Problem of inflation in nonlinear multidimensional cosmological models

Abstract

We consider a multidimensional cosmological model with nonlinear quadratic R 2 and quartic R 4 actions. As a matter source, we include a monopole form field, D-dimensional bare cosmological constant and tensions of branes located in fixed points. In the spirit of the Universal Extra Dimensions models, the Standard Model fields are not localized on branes but can move in the bulk. We define conditions which ensure the stable compactification of the internal space in zero minimum of the effective potentials. Such effective potentials may have rather complicated form with a number of local minima, maxima and saddle points. Then, we investigate inflation in these models. It is shown that R 2 and R 4 models can have up to 10 and 22 e-foldings, respectively. These values are not sufficient to solve the homogeneity and isotropy problem but big enough to explain the recent CMB data. Additionally, R 4 model can provide conditions for eternal topological inflation. However, the main drawback of the given inflationary models consists in a value of spectral index ns which is less than observable now ns ≈ 1. For example, in the case of R 4 model we find ns ≈ 0.61.

f(R) Theories

“…3There are some other works about theoretical constructions of f ( R ) models based on quantum gravity, super-gravity and extra dimensional theories [341, 345, 537, 406, 163, 287, 288, 518, 519]. …”

Inflation from higher dimensions

“…However, as was demonstrated in Refs. [1,2,3,4], the higher-dimensional (R + γR n − 2Λ) gravity models together with their spontaneous compactification to four dimensions do not lead to a successful phenomenological description of dark energy, because of a necessarily negative (induced) cosmological constant in four dimensions. These models also fail to describe the early universe inflation because of low values of the scalar index n s and the e-foldings number N e .…”

“…Adding extra (matter) p-form fields with a Freund-Rubin-like compactification ansatz [5] can stabilize extra dimensions for a certain range of parameters [2], but still does not lead to a successful phenomenology. In particular, the four-dimensional inflationary models based on the compactified (R + γR n − 2Λ) gravity in dimensions D < 8 were found to be not viable [4]. It raises a question about whether this situation can be improved by changing or relaxing some of the assumptions used in Refs.…”

Bouncing inflation in a nonlinearR2+R4gravitational model

“…So, we use numerical calculations. To do it, we apply a Mathematica package proposed in [26] and adjusted to our models and notations in Appendix A of our paper [18]. According to these notations, all dimensional quantities in our graphics are given in the Planck units.…”

“…Such modification of gravity may result in the late-time acceleration of our Universe [12]. Nonlinear models with polynomial as well as R −1 -type correction terms have also been generalized to the multidimensional case (see e.g., [10,11,[13][14][15][16][17][18]). …”