Abstract
We show that a simple sub-class of Horndeski theory can describe a time crystal Universe. The time crystal Universe can be regarded as a baby Universe nucleated from a flat space, which is mediated by an extension of Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory. Remarkably, when a cosmological constant is included, de Sitter Universe can be created by tunneling from the time crystal Universe. It gives rise to a past completion of an inflationary Universe.
Highlights
Inflation has succeeded in explaining current observations of the large scale structure of the Universe [1,2]
Since gravitational theory has a symmetry of a time reparametrization, any cyclic solution which is completely periodic in time is called time crystal universe [13,14,15,16,17,18] by an analogy of a time crystal in the condensed matter physics
We find a time crystal universe as a baby universe nucleated from a flat space, which is mediated by an extension of Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory
Summary
Inflation has succeeded in explaining current observations of the large scale structure of the Universe [1,2]. Since a scalar field minimally coupled with gravity in a flat universe satisfies the null energy condition, we need to consider more general situations It is Horndeski theory [19,20,21](see [22] for a recent review) that is the general class of scalar-tensor theory whose. We find a time crystal universe as a baby universe nucleated from a flat space, which is mediated by an extension of Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory. IV, we solve Euclidean equation of motion in 2-form theory without a cosmological constant and construct an extension of Giddings-Strominger instanton This instanton describes a nucleation of a time crystal universe from a flat space. We study the above action and obtain an extension of the Giddings-Strominger instanton, which is an instanton solution in free 2-form theory with gravity
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