Search Results (5)

We study the Stueckelberg field in de Sitter space, which is a massive vector field with the gauge fixing (GF) term ${\displaystyle \frac{1}{2\zeta }}{({A^{\mu }}_{;\mu })}^2$. We obtain the vacuum stress tensor, which consists of the transverse, longitudinal, temporal, and GF parts, and each contains various UV divergences. By the minimal subtraction rule, we regularize each part of the stress tensor to its pertinent adiabatic order. The transverse stress tensor is regularized to the 0th adiabatic order, while the longitudinal, temporal, and GF stress tensors are regularized to the 2nd adiabatic order. The resulting total regularized vacuum stress tensor is convergent and maximally symmetric, has a positive energy density, and respects the covariant conservation, and thus, it can be identified as the cosmological constant that drives the de Sitter inflation. Under the Lorenz condition ${A^{\mu }}_{;\mu }=0$, the regularized Stueckelberg stress tensor reduces to the regularized Proca stress tensor that contains only the transverse and longitudinal modes. In the massless limit, the regularized Stueckelberg stress tensor becomes zero, and is the same as that of the Maxwell field with the GF term, and no trace anomaly exists. If the order of adiabatic regularization were lower than our prescription, some divergences would remain. If the order were higher, say, under the conventional 4th-order regularization, more terms than necessary would be subtracted off, leading to an unphysical negative energy density and the trace anomaly simultaneously. Full article

It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic evolution of viscous hadron and parton epochs in casual and non-casual Eckart frame is analyzed. By proposing equations of state deduced from recent lattice QCD simulations including pressure p, energy density $\rho$, and temperature T, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter $\dot{H}$, the cosmic energy density $\dot{\rho }$, and the share $\dot{\eta }$ and the bulk viscous coefficient $\dot{\zeta }$. We also suggest how the bulk viscous pressure $\mathsf{\Pi }$ could be related to H. We conclude that the relativistic theory of fluids, the Eckart frame, and the finite viscous coefficients play essential roles in the cosmic evolution, especially in the hadron and parton epochs. Full article

Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel–Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel–Stewart, the differential equations are very sophisticated to be solved. They are outlined here as road-maps for future studies. For Eckart theory, the only possible solution is the functionality, $H\left(a\right(t\left)\right)$, where $H\left(t\right)$ is the Hubble parameter and $a\left(t\right)$ is the scale factor, but none of them so far could to be directly expressed in terms of either proper or cosmic time t. For Eckart-type viscous background, especially at finite cosmological constant, non-singular $H\left(t\right)$ and $a\left(t\right)$ are obtained, where $H\left(t\right)$ diverges for QCD/EW and asymptotic EoS. For non-viscous background, the dependence of $H\left(a\right(t\left)\right)$ is monotonic. The same conclusion can be drawn for an ideal EoS. We also conclude that the rate of decreasing $H\left(a\right(t\left)\right)$ with increasing $a\left(t\right)$ varies from epoch to epoch, at vanishing and finite cosmological constant. These results obviously help in improving our understanding of the nucleosynthesis and the cosmological large-scale structure. Full article

The definition of a length operator in quantum cosmology is usually influenced by a quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of a semiclassical wave-functional state are investigated, for which the modern measure(ment)s is consistent. The results of a length measurement at present times are compared with the same measurement operation at cosmological times. By this measure, it is possible to discriminate, within the same Planck-length expansion, the corrections to a Minkowski flat space possibly due to classicalization of quantum phenomena at the Planck time and those due to possible quantum-gravitational manifestations of present times. This analysis and the comparison with the previous literature can be framed as a test for the verification of the time at which anomalies at present related to the gravitational field, and, in particular, whether they are ascribed to the classicalization epoch. Indeed, it allows to discriminate not only within the possible quantum features of the quasi (Minkowski) flat spacetime, but also from (possibly Lorentz violating) phenomena detectable at high-energy astrophysical scales. The results of two different (coordinate) length measures have been compared both at cosmological time and as a perturbation element on flat Minkowski spacetime. The differences for the components of the corresponding classical(ized) metric tensor have been analyzed at different orders of expansions. The results of the expectation values of a length operator in the universe at the Planck time must be comparable with the same length measurements at present times, as far as the metric tensor is concerned. The comparison of the results of (straight) length measures in two different directions, in particular, can encode the pertinent information about the parameters defining the semiclassical wavefunctional for (semiclassicalized) gravitational field. Full article

We review inflationary cosmology in modified gravity such as R² gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the R² term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of scalar modes of the density perturbations and the tensor-to-scalar ratio can be consistent with the Planck results. Bounce cosmology in F(R) gravity is also explained. Full article