A Simple Operator Check of the Effective Fermion Mode Function during Inflation
Shun-Pei Miao, R. P. Woodard
备注：
39 pages, no figuire.(1) New version has clarified the ultimate motivation by adding sentences to the abstract and to the penultimate paragraph of the introduction. (2) By combining a number of references and equations we have managed to reduce the length by 2 pages
We present a relatively simple operator formalism which reproduces the leading infrared logarithm of the one loop quantum gravitational correction to the fermion mode function on a locally de Sitter background. This rule may serve as the basis for an eventual stochastic formulation of quantum gravity during inflation. Such a formalism would not only effect a vast simplification in obtaining the leading powers of $\ln(a)$ at fixed loop orders, it would also permit us to sum the series of leading logarithms. A potentially important point is that our rule does not seem to be consistent with any simple infrared truncation of the fields. Our analysis also highlights the importance of spin as a gravitational interaction that persists even when kinetic energy has redshifted to zero.
The four-fermion gravitational interaction is induced by torsion, and gets dominating on the Planck scale. The regular, axial-axial part of this interaction by itself does not stop the gravitational compression. However, the anomalous, vector-vector interaction results in a natural way both in big bounce and in inflation.
We solve the effective Dirac equation for massless fermions during inflation in the simplest gauge, including all one loop corrections from quantum gravity. At late times the result for a spatial plane wave behaves as if the classical solution were subjected to a time dependent field strength renormalization of Z_2(t) = 1 - \frac{17}{4 π} G H^2 \ln(a) + O(G^2). We show that this also follows from making the Hartree approximation, although the numerical coefficients differ.
We estimate fermion loop corrections to the two-point correlation function of primordial tensor perturbations in a slow-roll inflationary background. We particularly compute an explicit term of one-loop correction from a massless fermion, and then extend to the complete Interaction Hamiltonian. After that, we study one-loop corrections contributed by a massive fermion to primordial tensor fluctuations. The loop correction arisen from a massless fermion field contains logarithms and thus may constrain the validity of perturbation theory in inflationary cosmology, but the situation could be rela…
Remarkably, if $CP$ was spontaneously broken in the physics of inflation, fermions would notice and remember it. Based on that, we present a new (non-thermal) mechanism for generating self-interacting dark Dirac fermions prior to the Hot Big Bang. The non-Abelian gauge fields and axions are well-motivated matter contents for the particle physics of inflation. In this background, we analytical study Dirac fermion doublets charged under the $SU(2)$ gauge field and use point-splitting technique to regularize the currents. We show that the non-trivial $CP$-violating vacuum structure of $SU(2)$-axi…
Inflation has long been the accepted paradigm for understanding the early universe. Most models of inflation have a scalar field acting as the inflaton particle which decays after inflation during a process called reheating into standard model (SM) particles. In this work, we consider a fermion as the inflaton field. Noether symmetry arguments show that an exponentially expanding universe is possible with a fermion if it is coupled non-minimally to gravity. We use such a scenario in this model to study both inflation and reheating. We find relations between the various parameters involved in t…
We compute the one loop self energy, in a locally de Sitter background, for a massless fermion which is Yukawa-coupled to a massless, minimally coupled scalar. We then solve the modified Dirac equation resulting from inclusion of the self energy. We find faster-than-exponential growth in the fermion wave function, consistent with the production of fermions through a process in which a scalar and a fermion-anti-fermion pair are ripped out of the vacuum by inflation.
The inclusion of Dirac fermions in Einstein-Cartan gravity leads to a four-fermion interaction mediated by non-propagating torsion, which can allow for the formation of a Bardeen-Cooper-Schrieffer condensate. By considering a simplified model in 2+1 spacetime dimensions, we show that even without an excess of fermions over antifermions, the nonthermal distribution arising from preheating after inflation can give rise to a fermion condensate generated by torsion. We derive the effective Lagrangian for the spacetime-dependent pair field describing the condensate in the extreme cases of nonrelati…
A model of inflation realization driven by fermions with curvature-dependent mass is studied. Such a term is derived from the Covariant Canonical Gauge Theory of gravity (CCGG) incorporating Dirac fermions. We obtain an initial de Sitter phase followed by a successful exit, and moreover, we acquire the subsequent thermal history, with an effective matter era, followed finally by a dark-energy epoch. This behavior is a result of the effective `weakening' of gravity at early times, due to the decreased curvature-dependent fermion mass. Through the perturbation level, we obtain the scalar spectra…
In this work we show that the gravitational Chern-Simons term, aside from being a key ingredient in inflationary baryogenesis, modifies super-horizon gravitational waves produced during inflation. We compute the super-Hubble gravitational power spectrum in the slow-roll approximation and show that its overall amplitude is modified while its spectral index remains unchanged (at leading order in the slow-roll parameters). Then, we calculate the correction to the tensor to scalar ratio, T/S. We find a correction of T/S which is dependent on $\cal{N}$ (more precisely quadratic in ${\cal N}$), the …
A Unified Fermionic Origin for Density-Driven Waterfall Inflation and its Multi-Messenger Signatures
Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（台湾大学梁氏宇宙学与粒子天体物理中心）；Department of Physics and Graduate Institute of Astrophysics, National Taiwan University（台湾大学物理系及天体物理研究所）；Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University（斯坦福大学SLAC国家加速器实验室卡弗里粒子天体物理与宇宙学研究所）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Center for Field Theory and Particle Physics & Department of Physics, Fudan University（复旦大学场论与粒子物理中心及物理系）；Center for Astronomy and Astrophysics, Fudan University（复旦大学天体物理中心）；Laboratori Nazionali di Frascati INFN（INFN弗拉斯卡蒂国家实验室）；INFN sezione Roma Tor Vergata（INFN罗马托维加塔分部）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学前沿研究院宇宙物理数学卡弗里研究所（WPI））；Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理中心引力物理中心）
We consider several gauge invariant higher dimensional operators that couple gravity, gauge fields and scalar or fermionic fields and thus break conformal invariance. In particular, we consider terms that break conformal invariance by the photon coupling to heavy and light fermions. While the coupling to heavy fermions typically do not induce significant magnetic fields, the coupling to light fermions may produce observable magnetic fields when there are a few hundred light fermions. Next we consider Planck scale modifications of the kinetic gauge terms of the form f(phi) F_{mu nu} F^{mu nu} a…
We analyze the existence and stability of dynamical attractor solutions for cosmological inflation driven by the coupling between fermions and a gauge field. Assuming a spatially homogeneous and isotropic gauge field and fermion current, the interacting fermion equation of motion reduces to that of a free fermion up to a phase shift. Consistency of the model is ensured via the Stuckelberg mechanism. We prove the existence of exactly one stable solution, and demonstrate the stability numerically. Inflation arises without fine tuning, and does not require postulating any effective potential or n…
We compute the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. We employ dimensional regularization and obtain a fully renormalized result by absorbing all divergences with BPHZ counterterms. An interesting technical aspect of this computation is the need for a noninvariant counterterm owing to the breaking of de Sitter invariance by our gauge condition. Our result can be used in the quantum-corrected Dirac equation to search for inflation-enhanced quantum effects from gravitons, analogous to those which have been found for massless…
We compute the one loop graviton contribution to the self-energy of a very light fermion on a locally de Sitter background. This result can be used to study the effect that a small mass has on the propagation of fermions through the sea of infrared gravitons generated by inflation. We employ dimensional regularization and obtain a fully renormalized result by absorbing all divergences with BPHZ counterterms. An interesting technical aspect of this computation is the need for two noninvariant counterterms owing to the breaking of de Sitter invariance by our gauge condition.
We study the production and backreaction of massive vector-like fermions in the background of a classical SU(2) gauge field during axion-driven inflation. We demonstrate all ultraviolet divergences due to the interactions with the fermions can be absorbed by renormalization of the axion wavefunction and the gauge coupling. The effects of the fermion-axion interaction vanish in the massless limit as required by symmetry. For very massive fermions, contact interactions are induced between the axion, the gauge field and the gravitational field. In this massive limit, we find the usual axion-gauge…
Axion Inflation from Heavy-Fermion One-Loop Effects
International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（国际理论物理中心亚太分中心，中国科学院大学）；Taiji Laboratory for Gravitational Wave Universe, University of Chinese Academy of Sciences（太极引力波宇宙实验室，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Physics, Anhui Normal University（安徽师范大学物理系）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学学院）
Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation
Institute for Theoretical Physics, University of Münster（明斯特大学理论物理研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙粒子与宇宙学研究所（WPI））；Physics Faculty, Taras Shevchenko National University of Kyiv（基辅塔拉斯·舍甫琴科国立大学物理系）
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Fermion creation during preheating in the presence of multiple scalar fields exhibits a range of interesting behaviour relevant to estimating post-inflation gravitino abundances. We present non-perturbative analysis of this phenomenon over a 6-dimensional parameter space in an expanding background paying particular attention to the interplay between instant and direct fermion preheating. In the broad resonance regime we find that instant fermion production is sensitive to suppression of the long wavelength scalar field modes during inflation. Further, the standard scenario of resonant fermioni…
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This paper study the evolution of the universe filled with a neutral mass dimension one fermionic field, sometimes called Elko. The numerical analysis of the coupled system of equations furnish a scale factor growth and energy density evolution that correctly reproduces the inflationary phase of the universe. After that, supposing a mechanism of energy transference to ordinary matter, the initial conditions generated after inflation drives the radiation dominated phase and also the subsequent dark matter evolution, since the Elko field is a good dark matter candidate. The energy density of the…
Quark, lepton and right-handed neutrino production via inflation
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；China Center of Advanced Science and Technology（中国高等科学技术中心）；University of Warsaw（华沙大学）
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