122660242
Adiabatic regularization and particle creation for spin one-half fields
The extension of the adiabatic regularization method to spin-$1/2$ fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-$1/2$ fields. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.
53551802
Spacetime correlators of perturbations in slow-roll de Sitter inflation
(Dated: January 27, 2014)Two-point correlators and self-correlators of primordial perturbations in quasi-de Sitter space-time backgrounds are considered. For large separations two-point correlators exhibit nearlyscale invariance, while for short distances self-correlators need standard renormalization. Westudy the deformation of two-point correlators to smoothly match the self-correlators at coinci-dence. The corresponding angular power spectrum is evaluated in the Sachs-Wolfe regime of lowmultipoles. Scale invariance is maintained, but the amplitude of C
119107431
Adiabatic regularization for spin-1/2 fields
J.N.-S. would like to thank Leonard Parker for very useful discussions. This work is supported by the Spanish Grant No. FIS2011-29813-C02-02 and the Consolider Program CPANPHY-1205388.
44276907
Renormalized stress-energy tensor for spin-1/2 fields in expanding universes
We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-$1/2$ field in a spatially flat FLRW universe. Its computation is based on the extension of the adiabatic regularization method to fermion fields introduced recently in the literature. The tensor is given in terms of UV-finite integrals in momentum space, which involve the mode functions that define the quantum state. As illustrative examples of the method efficiency, we see how to compute the renormalized energy density and pressure in two interesting cosmological scenarios: a de Sitter spacetime and a radiation-dominated universe. In the second case, we explicitly show that the late-time renormalized stress-energy tensor behaves as that of classical cold matter. We also check that, if we obtain the adiabatic expansion of the scalar field mode functions with a similar procedure to the one used for fermions, we recover the well-known WKB-type expansion.
118148302
Conformal anomaly and primordial magnetic fields
The conformal symmetry of the quantized electromagnetic field breaks down in curved space-time. We point out that this conformal anomaly is able to generate a sizable magnetic field during a phase of slow-roll inflation. Such primordial magnetism is characterized by the expectation value of the squared of the magnetic field for comoving observers, which at leading order in slow-roll takes the value $\ =\frac{8}{15(4\pi)^2}\, H^4\epsilon$, where $\epsilon$ is the standard slow-roll parameter. This result is insensitive to the intrinsic ambiguities of renormalization in curved space-times. The information in the quantum state gets diluted during inflation and does not affect the prediction. A primordial field of this strength is able to seed the observed cosmic magnetism.
119048676
Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus: II. Triangular and hexagonal lattices
We compute the finite-size corrections to the free energy, internal energy and specific heat of the critical two-dimensional spin-1/2 Ising model on triangular and hexagonal lattices wrapped on a torus. We find the general form of the finite-size corrections to these quantities, as well as explicit formulae for the first coefficients of each expansion. We analyse the implications of these findings for the renormalization-group description of the model.