Abelian-Higgs strings in Rastall gravity

In this paper we analyze Abelian-Higgs strings in a phenomenological model that takes quantum effects in curved space-time into account. This model, first introduced by Rastall, cannot be derived from an action principle. We formulate phenomenological equations of motion under the guiding principle of minimal possible deformation of the standard equations. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to $2pi$ at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map $S^1 rightarrow S^1$. Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.

Quantum corrections to gravity and their implications for cosmology and astrophysics

The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the post-inflationary cosmology and astrophysics require the corrections to the Einstein-Hilbert action and to the cosmological constant, and those we can not derive yet in a consistent and safe way. At the same time, if we assume that these quantum terms are covariant and that they have relevant magnitude, their functional form can be defined up to a single free parameter, which can be defined on the phenomenological basis. It turns out that the quantum correction may lead, in principle, to surprisingly strong and interesting effects in astrophysics and cosmology.

Testing dark matter warmness and quantity via the reduced relativistic gas model

We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for $Omega$s of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary warmness of Dark Matter. An equivalent equation of state has been used by Sakharov to predict the oscillations in the matter power spectrum. Two kind of tests are accounted for in what follows, namely the ones coming from the dynamics of the conformal factor of the homogeneous and isotropic metric and also the ones based on linear cosmic perturbations. The RRG model demonstrated its high effectiveness, permitting to explore a large volume in the space of mentioned parameters in a rather economic way. Taking together the results of such tests as Supernova type Ia (Union2 sample), $H(z)$, CMB ($R$ factor), BAO and LSS (2dfGRS data), we confirm that $La$CDM is the most favored model. At the same time, for the 2dfGRS data alone we found that an alternative model with a very small quantity of a Dark Matter is also viable. This output is potentially relevant in view of the fact that the LSS is the only test which can not be affected by the possible quantum contributions to the low-energy gravitational action.