标度宇宙学、测地线运动和伪SUSY
Scaling cosmologies, geodesic motion and pseudo-susy
摘要：
超引力中标量流形上的标量单参数解和度规迹线。在无规范的超引力中，这些曲线描述了测地线运动。众所周知，测地线运动有时会发生在标量势的存在下，对于时间依赖的解，这可能发生在标度宇宙学中。本文在多场系统的伪超对称性背景下进一步研究了这类解，我们用Bogomol'nyi方法导出了这类解的一阶方程。特别是，我们表明，缩放的解决方案是伪BPS必须描述测地线曲线。此外，我们阐明了如何解决的测地线运动方程时，标量流形是一个最大的非紧陪集，如发生在最大超引力。这依赖于Borel规范中陪集的参数化。然后，我们说明了这与宇宙学解决方案的高维引力紧致的$n$ -环面。
英文摘要：
One-parameter solutions in supergravity carried by scalars and a metric trace out curves on the scalar manifold. In ungauged supergravity these curves describe a geodesic motion. It is known that a geodesic motion sometimes occurs in the presence of a scalar potential and for time-dependent solutions this can happen for scaling cosmologies. This note contains a further study of such solutions in the context of pseudo-supersymmetry for multi-field systems whose first-order equations we derive using a Bogomol'nyi-like method. In particular we show that scaling solutions that are pseudo-BPS must describe geodesic curves. Furthermore, we clarify how to solve the geodesic equations of motion when the scalar manifold is a maximally non-compact coset such as occurs in maximal supergravity. This relies upon a parametrization of the coset in the Borel gauge. We then illustrate this with the cosmological solutions of higher-dimensional gravity compactified on a $n$-torus.
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