A p-Adic Matter in a Closed Universe

Branko Dragovich

doi:10.3390/sym14010073

Abstract

In this paper, we introduce a new type of matter that has origin in p-adic strings, i.e., strings with a p-adic worldsheet. We investigate some properties of this p-adic matter, in particular its cosmological aspects. We start with crossing symmetric scattering amplitudes for p-adic open strings and related effective nonlocal and nonlinear Lagrangian which describes tachyon dynamics at the tree level. Then, we make a slight modification of this Lagrangian and obtain a new Lagrangian for non-tachyonic scalar field. Using this new Lagrangian in the weak field approximation as a matter in Einstein gravity with the cosmological constant, one obtains an exponentially expanding FLRW closed universe. At the end, we discuss the obtained results, i.e., computed mass of the scalar p-adic particle, estimated radius of related closed universe and noted p-adic matter as a possible candidate for dark matter.

Highlights

We are going to slightly modify Lagrangian (10) with the intention to obtain a new Lagrangian for a similar scalar particle which is not a tachyon. Another direction of research based on Lagrangian (10) is towards zeta strings that take into account the effects of p-adic strings over all primes p; see [24] and references therein
Λ and mass m of a p-adic scalar particle
One obtains Λ ≈ 3m2, which is written in the natural units (h = c = 1)

Summary

Introduction

Let us mention some interesting points related to the effective Lagrangian (10) for p-adic open strings, which was constructed in 1988 [10,11] Since it does not contain padic ingredients, but only real terms, there is no need to know and use p-adic analysis, which simplifies further elaboration of p-adic string theory. This article is organized as follows: In Section 2, some basic facts about p-adic numbers, adeles, amplitudes for scattering of open p-adic strings and an effective nonlocal Lagrangian with an equation of motion are presented. There is an Appendix with some details on derivation of the equations of motion in the case of a nonlocal scalar field

On p-Adic Strings

Effective Field Theory for p-Adic Open Strings

Scalar p-Adic Matter

Non-Tachyonic p-Adic Scalar Field in Minkowski Space

A Closed Universe with p-Adic Matter

Concluding Remarks