 shows that the main contribution to the 2-point function comes from long wave modes. In particular, in the vanishing mass limit, P phys becomes proportional to ðkÞ as pointed out in [1]. If we now introduce a maximal wavelength, k min > 0, and compute the magnetic field from modes above this cutoff, we obtain hBðx; tÞ 2 i ¼ limindependent of the value of k min . This means that, by discarding the modes that are outside the horizon at any fixed beginning of the de Sitter inflationary phase, the amplification of the magnetic field vanishes. Hence, the adiabatic subtraction affects significantly the infrared tail of the physical power spectrum.On the other hand, in a realistic inflationary scenario, where quantum fluctuations take on a time-dependent effective mass, adiabatic subtraction does not alter the spectrum of infrared modes with k=a ( mð . Let us just remark here that in Refs. [4,5] we do not introduce any infrared cutoff, hen...

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Section: Comment On ''Origin Of Cosmic Magnetic Fields''supporting

confidence: 88%

Comment on “Origin of Cosmic Magnetic Fields”

2013

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“…We set also z = 1 (the chemical potential to be zero) as usually one assumes. Now, the number of particles and pressure in quantum gravity regime can be obtained from the relations (30) and (31) as…”

Section: A the Methodsmentioning

confidence: 99%

“…The coherent state approach to the noncommutative geometry was extended in Ref. [7] by means of the kernels in Feynman path integral approach in quantum field theory (see also [30]) . The noncommutativity affects the Feynman propagator in momentum space as…”

Section: Appendix A: Jacobian In Noncommutative Spacesmentioning

confidence: 99%

Spacetime singularity resolution in Snyder noncommutative space

Gorji

Nozari²,

Vakili³

2014

Phys. Rev. D

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Inspired by quantum gravity proposal, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early Universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for natural realization of inflation as a phase transition from quantum gravity regime to the standard radiation dominated era. Also we obtain finite energy and entropy densities for the Universe, when at least the Weak Energy Condition is satisfied. We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the Big Bang singularity is removed.

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“…A general context in which modified dispersion relations finds theoretical grounding is in the of high energy Lorentz invariance violation, either considered phenomenologically [267][268][269] or in the context of a specific construction (such as Hořava gravity [270][271][272][273]). Related contexts where short distance modifications to mode propagation lead to Lorentz invariance violation as a corollary includes non-commutative geometry [274][275][276][277][278][279][280][281][282][283][284][285][286][287][288] and inflation in the presence of a minimal length scale [289][290][291][292][293][294][295][296][297][298][299][300][301][302][303].…”

Section: Initial State Effects?mentioning

confidence: 99%

Features and new physical scales in primordial observables: Theory and observation

Chluba

Hamann

Patil

2015

Int. J. Mod. Phys. D

212

233

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June 22, 20152 All cosmological observations to date are consistent with adiabatic, Gaussian and nearly scale invariant initial conditions. These findings provide strong evidence for a particular symmetry breaking pattern in the very early universe (with a close to vanishing order parameter, ), widely accepted as conforming to the predictions of the simplest realizations of the inflationary paradigm. However, given that our observations are only privy to perturbations, in inferring something about the background that gave rise to them, it should be clear that many different underlying constructions project onto the same set of cosmological observables. Features in the primordial correlation functions, if present, would offer a unique and discriminating window onto the parent theory in which the mechanism that generated the initial conditions is embedded. In certain contexts, simple linear response theory allows us to infer new characteristic scales from the presence of features that can break the aforementioned degeneracies among different background models, and in some cases can even offer a limited spectroscopy of the heavier degrees of freedom that couple to the inflaton. In this review, we offer a pedagogical survey of the diverse, theoretically well grounded mechanisms which can imprint features into primordial correlation functions in addition to reviewing the techniques one can employ to probe observations. These observations include cosmic microwave background anisotropies and spectral distortions as well as the matter two and three point functions as inferred from large-scale structure and potentially, 21 cm surveys.

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Explosive particle production in non-commutative inflation

Cited by 6 publications

References 31 publications

Comment on “Origin of Cosmic Magnetic Fields”

Comment on “Origin of Cosmic Magnetic Fields”

Spacetime singularity resolution in Snyder noncommutative space

Features and new physical scales in primordial observables: Theory and observation

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