In this paper, we explore a novel observational signature of gravitational corrections during slow-roll inflation. We study the coupling of the inflaton field to highercurvature tensors in models with a minimal breaking of conformal symmetry. In that case, the most general correction to the tensor two-point function is captured by a coupling to the square of the Weyl tensor. We show that these ...

We review the possible violation of Equivalence Principle at finite temperature [Formula: see text] in framework curvature-based Extended Theories Gravity. Specifically, we first show how it is to derive from Quantum Field Theory text]. Subsequently, exhibit this result can be precisely recovered by following an alternative path that envisages employment generalized Einstein equations with a te...

An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case. As a consequence, complete minimal surfaces in...

An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case. As a consequence, complete minimal surfaces in...

Consider a manifold constructed by identifying the boundaries of Euclidean triangles or Euclidean tetrahedra. When these form a closed topological manifold, we call such spaces piecewise flat manifolds (see Definition 1) as in [8]. Such spaces may be considered discrete analogues of Riemannian manifolds, in that their geometry can be described locally by a finite number of parameters, and the s...

The regularized expectation value of the stress-energy tensor for a massless bosonic or fermionic field in 1+1 dimensions is calculated explicitly for the instantaneous vacuum relative to any Cauchy surface (here a spacelike curve) in terms of the length L of the curve (if closed), the local extrinsic curvature K of the curve, its derivative K ′ with respect to proper distance x along the curve...

Let us define a curvature invariant of the order k as a scalar polynomial constructed from gαβ, the Riemann tensor Rαβγδ, and covariant derivatives of the Riemann tensor up to the order k. According to this definition, the Ricci curvature scalar R or the Kretschmann curvature scalar RαβγδR αβγδ are curvature invariants of the order zero and Rαβγδ;εR αβγδ;ε is a curvature invariant of the order ...

An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case. As a consequence, complete minimal surfaces in...

Michor and Mumford have shown that the distances between planar curves in the simplest metric (not involving derivatives) are identically zero. We derive geodesic equations and a formula for sectional curvature for conformally equivalent metrics. We show if the conformal factor depends only on the length of the curve, the metric behaves like an L metric, the sectional curvature is not bounded f...

We obtain the evolution equations for the Riemann tensor, the Ricci tensor and the scalar curvature induced by the mean curvature flow. The evolution for the scalar curvature is similar to the Ricci flow, however, negative, rather than positive, curvature is preserved. Our results are valid in any dimension.