Cosmological solutions from models with unified dark energy and dark matter and with inflaton field

Recently, few cosmological models with additional non-Riemannian volume form(s) have been proposed. In this article we use Supernovae type Ia experimental data to test one of these models which provides a unified description of both dark energy via dynamically generated cosmological constant and dark matter as a "dust" fluid due to a hidden nonlinear Noether symmetry. It turns out that the model allows various scenarios of the future Universe evolution and in the same time perfectly fits contemporary observational data. Further, we investigate the influence of an additional inflaton field with a step like potential. With its help we can reproduce the Universe inflation epoch, matter dominated epoch and present accelerating expansion in a seamless way. Interesting feature is that inflaton undergoes a finite change during its evolution. It can be speculated that the inflaton asymptotic value is connected to the vacuum expectation value of the Higgs field.Comment: 10 pages, 4 figures, prepared for the Proceedings of the XII. International Workshop Lie Theory And Its Applications In Physics (2017

Scale Symmetry Breaking from the Dynamics of Maximal Rank Gauge Field Strengths

Scale invariant theories which contain maximal rank gauge field strengths (of $D$ indices in $D$ dimensions) are studied. The integration of the equations of motion of these gauge fields leads to the s.s.b. of scale invariance. The cases in study are: i) the spontaneous generation of $r^{-1}$ potentials in particle mechanics in a theory that contains only $r^{-2}$ potentials in the scale invariant phase, ii) mass generation in scalar field theories iii) generation of non trivial dilaton potentials in generally covariant theories, iv) spontaneous generation of confining behavior in gauge theories. The possible origin of these models is discussed.Comment: 14 pages, latex, no figures, references adde

Scale Invariance and Vacuum Energy

The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form $S = \int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" $\phi$ has to be introduced, with non-trivial potentials $V(\phi)$ = $f_{1}e^{\alpha\phi}$ in $L_1$ and $U(\phi)$ = $f_{2}e^{2\alpha\phi}$ in $L_2$. This leads to non-trivial mass generation and a potential for $\phi$ which is interesting for new inflation. Scale invariant mass terms for fermions lead to a possible explanation of the present day accelerated universe and of cosmic coincidences.Comment: Essay awarded an honorable mention in the 1999 Gravity Research Foundation Competition, Published in Mod. Phys. Lett. A14: 1397 (1999

Strings and branes with a modified measure

In string theory, the consequences of replacing the measure of integration $\sqrt{-\gamma}d^2 x$ in the Polyakov's action by $\Phi d^2 x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric $\gamma_{ab}$ defined in the string are studied. The string tension appears as an integration constant of the equations of motion. The string tension can change in different parts of the string due to the coupling of gauge fields and point particles living in the string. The generalization to higher dimensional extended objects is also studied. In this case there is no need of a fine tuned cosmological term, in sharp contrast to the standard formulation of the generalized Polyakov action for higher dimensional branes