A $p$-Adic Matter in a Closed Universe

TL;DR

This paper introduces a novel $p$-adic matter derived from string theory, explores its properties, and demonstrates its potential to explain an exponentially expanding closed universe and dark matter.

Contribution

It develops a new scalar field Lagrangian from $p$-adic string theory and applies it to cosmology, showing its role in universe expansion and dark matter candidates.

Findings

Derived a $p$-adic scalar field Lagrangian for cosmological models.

Showed that this matter leads to an exponentially expanding closed universe.

Suggested $p$-adic matter as a candidate for dark matter.

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.