On warped string vacuum profiles and cosmologies. Part II. Non-supersymmetric strings

We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetric strings in warped products of flat geometries of the type Mp+1× R × T10−p−2 depending on a single coordinate. In the absence of fluxes and for p < 8, there are two families of these vacua for the orientifold disk-level potential, both involving a finite internal interval. Their asymptotics are surprisingly captured by tadpole-free solutions, isotropic for one family and anisotropic at one end for the other. In contrast, for the heterotic torus-level potential there are four types of vacua. Their asymptotics are always tadpole-dependent and isotropic at one end lying at a finite distance, while at the other end, which can lie at a finite or infinite distance, they can be tadpole-dependent isotropic or tadpole-free anisotropic. We then elaborate on the general setup for including symmetric fluxes, and present the three families of exact solutions that emerge when the orientifold potential and a seven-form flux are both present. These solutions include a pair of boundaries, which are always separated by a finite distance. In the neighborhood of one, they all approach a common supersymmetric limit, while the asymptotics at the other boundary can be tadpole-free isotropic, tadpole-free anisotropic or again supersymmetric. We also discuss corresponding cosmologies, with emphasis on their climbing or descending behavior at the initial singularity. In some cases the toroidal dimensions can contract during the cosmological expansion.

String excitation by initial singularity of inflation

We discuss excitation of string oscillation modes by an initial singularity of inflation. The initial singularity of inflation is known to occur with a finite Hubble parameter, which is generally lower than the string scale, and hence it is not clear that stringy effects become significant around it. With the help of Penrose limit, we find that infinitely heavy oscillation modes get excited when a singularity is strong in the sense of Krolak’s classification. We demonstrate that the initial singularities of Starobinsky and hill top inflation, assuming the slow roll inflation to the past infinity, are strong. Hence stringy corrections are inevitable in the very early stage of these inflation models. We also find that the initial singularity of the hill top inflation could be weak for non-slow roll case.

On Bianchi Type VI$$_0$$ Spacetimes with Orthogonal Perfect Fluid Matter

We study the asymptotic behaviour of Bianchi type VI$$_0$$ 0 spacetimes with orthogonal perfect fluid matter satisfying Einstein’s equations. In particular, we prove a conjecture due to Wainwright about the initial singularity on such backgrounds. Using the expansion-normalized variables of Wainwright–Hsu, we demonstrate that for a generic solution the initial singularity is vacuum dominated, anisotropic and silent. In addition, by employing known results on Bianchi backgrounds, we obtain convergence results on the asymptotics of solutions to the Klein–Gordon equation on all backgrounds of this type, except for one specific case.

Exact vacuum solutions to modified Einstein field equations in f(R) gravity

Considering the plane symmetric non-static spacetimes in the context of [Formula: see text] gravity, we obtain exact solutions of the vacuum field equations by assuming constant scalar curvature. By suitable transformations, it is shown that the obtained solutions can be transformed to Bianchi type [Formula: see text], a type of Taub’s and the De Sitter solutions. Of particular interest is a solution that represents a model that has initial singularity and under an appropriate transformation can be converted to a Bianchi-type V model. This solution, like the Bianchi type V model, leads to predictions about evolution in the sense of an expanding universe starting from an initial singularity. In this context, we show that the expansion of the universe in [Formula: see text] gravity can be explained without invoking the cosmological constant [Formula: see text].

The singularity of the universe

We address a discussion on the finite nature of the initial singularity and proposes a justification for a more general principle of energy conservation.