We explore the consequences of a time-dependent inflaton Equation-of-State (EoS) parameter in the context of the post-inflationary perturbative Boltzmann reheating. In particular, we numerically solve the perturbative coupled system of Boltzmann equa
tions involving the inflaton energy density, the radiation energy density and the related entropy density and temperature of the produced particle thermal bath. We exploit reasonable Ansatze for the EoS and discuss the robustness of the Boltzmann system. We also comment on the possible microscopic origin related to a time dependent inflaton potential, discussing the consequences on a preheating stage and the related (primordial) gravitational waves.
According to the most popular scenario, the early Universe should have experienced an accelerated expansion phase, called Cosmological Inflation, after which the standard Big Bang Cosmology would have taken place giving rise to the radiation-dominate
d epoch. However, the details of the inflationary scenario are far to be completely understood. Thus, in this paper we study if possible additional (exotic) cosmological phases could delay the beginning of the standard Big Bang history and alter some theoretical predictions related to the inflationary cosmological perturbations, like, for instance, the order of magnitude of the tensor-to-scalar ratio $r$.
The moduli space of toroidal type I vacua, which are consistent at the non-perturbative level, consists of independent branches characterized by the number (0, 16 or 32) of rigid branes sitting on top of orientifold planes. This structure persists al
so when supersymmetry is spontaneously broken a la Scherk-Schwarz. We show that all the components of the moduli space in dimension $Dge 5$ indeed admit heterotic dual components, by explicitly constructing heterotic-type I dual pairs with the rank of the gauge group reduced by 0, 8 or 16 units. In the presence of spontaneous breaking of supersymmetry, the dual pairs we consider are also free of tachyonic instabilities at the one-loop level, provided the scale of supersymmetry breaking is lower than the string scale.
We discuss the perturbative decay of the energy density of a non standard inflaton field $rho_{phi}$ and the corresponding creation of the energy density of the relativistic fields $rho_r$ at the end of inflation, in the perfect fluid description, re
fining some concepts and providing some new computations. In particular, the process is characterized by two fundamental time scales. The first one, $t_text{max}$, occurs when the energy density $rho_r$ reaches its largest value, slightly after the beginning of the reheating phase. The second one, $t_text{reh}$, is the time in which the reheating is completely realized and the thermalization is attained. By assuming a non-instantaneous reheating phase, we are able to derive the energy densities and the temperatures of the produced relativistic bath at $t_text{max}$ and $t_text{reh}$, as well as the value of the corresponding horizon entropy $S_text{hor}$, for an Equation-of-State (EoS) parameter $w e 0$.
In this paper, we discuss the constraints on the reheating temperature supposing an early post-reheating cosmological phase dominated by one or more simple scalar fields produced from inflaton decay and decoupled from matter and radiation. In additio
n, we explore the combined effects of the reheating and non-standard scalar field phases on the inflationary number of $e$-foldings.
We analyse open strings with background electric fields in the internal space, T-dual to branes moving with constant velocities in the internal space. We find that the direction of the electric fields inside a two torus, dual to the D brane velocitie
s, has to be quantised such that the corresponding direction is compact. This implies that D-brane motion in the internal torus is periodic, with a periodicity that can be parametrically large in terms of the internal radii. By S-duality, this is mapped into an internal magnetic field in a three torus, a quantum mechanical analysis of which yields a similar result, i.e. the parallel direction to the magnetic field has to be compact. Furthermore, for the magnetic case, we find the Landau level degeneracy as being given by the greatest common divisor of the flux numbers. We carry on the string quantisation and derive the relevant partition functions for these models. Our analysis includes also the case of oblique electric fields which can arise when several stacks of branes are present. Compact dimensions and/or oblique sectors influence the energy loss of the system through pair-creation and thus can be relevant for inflationary scenarios with branes. Finally, we show that the compact energy loss is always larger than the non-compact one.
We present constraints on the reheating era within the string Fibre Inflation scenario, in terms of the effective equation-of-state parameter of the reheating fluid, $w_{reh}$. The results of the analysis, completely independent on the details of the
inflaton physics around the vacuum, illustrate the behavior of the number of $e$-foldings during the reheating stage, $N_{reh}$, and of the final reheating temperature, $T_{reh}$, as functions of the scalar spectral index, $n_s$. We analyze our results with respect to the current bounds given by the PLANCK mission data and to upcoming cosmological experiments. We find that large values of the equation-of-state parameter ($w_{reh}>1/3$) are particularly favored as the scalar spectral index is of the order of $n_ssim 0.9680$, with a $sigma_{n_s}sim 0.002$ error. Moreover, we compare the behavior of the general reheating functions $N_{reh}$ and $T_{reh}$ in the Fibre Inflation scenario with that extracted by the class of the $alpha$-attractor models with $alpha=2$. We find that the corresponding reheating curves are very similar in the two cases.
We consider the non-supersymmetric magic theories based on the split quaternion and the split complex division algebras. We show that these theories arise as Ehlers $SL(2,mathbb{R})$ and $SL(3,mathbb{R})$ truncations of the maximal supergravity theor
y, exploiting techniques related to very-extended Kac-Moody algebras. We also generalise the procedure to other $SL(n,mathbb{R})$ truncations, resulting in additional classes of non-supersymmetric theories, as well as to truncations of non-maximal theories. Finally, we discuss duality orbits of extremal black-hole solutions in some of these non-supersymmetric theories.
We show that the number of half-supersymmetric p-branes in the Type II theories compactified on orbifolds is determined by the wrapping rules recently introduced, provided that one accounts correctly for both geometric and non-geometric T-dual config
urations. Starting from the Type II theories compactified on K3, we analyze their toroidal dimensional reductions, showing how the resulting half-supersymmetric p-branes satisfy the wrapping rules only by taking into account all the possible higher-dimensional origins. We then consider Type II theories compactified on the orbifold T^6/(Z_2 times Z_2 ), whose massless four-dimensional theory is an N=2 supergravity. Again, the wrapping rules are obeyed only if one includes the complete orbit of the T-duality group, namely either Type IIA or Type IIB theories compactified on either the geometric or the non-geometric T-dual orbifold. Finally, we comment on the interpretation of our results in the framework of the duality between the Heterotic string compactified on K3 times T^2 and the Type II string compactified on a Calabi-Yau threefold.
We discuss non-geometric supersymmetric heterotic string models in D=4, in the framework of the free fermionic construction. We perform a systematic scan of models with four a priori left-right asymmetric Z_2 projections and shifts. We analyze some 2
^{20} models, identifying 18 inequivalent classes and addressing variants generated by discrete torsions. They do not contain geometrical or trivial neutral moduli, apart from the dilaton. However, we show the existence of flat directions in the form of exactly marginal deformations and identify patterns of symmetry breaking where product gauge groups, realized at level one, are broken to their diagonal at higher level. We also describe an inverse Gepner map from Heterotic to Type II models that could be used, in certain non geometric settings, to define effective topological invariants.
