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Register a new userScalar Metric fluctuations in space time matter inflation
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Using the Ponce de Leon background metric, which describes a 5D universe in an apparent vacuum: $bar{G}_{AB}=0$, we study the effective 4D evolution of both, the inflaton and gauge-invariant scalar metric fluctuations, in the recently introduced model of space time matter inflation.
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We study a model of power-law inflationary inflation using the Space-Time-Matter (STM) theory of gravity for a five dimensional (5D) canonical metric that describes an apparent vacuum. In this approach the expansion is governed by a single scalar (neutral) quantum field. In particular, we study the case where the power of expansion of the universe is $p gg 1$. This kind of model is more successful than others in accounting for galaxy formation.
We develop a non-perturbative formalism for scalar metric fluctuations from a 5D extended version of general relativity in vacuum. In this work we concentrate our efforts on calculations valid on large cosmological scales, which are the dominant during the inflationary phase of the universe. The resulting metric in this limit is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution. We calculate the spectrum of these fluctuations with an effective 4D Schwarzschild-de Sitter spacetime on cosmological scales, which is obtained after we make a static foliation on the non-compact extra coordinate. Our results show how the squared metric fluctuations of the primordial universe become scale invariant with the inflationary expansion.
In this letter we investigate gauge invariant scalar fluctuations of the metric in a non-perturbative formalism for a Higgs inflationary model recently introduced in the framework of a geometrical scalar-tensor theory of gravity. In this scenario the Higgs inflaton field has its origin in the Weyl scalar field of the background geometry. We found a nearly scale invariance of the power spectrum for linear scalar fluctuations of the metric. For certain parameters of the model we obtain values for the scalar spectral index $n_s$ and the scalar to tensor ratio $r$ that fit well with the Planck 2018 results. Besides we show that in this model the trans-planckian problem can be avoided.
We investigate gauge invariant scalar fluctuations of the metric during inflation in a non-perturbative formalism in the framework of a recently introduced scalar-tensor theory of gravity formulated on a Weyl-Integrable geometry. We found that the Weyl scalar field can play the role of the inflaton field in this theory. As an application we study the case of a power law inflation. In this case the quasi-scale invariance of the spectrum for scalar fluctuations of the metric is achieved for determined values of the $omega$ parameter of the scalar-tensor theory. In our formalism the physical inflaton field has a geometrical origin.
A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this paper is twofold. First, we find that box-counting dimension in face of finite resolution of space-time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newtons inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections.
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