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Mazumdar A.,Lancaster University | Zaldivar B.,Institute Fisica Teorica
Nuclear Physics B | Year: 2014

The aim of this paper is to determine an exact definition of the reheat temperature for a generic perturbative decay of the inflaton. In order to estimate the reheat temperature, there are two important conditions one needs to satisfy: (a) the decay products of the inflaton must dominate the energy density of the universe, i.e. the universe becomes completely radiation dominated, and (b) the decay products of the inflaton have attained local thermodynamical equilibrium. For some choices of parameters, the latter is a more stringent condition, such that the decay products may thermalise much after the beginning of radiation-domination. Consequently, we have obtained that the reheat temperature can be much lower than the standard-lore estimation. In this paper we describe under what conditions our universe could have efficient or inefficient thermalisation, and quantify the reheat temperature for both the scenarios. This result has an immediate impact on many applications which rely on the thermal history of the universe, in particular gravitino abundance. © 2014 The Authors.

Sierra G.,Institute Fisica Teorica | Rodriguez-Laguna J.,Charles III University of Madrid
Physical Review Letters | Year: 2011

Berry and Keating conjectured that the classical Hamiltonian H=xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, on average, as the nontrivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this Letter, we show that the Hamiltonian H=x(p+p2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet L functions using different self-adjoint extensions of H. We discuss the relation of our work to Polyas fake zeta function and suggest an experimental realization in terms of the Landau model. © 2011 American Physical Society.

Sierra G.,Institute Fisica Teorica
Journal of Physics A: Mathematical and Theoretical | Year: 2012

We study a general class of models whose classical Hamiltonians are given by H = U(x)p + V(x)/p, where x and p are the position and momentum of a particle moving in one dimension, and U and V are positive functions. This class includes the Hamiltonians H I = x(p + 1/p) and H II = (x + 1/x)(p + 1/p), which have been recently discussed in connection with the nontrivial zeros of the Riemann zeta function. We show that all these models are covariant under general coordinate transformations. This remarkable property becomes explicit in the Lagrangian formulation which describes a relativistic particle moving in a (1+1)-dimensional spacetime whose metric is constructed from the functions U and V. General covariance is maintained by quantization and we find that the spectra are closely related to the geometry of the associated spacetimes. In particular, the Hamiltonian H I corresponds to a flat spacetime, whereas its spectrum approaches the Riemann zeros on average. The latter property also holds for the model H II, whose underlying spacetime is asymptotically flat. These results suggest the existence of a Hamiltonian whose underlying spacetime encodes the prime numbers, and whose spectrum provides the Riemann zeros. © 2012 IOP Publishing Ltd.

Lavalle J.,University of Turin | Lavalle J.,Institute Fisica Teorica
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2010

Recent measurements performed with some direct dark matter detection experiments, e.g. CDMS-II and CoGENT (after DAMA/LIBRA), have unveiled a few events compatible with weakly interacting massive particles. The preferred mass range is around 10 GeV, with a quite large spin-independent cross section of 10⊃-43-10⊃-41cm2. In this paper, we recall that a light dark matter particle with dominant couplings to quarks should also generate cosmic-ray antiprotons. Taking advantage of recent works constraining the Galactic dark matter mass profile on the one hand and on cosmic-ray propagation on the other hand, we point out that considering a thermal annihilation cross section for such low mass candidates very likely results in an antiproton flux in tension with the current data, which should be taken into account in subsequent studies. © 2010 The American Physical Society.

Sierra G.,Institute Fisica Teorica
Journal of Physics A: Mathematical and Theoretical | Year: 2014

We construct a Hamiltonian HRwhose discrete spectrum contains, in a certain limit, the Riemann zeros. HRis derived from the action of a massless Dirac fermion living in a domain of Rindler spacetime, in 1 + 1 dimensions, which has a boundary given by the world line of a uniformly accelerated observer. The action contains a sum of delta function potentials that can be viewed as partially reflecting moving mirrors. An appropriate choice of the accelerations of the mirrors, provide primitive periodic orbits that are associated with the prime numbers p, whose periods, as measured by the observers clock, are log p. Acting on the chiral components of the fermion χ ±, HRbecomes the Berry-Keating Hamiltonian ±(xp + px)/2, where x is identified with the Rindler spatial coordinate and with the conjugate momentum. The delta function potentials give the matching conditions of the fermion wave functions on both sides of the mirrors. There is also a phase shift eiθfor the reflection of the fermions at the boundary where the observer sits. The eigenvalue problem is solved by transfer matrix methods in the limit where the reflection amplitudes become infinitesimally small. We find that, for generic values of θ, the spectrum is a continuum where the Riemann zeros are missing, as in the adelic Connes model. However, for some values of θ, related to the phase of the zeta function, the Riemann zeros appear as discrete eigenvalues that are immersed in the continuum. We generalize this result to the zeros of Dirichlet L-functions, which are associated to primitive characters, that are encoded in the reflection coefficients of the mirrors. Finally, we show that the Hamiltonian associated to the Riemann zeros belongs to class AIII, or chiral GUE, of the Random Matrix Theory. © 2014 IOP Publishing Ltd.

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